Net Point Value (NickS, 2007)

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NickS



Joined: 30 Dec 2004
Posts: 384


PostPosted: Mon May 21, 2007 1:33 pm Post subject: Net Point Value: Draft for a new linear weight rating system Reply with quote
The discussion this wekeend on the PER vs EFF thread got me to think about designing a new summary statistic.

I know that the APBRmetric world hardly needs a new statistic, but I believe both that the process by which I arrived at this statistic and the statistic iteself raise interesting points about rating systems and that the ubiquity of PER and, now, WinsProduced shows that there is value in a good summary statistic.

This is a linear weight statistic with all of the limitations that implies, but it attempts to combine the existing results of empirical research about the value of events (e.g., the weighting of offensive and defensive rebounds) with a clear and consistent formula for applying those weights.

I will explain the statistic in detail below but here are the league leaders in NPV40. This means that if you were to play that player for 40 minutes on a team with 4 average players their team would be expected to outscore their opponent by an amount equal to their rating.

The top 30 players in the league last year, per minute, by this rating were:

Update: I realized after looking at these ranking there was an error in the code. Revised rankings posted later in the thread.

Code:
Rank Player Rating Rank player rating
1 duncan,tim 6.240 16 camby,marcus 3.999
2 boozer,carlos 6.179 17 anthony,carmelo 3.968
3 ming,yao 6.088 18 okafor,emeka 3.923
4 nowitzki,dirk 5.987 19 bosh,chris 3.842
5 wade,dwyane 5.940 20 mcgrady,tracy 3.760
6 nash,steve 5.758 21 o'neal,shaquille 3.752
7 stoudemire,amare 5.377 22 carter,vince 3.716
8 gasol,pau 5.366 23 davis,baron 3.699
9 bryant,kobe 5.293 24 jefferson,al 3.549
10 garnett,kevin 5.105 25 lee,david 3.434
11 brand,elton 4.808 26 howard,dwight 3.296
12 marion,shawn 4.610 27 allen,ray 3.263
13 ginobili,manu 4.484 28 randolph,zach 3.234
14 james,lebron 4.253 29 may,sean 3.040
15 arenas,gilbert 4.058 30 lewis,rashard 3.026


The league average players by this metric are Andre Miller or Eduardo Najera and the worst player in the league to play significant minutes was Bruce Bowen -- demonstrating again that he will always look bad on measures of production that don't include individual defense.

These number are NOT pace adjusted, and that is something I will do when I have time. Also, as the Bruce Bowen example demonstrates, they do not include an adjustment for team defense.

Last edited by NickS on Tue May 22, 2007 7:35 pm; edited 1 time in total
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NickS



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PostPosted: Mon May 21, 2007 1:33 pm Post subject: Reply with quote
Now for a slightly more detailed description of the system.

This rating system was designed with 3 goals in mind:

Code:
(1) To be a simple linear weight that would summarize a player's total box score contributions.


Code:
(2) To scale to known factor. In this case points scored.


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(3) In order to achive point (2), being rigorous about that fact that when an event involves two players the total credit assigned to the two players must equal the value of the event.


The first goal is that I want something analogous to PER -- a single number that can be used as a rough approximation of a player's contributions.

I have derived the weights for NPV based on the contributions that a player makes toward either getting possessions for a team (through rebounds or steals) or toward scoring possesions at a rate greater than a baseline rate. I have used as my baseline 1.04 point per possession because that was the offensive efficiency of the worst team in the league last season.

That is, to a large extent, a provisional value. One of the conversations that I would hope NPV would spark would be the meaning of various values that could be used as a baseline efficiency.

The above anticipates my second goal. Attempting to match my metric to points means that if you have two teams that play the same number of possessions and you compute the total NPV for each team the difference in NPV will equal the difference in points on the scoreboard.

This is only partially achieved. NPV, would match the difference in points on the scoreboard if it didn't include assists, steals, block, or fouls. As it is, it assumes standard rates of assists, blocked shots, etc . . . so the NPV will on average work out to the difference in points scored for a fixed number of possessions, but it will be slightly off for any given game. But, again, a simplified NPV would be exactly correct.

The third point is crucial to my inspiration for NPV. In the thread about EFF vs PER DLew made a comment about the dangers of double counting events. Point 3 is just a statement that I want to avoid double counting events.

The most familiar example is dividing credit between a made basket and an assists. From the point at which John Hollinger created PER he pointed out that if you want to credit a player for an assist you have to deduct credit from the scorer to match. Another example would be the fact that if a missed basket and a defensive rebound together complete a single change of possession, the values for a missed basket and a defensive rebound should add up to the value of a possession.

I have extended this idea by saying that whatever credit a player gets for a steal must be deducted from the penalty to the player who commits the TO, and that whatever penalty a player gets for committing a foul must be deducted from the credit a player gets for hitting free throws.

This results in the most notably difference between NPV and most other rating systems -- that it does not penalize players as heavily for TO's because it assumes that, in some cases, players are just the victim of a good play by the defense making a steal.

I can post the entire formula if people are interested, and will provide a copy of my spreadsheet to anyone who wants.
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NickS



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PostPosted: Mon May 21, 2007 1:37 pm Post subject: Reply with quote
A final, trivial comment. I'm sure that the acronym will be familiar to the econ and business people reading this. I'm sure that I found myself using that acronym because it was familiar.

I wanted to include the concept of "Net" production since this is a measurement of production above a baseline standard of efficiency.
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HoopStudies



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PostPosted: Mon May 21, 2007 1:46 pm Post subject: Reply with quote
I will post the same question I posed another time this kind of thing came up: How do we know that even the range of best to worst is right? It looks like your top guy is 6 pts/40 minutes (about 7 marginal pts/48 minutes) better than average. Is your worst -6/40? That's a range of about 14/48. Adj +/- systems have ranges of over 20. I've definitely seen lower, too. These are pretty big ranges with no apparent calibration of them. Can we at least understand those ranges?
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Mark



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PostPosted: Mon May 21, 2007 2:21 pm Post subject: Reply with quote
Yes the full formula would be of interest.

To what extent did you accept the values presented in "The Starting Point" article? You say further work is needed to fit into linear formula and add up sides of the action but will you be presenting a case for any variance in the underlying values?
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NickS



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PostPosted: Mon May 21, 2007 3:06 pm Post subject: Reply with quote
HoopStudies wrote:
I will post the same question I posed another time this kind of thing came up: How do we know that even the range of best to worst is right? It looks like your top guy is 6 pts/40 minutes (about 7 marginal pts/48 minutes) better than average. . . . These are pretty big ranges with no apparent calibration of them. Can we at least understand those ranges?


Quick answer, the calibration is, as I said, how many points that player would add to an average team.

If we believe that, on average, a change in point differential of +1 is worth approximately 2 wins over an 82 game season that means that a top player would add about 12-13 wins to a team, playing 40 minutes a night.

I take some comfort in the fact that this is close to the range for Net wins. According to b-r.com the top player in the legue by net wins (Dirk) had 12.2 net wins in 36.2 mpg. This implies that playing 40 mpg he would have added about 13.5 wins to his team.

The fact that those are similar numbers doesn't mean that they're correct but, I think we're working on a similar scale.
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NickS



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PostPosted: Mon May 21, 2007 3:16 pm Post subject: Reply with quote
Mark wrote:
Yes the full formula would be of interest.

To what extent did you accept the values presented in "The Starting Point" article? You say further work is needed to fit into linear formula and add up sides of the action but will you be presenting a case for any variance in the underlying values?


Thank you for the interest. I will post the full formula when I have time to finish writing up a full explanation. If you want to send me a message with your e-mail I can send you a copy of the spreadsheet and a short explanation of the formula.

There are a bunch of facotrs in the formula that are constants that should be derived from some empirical evidence. The three most important are the (1) the baseline value of a possession, (2) the ratio of weight given to offensive and defensive rebounds, and (3) the value given to an assist.

For the first I have provisionally used 1.04, for the reasons given, though aesthetically I would like use a lower value to give more weight to scoring and less to rebounding, I do feel like that's the best number I have that doesn't feel completely arbitrary.

For the second value I am using a ratio of .7/.3 and that is based on "The Starting Point."

For the third value I am using a value of .5 points/assist which, I admit, is somewhat arbitrary and is mostly taken from the Wages of Wins in which he estimates the value of an assist at .6.

I was trying to be conservative in my valuation of assists, and I will note that on an assisted 2 pointer, the total amount of credit available is .96 points (a possession has been used, so that is debited from the score), so that essentially gives a passer half the value of a made shot.

Also, MikeG mentioned, in the Eff vs PER thread, that in his regression he ended up counting an assist as .66 the value of a made shot so, again, that reassures me that I'm probably off in my valuation of assists, but I'm within a reasonable range.
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Mark



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PostPosted: Mon May 21, 2007 3:51 pm Post subject: Reply with quote
No rush. I can wait til you feel ready to post an explanation here. Maybe I'll ask for the spreadsheet after you're done.

Last edited by Mark on Mon May 21, 2007 7:05 pm; edited 1 time in total
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NickS



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PostPosted: Mon May 21, 2007 6:14 pm Post subject: Reply with quote
HoopStudies wrote:
I will post the same question I posed another time this kind of thing came up: How do we know that even the range of best to worst is right? It looks like your top guy is 6 pts/40 minutes (about 7 marginal pts/48 minutes) better than average. . . . These are pretty big ranges with no apparent calibration of them. Can we at least understand those ranges?


I want to ammend my answer to this question. The rating shows that, per 40 minutes, Tim Duncan, got credit for 6.24 points of porduction above what Eduardo Najera got credit for. This means that replacing Najera with Duncan would add 6.24 points per game to a team assuming that the production of all the other players stayed the same.

This assumption is both obviously false, and a basic assumption of any linear weight system. Players are always competing with teammates for shots and rebounds to some extent.

I say this because I think it presents a particular challenge at the low end of the scale. The problem that any single summary statistic faces is that there are really at least two critical aspects to any players performance -- how much do they do, and how well do they do what they do. combining those two aspects into one number means that, inevitably, you're going to be producing the same rating for two players, one of whom does very little but does it efficiently, and one of whom does a lot, but at average efficiency (contrast Monta Ellis and Najera, for example, who rank similarly on my scale).

That's an important point to recognize about any attempt to "add up" prduction and one I didn't emphasize in my original post.

Compare Adam Morrison (who does a lot very badly) and Bruce Bowen (who does almost nothing).

A team that substituted Adam Morrison for Bruce Bowen would get a player who shot worse, shot a lot more, had more turnovers, but had more rebounds and assists. Not good trade-off for most teams, and yet, they both rank equally badly in a linear weight system.

I don't think that's a flaw, precisely, as much as something that comes with the territory and has to be recognized.
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Mike G



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PostPosted: Tue May 22, 2007 6:16 am Post subject: Reply with quote
NickS wrote:
...
Also, MikeG mentioned, in the Eff vs PER thread, that in his regression he ended up counting an assist as .66 the value of a made shot so, again, that reassures me that I'm probably off in my valuation of assists...


Or maybe not. I basically double-count everything, since my 'total ratings' add up to almost twice what points are scored. I assume many (or most) counted stats serve as proxies for additional contributing plays that aren't counted. I guess I could scale things down to 'points' level.

I also don't microanalyze at the quantum level to get a theoretical justification for my weights. These arguments are very interesting, but I don't feel confident about covering every possible thing. So I shoot for a sort of retro- +/- , assigning values to boxscore stats because they seem to add up right.

Independence is nice, so I'm following this development with interest, without trying to influence. Like many fans, I instinctively reject a ranking system by it's 'sore thumbs'. Not every coach in the league can be wrong about the same players. Imperfect players aren't 'terrible' players. LeBron only #14 ?
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NickS



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PostPosted: Tue May 22, 2007 10:30 am Post subject: Reply with quote
I will post the full formula today, but before I do, I want to show a little bit of the derivation. The first idea that started me on this path was in the PER vs EFF thread

I was working with an example of a game between two players. Both players use 100 possessions. Player A shoots 115 three pointers, hits 39 of them, gets 15 offensive rebounds, and scored 117 points. Player B shoots 111 two pointers, hits 56 of them, gets 11 offensive rebounds, and scores 112 points.

My first realization was that a made basket does complete a possession. So, even though the value of a missed basket is equal (but opposite) to the value of an offensive rebound, the debit against a made basket should be a full possession.

NickS wrote:
If add a penalty to made shots equivalent to the value of a defensive rebound (to account for the fact that a made shot is a complete change of possession, rather than just .7 of a change of possession we would have.


Player A's total Win Score:
117 points scored = 117
115 shot attempts = -80.5
39 made shots = -11.7
44 defensive rebounds = +13.2
15 offensive rebounds = +10.5
= 48.5

Player B's total Win Score:
112 points scored = 112
111 shot attempts = -77.7
56 made shots = -16.8
61 defensive rebounds = +18.3
11 offensive rebounds = +7.7
= 43.5

The two players WS differ by exactly the difference on the scoreboard!


(there is a little bit more explanation of those numbers in that thread).

This is a simple model that doesn't include anything other than scoring or rebounds. To demonstrate the methods I'm using to distribute credit let's turn 10 of player B's misses into Turnovers and give player A 5 steals (player B dribbled it off his foot 5 times).

If we valued a steal and a turnover at one possession each we would get, highlighting the values that have changed:

Player A's total Net Points:
117 points scored = 117
115 shot attempts = -80.5
39 made shots = -11.7
34 defensive rebounds = +10.2
15 offensive rebounds = +10.5
5 steals = +5
= 50.5

Player B's total Net Points:
112 points scored = 112
101 shot attempts = -70.7
56 made shots = -16.8
61 defensive rebounds = +18.3
11 offensive rebounds = +7.7
10 turnovers = -10
= 40.5

The difference in Net Points is no longer equal to the difference on the scoreboard. Because we double counted the 5 steals the difference in net points has grown from 5 to 10.

So let us say, somewhat arbitrarily, that player A will get credit for 80% of his steals (figuing that a steal is mostly to his credit, but it is partially caused by carelessness on the part of the offensive player).

That would make the value of a steal equal to 80% of the value of a possession or .8 in this example.

To figure out the value of a turnover we would take the value of a possession (1 in this example) and subtract the value of of a steal multiplied by the percentage of all turnovers that are caused by steals, 50% in this example, and close to that in the NBA.

1 - (0.8) *(0.5) = .6

So the value of a turnover is -.6

This gives us the following totals:
Player A's total Net Points:
117 points scored = 117
115 shot attempts = -80.5
39 made shots = -11.7
34 defensive rebounds = +10.2
15 offensive rebounds = +10.5
5 steals = +4
= 49.5

Player B's total Net Points:
112 points scored = 112
101 shot attempts = -70.7
56 made shots = -16.8
61 defensive rebounds = +18.3
11 offensive rebounds = +7.7
10 turnovers = -6
= 44.5

The difference in net points is now equal, again, to the difference on the scoreboard.
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Harold Almonte



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PostPosted: Tue May 22, 2007 11:03 am Post subject: Reply with quote
Quote:
(0.Cool*(0.5) = .6
?

I think it will never be equal net point rating diferential and total point differential. I think the problem is a 3p scoring possession is not 1 possession, is 1.5 possession, and all the other action around it: pass, defense, steal, block, etc. must be multiplied by 1.5. You are avoiding 3 points, not 2.

Maybe every TO (0.8*0.5=0.4) cost 1.5 (3p)=0.6
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NickS



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PostPosted: Tue May 22, 2007 11:16 am Post subject: Reply with quote
Harold Almonte wrote:
Quote:
(0.8)*(0.5) = .6
?

I think it will never be equal net point rating diferential and total point differential. I think the problem is a 3p scoring possession is not 1 possession, is 1.5 possession, and all the other action around it: pass, defense, steal, block, etc. must be multiplied by 1.5. You are avoiding 3 points, not 2.


The .8 in that equation is the portion of the credit for a steal that we give to the defender. That number has to be between 0 and 1. Whatever credit you give to the defender has to be deducted from the penalty to the offensive player.

As far as counting 3 point attempts as 1.5 possesions, that isn't right though. A 3 point shot still uses 1 possession, it's just worth more points if it goes in.

Think about it, a missed 3 pointer and a missed 2 pointer are exactly the same. A defensive rebound or offensive rebound is worth just as much regardless of whether the shot was a 2 pointer or a 3 pointer. So why would it be worth 1 possession if it misses, but 1.5 if it hits?
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NickS



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PostPosted: Tue May 22, 2007 11:52 am Post subject: Reply with quote
I just realized I have to confess to having some serious egg on my face.

DeanO's question had got me trying to figure out how this rating could rank Bruce Bowen below Adam Morrison, which didn't pass the laugh test for me.

I realized that I had a typo in my formula, because, at the last minute I had been trying to simplify it from having one term for FGA, one term for made field goals, and another term for missed field goals. So I had juggled the equations to have one term each for made and missed field goals, and made an error.

To make a long story short, I was overvaluing made field goals.

When I correct that error, rebounders shoot to the top of the rankings.

But, working through the logic I realized that I think I have set the value of a possession too high. I think it would be more accurate to set the value of possession as equal to expected value of an unassisted shot, rather than, as I'm doing now, the expected value of all shots.

I will think through this, revise my possession weight, double check and post again later in the day.

I still think the logic is sound, but I had a typo in the formula.
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kjb



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PostPosted: Tue May 22, 2007 12:38 pm Post subject: Reply with quote
Don't worry about the typo -- you're working on a draft here. This is the time to screw things up.

NickS



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PostPosted: Tue May 22, 2007 12:54 pm Post subject: Reply with quote
kjb wrote:
Don't worry about the typo -- you're working on a draft here. This is the time to screw things up.


Thanks.

I think it's actually good. Discovering the problem got me to look closely at the various components of the score and, now, thinking about how to set an appropriate possession value and what it actually means, is helpful.

I think I'm actually starting to figure it out, and will post again soon.
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NickS



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PostPosted: Tue May 22, 2007 2:04 pm Post subject: Reply with quote
Thinking about it I think I've settled on a possession value but I want to walk through some of what's involved in setting these values.

This gets tricky quickly, so I'm going to break it into chunks, I'm still working through it myself.

Start by thinking about how adjustments shift points from one team to another. If we set the value of an offensive rebound equal to a possession and set the value of a defensive rebound equal to 0 then, as you can see from the earlier example, Total credit will equal points scored above the baseline possession rate.

If you take the examples above with Player A who scores 117 points in 100 possessions, and player B who scored 111 points in 100 possessions. If you set the value of a possession = 1, offensive rebound =1, defensive rebound = 0 you end up with:

Player A: 117 (points scored) - 115 (shots taken) + 15 (offensive rebounds) = 17
Player A: 112 (points scored) - 111 (shots taken) + 11 (offensive rebounds) = 12

If you shift the ratio of value of offensive rebounds from 1/0 to .7/.3 you end up with the numbers we saw earlier. Player A = 48.5, Player B = 43.5.

The difference in credits is the same, but both players have more credits and, more importantly, how the players have acquired the credits has changed.


Code:
With the 1/0 ratio the points looked like this:
Player A: 2 points (shooting), 15 points (offensive rebounds), 0 points (defensive rebounds)
Player B: 1 point (shooting), 11 points (offensive rebounds), 0 points (defensive rebounds)

With the .7/.3 ratio it looks like this
Player A: 24.8 points (shooting), 10.5 points (offensive rebounds), 13.2 points (defensive rebounds)
Player B: 17.5 point (shooting), 7.7 points (offensive rebounds), 18.3 points (defensive rebounds)


You have reduced the penalty for each players missed shots and added those points onto the other player's defensive rebounding total.

In that case, with one player doing both the shooting and the rebounding, what matters is that the difference between them stays the same. But if you had a team of two players, with one player doing all of the shooting and one player doing all of the rebounding, just changing the ratio between the contribution of an offensive and defensive rebound changes the distribution of credit between the players.

Let's watch this a little more closely. Imagine two teams, A &B (with A doing all of the shooting, and B doing all of the rebounding) and X & Y (same thing)

Code:
With a 1/0 split in value of offensive and defensive rebounds the two teams look like this:
Player A: 2 "credits" (shooting)
player B: 15 "credits" (rebounding)

Player X: 1 "credits" (shooting)
player Y: 11 "credits" (rebounding)

Now change the split to .7/.3
Player A: 24.8 "credits" (shooting)
player B: 23.7 "credits" (rebounding)

Player X: 17.5 "credits" (shooting)
player Y: 26 "credits" (rebounding)


!!!!

Think about that, I'll post more this afternoon.

Last edited by NickS on Tue May 22, 2007 4:08 pm; edited 1 time in total
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NickS



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PostPosted: Tue May 22, 2007 4:07 pm Post subject: Reply with quote
The meaning of 0 (with a digression on wages of wins):

A shorter chunk this time:

One of the ideas I had for my rating system, which I stole from wages on wins, was to standardize my ratings so that 0 was an average player and ratings were positive or negative denoting a player who is above average. This is one meaning of 0.

Having some efficiency component of a rating system means that there is some level of scoring efficiency at which the net production is 0. The costs of the possessions used negates the benefits of the points scored. Let us call that the "break-even" level. That is another meaning of 0.

Let's play with the first meaning a little bit. I don't know how WoW normalizes the scores to 0, but I didn't think about it too hard and just created a rating for the average player and then subtracted that value from everyone's score.

Let me show how that works using the examples of A,B & X,Y above.

Code:
With a 1/0 split average player credits are 2+15+1+11/4 = 7.25:
player B: +7.75
player Y: +3.75
Player A: -5.25
Player X: -6.25

Now change the split to .7/.3 average = 23
player Y: +3
Player A: +1.8
player B: +0.7
Player X: -5.5


Both the total scores and the rankings have changed dramatically.

It's worth noting, however, that in neither case was the average player rating 0 before normalization. In both cases we had 4 positive numbers, from which we subtracted the average to center the range on 0.

In Wages of Win, Dave Berri says that the break-even level of scoring efficiency should be set at the average level of scoring efficiency. In other words, a player who scores more efficiently than the average helps their team, and one that scores less efficiently than average hurts their team.

But this confuses the two meanings of 0 introduced above. In a linear weight rating system, a player with 0 credits is defined as being equal to a player who performs no actions on the basketball court. A player who scores at the break-even efficiency is equal to a player who doesn't score a single basket. An average player, however, does not do nothing on the basketball court, an average player does something on the basketball court.

A player who scores at the average rate of the team isn't contributing no value to their team with their scoring, they are just contributing average value. An average value may end up being defined as a rating of +0, but that is not the same thing as accumulating 0 credits.

Unless you define your system so that the total of all credits accumulated is 0, it is a mistake to set the break even level of efficiency to average efficiency. Doing so means that, after you normalize all the credits to 0 an average scorer will suddenly look like a below average player.
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NickS



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PostPosted: Tue May 22, 2007 7:34 pm Post subject: Reply with quote
Okay, I hope everyone enjoyed the last two posts, because writing them clarified a lot of things for me.

Unfortunately, I wasn't able to come up with anything quite as theoretically rigorous for setting the value of a possession, so this may be a bit anticlimactic.

I tried a number of different approaches to setting a possession weight and ended up getting a variety of values in the same range. I decided that the one that seemed reasonable was to say that for an average NBA team, if you only looked at shooting and defensive rebounding, that the credits allocated to the shooters (after deducting for assists) was equal to the credits that the defensive rebounders on the other team received.

That sounds fancy, but the math ended up being simple enough that I will spare you that for now.

Using that I arrived at a possession value of .85

Using that value here are the top 30 in the league. I like the fact that the top rankings include a variety of scorers, passers, and rebounders.

Code:
Rank Player NPV40 Rank Player NPV40
1 nash,steve 5.442 16 kidd,jason 3.227
2 wade,dwyane 4.918 17 marion,shawn 3.179
3 nowitzki,dirk 4.475 18 james,lebron 3.165
4 duncan,tim 4.406 19 bosh,chris 2.859
5 ming,yao 4.189 20 mcgrady,tracy 2.818
6 bryant,kobe 4.138 21 carter,vince 2.811
7 ginobili,manu 4.047 22 lee,david 2.668
8 gasol,pau 3.866 23 okafor,emeka 2.597
9 boozer,carlos 3.829 24 paul,chris 2.594
10 arenas,gilbert 3.784 25 pierce,paul 2.535
11 garnett,kevin 3.725 26 allen,ray 2.530
12 stoudemire,amare 3.590 27 billups,chauncey 2.485
13 camby,marcus 3.283 28 howard,dwight 2.398
14 davis,baron 3.278 29 lewis,rashard 2.367
15 brand,elton 3.246 30 anthony,carmelo 2.339


Again, the numbers are not pace adjusted and no adjustments are made for team defense.

I don't think I have any typos this time.
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NickS



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PostPosted: Tue May 22, 2007 7:46 pm Post subject: Reply with quote
And, for Mike G, I will think about why Baron Davis is ranking ahead of LBJ. He had a lot more assists and steals, but is worse in every other way.

I'm pretty sure that I'm not overvaluing steals, so this makes me think I'm overvaluing assists a little bit. As I said, that's one of the numbers I'm not too sure about.

Further refinements will come, but my plan at this point is to refine it by changing the constants, not by changing the formula.
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Harold Almonte



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PostPosted: Wed May 23, 2007 7:55 am Post subject: Reply with quote
Quote:
As far as counting 3 point attempts as 1.5 possesions, that isn't right though. A 3 point shot still uses 1 possession, it's just worth more points if it goes in.

Think about it, a missed 3 pointer and a missed 2 pointer are exactly the same. A defensive rebound or offensive rebound is worth just as much regardless of whether the shot was a 2 pointer or a 3 pointer. So why would it be worth 1 possession if it misses, but 1.5 if it hits?

Are you talking about a scoring possession is (1 possession= 1 potential point) just until the ball goes in, and then becomes in (2, or 3) and the possession look finished once the ball crosses the ring and becomes in another kind of metric?
If there is no democracy in basketball, and scorers (3 pointers) have privilege (they can give same points with less efficiency); why some metrics insist every player must be measured with the same efficiency rules, making your 112(2p) player be rated above the 117(3p) player? WP would made him the best player even losing the game.
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Harold Almonte



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PostPosted: Wed May 23, 2007 10:24 am Post subject: Reply with quote
What does it mean a 2pFGM is worth 0.33, and a 3p, 0.066? There is some logic behind, or is just one of those forced fits?
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NickS



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PostPosted: Wed May 23, 2007 10:55 am Post subject: Reply with quote
Harold Almonte wrote:
What does it mean a 2pFGM is worth 0.33, and a 3p, 0.066? There is some logic behind, or is just one of those forced fits?


Shouldn't this go on the other thread? Despite my WoW digression above, I'd like to segregate the two threads a little bit. I will answer your question about three pointers in a minute.
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NickS



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PostPosted: Wed May 23, 2007 11:26 am Post subject: Reply with quote
Harold Almonte wrote:
Are you talking about a scoring possession is (1 possession= 1 potential point) just until the ball goes in, and then becomes in (2, or 3) and the possession look finished once the ball crosses the ring and becomes in another kind of metric?
If there is no democracy in basketball, and scorers (3 pointers) have privilege (they can give same points with less efficiency);


First of all, if you look at the derivations that I do above, it's entirely possible to treat 2-pointers and 3-pointers consistently and get consistent results. There's nothing inherently problematic about 3 pointers.

Secondly, points and possessions are to different things. The goal of any team is to get more points than the opponent, and the general way to do that is to turn possessions into points by shooting the basketball, but they measure separate things.

When someone takes a shot, regardless of whether it's a 2 pointer or 3 pointer, they are using the exact same amount of possessions. They just get more points if they hit a 3 pointer. And, yes, if people could shoot as high a percentage from 3 point range as they do from 2 point range there would never be a reason to shoot 2 pointers (the Phoenix Suns theory).

Think about a simple example, two teams are tied, one team comes down and hits a three, they are now ahead by three and the other team has possession. If the other team comes down and hits a two pointer, the possession situation is exactly the same as it was at the beginning of the scenario (the first team has the ball) but the relative score has changed (the first team is up by 1). Both teams had one possession, and took one shot, but the first team got more points from their one possession.

Last edited by NickS on Thu May 24, 2007 12:34 pm; edited 1 time in total
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Harold Almonte



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PostPosted: Wed May 23, 2007 6:07 pm Post subject: Reply with quote
-Oh my god!, I was blinded in the clear air. A 40% 3 pointer = 60% 2 pointer, but is the 60% missedFG (3 pointer) that is penalized more than the 40% missedFG (2 pointer). Forget the post.
-But the 2 pointer would need the same usage than the 3 pointer to be just a 25% rated FGM-(FGA-FGM) above, once you increase the usage of the 3 pointer, his rating surpasses the 2 pointer. (the 3 pointer needs 50% more usage to be above)
-Higher usage not only makes up less efficiency, also rises the rating. Is WP doublecounting or doublepenalizing something at the offensive end?
-We come back with the chicken and the egg. Is a player a higher usager because he is considered a better scorer, or is he rated better as a scorer because his usage? I'm from the school which thinks the first.

Can I say this is true? If Ben Gordon only shot 3pFGA and nothing more, would be even a better scorer than David Lee's 60% 2pFGA?...(I'm not talking about defense)

Would be possible to weight the win value of scoring or defensive usage regressing to team wins? It's something that can be done, or is already implicit inside the stats summatory?
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NickS



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PostPosted: Thu May 24, 2007 12:20 pm Post subject: Reply with quote
I was asked a question about choosing the value of a possession, and I wanted to clarify a little bit, because as I've thought about this I've changed my definition a little bit.

What I'm using in my formula isn't the value of a possession, it's a way of dividing credit between the defense for securing a possession and the offense for creating a scoring opportunity.

There are two elements of scoring, getting possession of the ball, and scoring it. What I realized on Tuesday is that as long as we're assigning a non-zero value to the ability to get the ball at an average rate, we have to assign a non-zero value to the ability to score the ball at an average rate.

Consider this sequence:

0) 00:40 Team A has possession Score: 88 to 88
1) 00:35 Team A shoots the ball
2) 00:35 Miss
3) 00:33 Team B secures defensive rebound
4) 00:21 Team B shoots the ball

The score at ever instance is 88 to 88. But let's look at the expected value for each teams score at each point.

1) expected value 89 to 88 favoring team A
2) ??
3) ??
4) 88 to 89 favoring team B

There has been a swing in expected value of two points, which is divided between 3 actions, the shot and miss for team A, the rebound for team B, and the shot for team B.

Let's say that you set the likelyhood of a defensive rebound at 70%, and the value of a possession at 1 point.

then the expected value looks like:

1) 89 to 88
2) 88.3 to 88.7
3) 88 to 89
4) 88 to 89

At that point you say that all the work of capturing the expected value has been done at the point that the rebound has been collected. You have credited the player who missed for team A with -.7 expected value, and the player who collected the rebound with +.3 expected value.

But it seems wrong to me to say that no work is being done from the point at which the rebound is collected, to the point at which the team sets up the offense and gets off a shot. I want to share the credit for that change in expected value between the rebounder and the offense. So let's say, to make the math simple, that we value securing a possession at .8 points.

That would mean that the change in expected value would look like this:

1) 89 to 88
2) 88.24 to 88.56
3) 88 to 88.8
4) 88 to 89

We say that, in the 12 seconds between securing the rebound and taking the shot that team A has added .2 points of expected value and we credit that value to the person taking the shot.

Does that help anyone?

[Note: One last thing I should explain, because it's confused me at times while I've thought about it. I've shown that there's a 2 point swing in expected value when the ball changes hands and, yet, the system only credits 1 change in possession. Why is this?

I want to emphasize that this is a tricky point. A possession isn't credited until it ends. So what is actually happening in that sequence is that at the point that the possession changes the debits assigned to team A, and the credits assigned to team B add up to the loss in value to team A of using a possession without getting points. At that point, team A's possession is off the books, team B is now up 1 point in terms of "credit" in this system, and they have possession of the ball -- an asset, but not a credit. When team B uses their possession, either in a TO, miss, or made basket, they will then have turned that asset into either credits or debits.]
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NickS



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PostPosted: Thu May 24, 2007 1:22 pm Post subject: Reply with quote
Time to post the formula. Hopefully the various comments above give enough context that this will make some sense.

First, consider a very simple version that doesn't include assists, steals, blocks, or personal fouls. This is simply points scored - possessions used + possessions gained:

Code:
PTS
- FGM * Poss
- FGM * Poss * ORR
- FTA * .44 * Poss
- TO * poss
+ OR * ORR * poss
+ DR * DRR * poss


Perhaps at this point it would be helpful to have a glossery of the abbreviations that I have used. I have set up my spreadsheet so that the actual formula has almost no constants in it. Everything is defined as a parameter in a labled cell somewhere else in the spreadsheet, to both make them visible and easy to change. The only two elements I am treating as constants for now are .44 as the ratio of FTA to possessions, and that a person receiving a technical foul gets full penalty for the FTA by the other team.

Edit DeanO suggests FGX for missed field goals, and I'm stealing that idea

Code:
Terms
Poss = value of gaining possession
ORR = portion of the value of a possession assigned to offensive rebound
DRR = portion of the value of a possession assigned to deffensive rebound
FGX = missed field goal
AsV = assigned value to assist
AsRt = League average percentage of made field goals assisted
StCR = portion of credit for TO assigned to steal
StRt = League average percentage of turnovers credited as steals
BkCR = portion of credit for FG- assigned to block
BkRt = League average percentage of FG- credited as blocks
TcCR = 1 = portion of credit for FTA assigned to technical foul
TcRt = League average percentage of FTA credited as technical FTs
FlCR = portion of credit for FTA assigned to personal fouls
FlV = Calculated value reflecting the cost of FTs given up/foul


Just as a note, I found that I had to create an abbreviate for missed field goals (since FGM is taken). I don't know if one is standard, but I rather like FG-. (edit: changed to FGX)

So, then, here is the full formula.

Code:
= PTS
-(To * Poss *(1-(StCr * StRt))) 'turnovers - steals
-(FGM * Poss ) ' possessions lost for made baskets
-(FGM * AsRt* AsV) ' discounting made baskets for assists
-(FGX * (1-(BkCr * BkRt))* ORR * Poss ) ' missed baskets
-(FTM * TcRt) ' removing technical ft
-(FTA *0.44 * (1-TcRt) * Poss ) ' possessions lost for fta
-(FTM * (1- TcRt) * FlCr) ' discounting made fts for fouls
+(OR * ORR * Poss ) ' offensive rebounds
+(DR * DRR * Poss ) ' defensive rebounds
+(St * StCr * Poss ) ' steals
-(Tc * avFT%) ' technical ft
-(PF * FlV) ' personal fouls
+(Blk * BlkCr * ORR * Poss ) ' blocks
+(As * AsV) 'assists


Last edited by NickS on Fri May 25, 2007 10:43 am; edited 1 time in total
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PostPosted: Thu May 24, 2007 1:34 pm Post subject: Reply with quote
Using a value for possessions of .825, a value for assists of .39 (which credits an assist with ~1/3 the value of a made shot) I get the following leaderboard:



Code:
Rank Player NPV40 Rank Player NPV40
1 wade,dwyane 4.986 16 bosh,chris 3.208
2 nowitzki,dirk 4.876 17 carter,vince 3.117
3 ming,yao 4.841 18 anthony,carmelo 2.994
4 bryant,kobe 4.603 19 davis,baron 2.972
5 nash,steve 4.595 20 mcgrady,tracy 2.927
6 duncan,tim 4.520 21 pierce,paul 2.904
7 boozer,carlos 4.211 22 allen,ray 2.873
8 stoudemire,amare 4.163 23 camby,marcus 2.831
9 ginobili,manu 4.153 24 redd,michael 2.769
10 arenas,gilbert 4.061 25 lewis,rashard 2.688
11 gasol,pau 4.008 26 okafor,emeka 2.645
12 garnett,kevin 3.836 27 lee,david 2.644
13 brand,elton 3.401 28 howard,dwight 2.571
14 james,lebron 3.371 29 randolph,zach 2.399
15 marion,shawn 3.320 30 kidd,jason 2.363


Range from best to worst in the league is now about +5 to -5.5 which, if 1 PPG is worth about 2 wins, means a 21 win spread.

I'm still a little surprised to see Baron Davis (28th in the league in PER) that high, since I'm intentionally valuing scoring less than PER and I think of him as a gunner. But, looking at his stats, it makes some sense. He's a good rebounding guard, leads the league in steals per game, and is 5th in the league in assists per game. All of those increase in value relative to scoring, compared to PER, and that more than makes up for the value he looses in his scoring.

Interesting to see that, in the top 10, the two big dropoffs are from Yao to Kobe and from Duncan to Boozer.
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Mark



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PostPosted: Thu May 24, 2007 2:19 pm Post subject: Reply with quote
Nick would you be willing to construct a side by side comparison of the formula parts for NPV vs PER vs one or more of the WOW products (and maybe the starting point article values) and / or a side by side scoring of say the all nba first and maybe second teams? Your formula is your own but I would understand it better if i could see it in that context. Mike G.'s is his own too but I'd be interested in seeing those side by side formula parts and top 5-10 player ratings too.

I will have to review thread and formula before commenting on details. But I like the scale and you have thought deliberately about the approach. Hope you get good comments & questions.
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NickS



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PostPosted: Thu May 24, 2007 2:40 pm Post subject: Reply with quote
Let me elaborate a little bit on the "expected value" example above.

I want to clarify that the thinking of the value of getting a possesion in terms of expected value is a way to describe what that valuation means, but not the reason for choosing the value.

he reason for valuing gaining a possesion at less than the expected value of a possession is the reason that I gave in my post on "meanings of 0".

In this system, player receive credits and debits for actions that are recorded in the box score (linear weights). That adds up to some "raw" total of credits. This is then normalized so that the average player has a rating of 0.

But an average player has more than 0 credits in the system. Credits/40 range from about +12 to +1, and I the subtract 7 from all of those numbers to normalize to 0.

So, what I argue, is that if a team that is doing nothing other than what it's "supposed" to in rebounding, gets some positive credit for those rebounds, that a team that's doing nothing more than what it's "supposed to" on offense needs to get credit for it's scoring as well. That way an average rebounder and an average scorer are both getting credits for their action, and that is what gets normalized to 0.

Mark -- I like the idea of doing a comparison, I'll think about how I want to format that. I'm not going to do that today, but perhaps tomorrow.

And, thanks for the kind words. I feel like I've posted a lot on this topic in the last week, and I'm just hoping that people have read it and are now mulling it over and digesting it a bit.

It's been fun for me to work through all of this, and I've been a little astonished at how inspired I've felt -- I feel like I've just taken a bunch of ideas that have been accumulating sub-consciously for several years of reading this board and tried to work through them in a week. It's a little odd.

[Crow]

HoopStudies



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PostPosted: Thu May 24, 2007 2:49 pm Post subject: Reply with quote
NickS wrote:
Using a value for possessions of .825, a value for assists of .39 (which credits an assist with ~1/3 the value of a made shot) I get the following leaderboard:



Code:
Rank Player NPV40 Rank Player NPV40
1 wade,dwyane 4.986 16 bosh,chris 3.208
2 nowitzki,dirk 4.876 17 carter,vince 3.117
3 ming,yao 4.841 18 anthony,carmelo 2.994
4 bryant,kobe 4.603 19 davis,baron 2.972
5 nash,steve 4.595 20 mcgrady,tracy 2.927
6 duncan,tim 4.520 21 pierce,paul 2.904
7 boozer,carlos 4.211 22 allen,ray 2.873
8 stoudemire,amare 4.163 23 camby,marcus 2.831
9 ginobili,manu 4.153 24 redd,michael 2.769
10 arenas,gilbert 4.061 25 lewis,rashard 2.688
11 gasol,pau 4.008 26 okafor,emeka 2.645
12 garnett,kevin 3.836 27 lee,david 2.644
13 brand,elton 3.401 28 howard,dwight 2.571
14 james,lebron 3.371 29 randolph,zach 2.399
15 marion,shawn 3.320 30 kidd,jason 2.363


Range from best to worst in the league is now about +5 to -5.5 which, if 1 PPG is worth about 2 wins, means a 21 win spread.


Are there full time players down at -5.5? Defining the bottom can be tough, definitely tougher than the top.

The obvious question -- any ideas on how to better define your possession value and assist value? (I haven't followed this whole discussion, so maybe I missed something.)
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NickS



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PostPosted: Thu May 24, 2007 2:56 pm Post subject: Reply with quote
HoopStudies wrote:
Are there full time players down at -5.5? Defining the bottom can be tough, definitely tougher than the top.


This is absolutely true, and I want to thank you for asking this question originally. It not only got me to catch an error, but to think through things in more detail.

-5.5 is the absolute bottom for a full time player, there are a number of low minute part time players who are around -6, the practical range is more like +5 to -5.

HoopStudies wrote:
The obvious question -- any ideas on how to better define your possession value and assist value? (I haven't followed this whole discussion, so maybe I missed something.)


Yes, absolutely. I think the possession factor is absolutely crucial, and I still haven't found a value that I consider theoretically rigorous.

I do encourage you to read the whole thread. I have a number of digressions that I think are interesting regardless of their importance to this particular rating system, and I am very curious if you have any responses.
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Mark



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PostPosted: Thu May 24, 2007 4:34 pm Post subject: Reply with quote
Rereading the thread the different pieces begin to fall in place now that they are all there with the formula and definitions.

I guess my first question is how satisified you are with your assist weight? .39 seems within a reasonable zone but what steps got you to that value?

Last edited by Mark on Thu May 24, 2007 8:36 pm; edited 1 time in total
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Ed Küpfer



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PostPosted: Thu May 24, 2007 6:01 pm Post subject: Reply with quote
I hope I'm not addressing points that were already covered previously -- I don't think so, but I may have misses something.

NickS wrote:

Code:
Terms
AsV = assigned value to assist
AsRt = League average percentage of made field goals assisted


Code:

-(FGM * AsRt* AsV) ' discounting made baskets for assists

+(AsV * AsV) 'assists


I think you could do a little more work here. Assists, like steals, are one of those non-bookkeeping stats that record only successes, and not failures. Unlike steals, it is possible to esimate assist failures (that is, a potential assist that would have counted had the pass receiver made his shot). I'd have to think about this, but it could be done.

The other thing that could be done is to esmate the likely number of the player's own FGM that were assisted. As I read it, you have assigned the averaged assist rate here, which penalises high assist players (since their teammates have, necessarily,lower assist rates). But it's possible to do better. DeanO has a method in the appendix of BoP. But you could also do it by using (Team AST-Player AST)/(Team FGM - Player AST). Or you could count them directly from the play by plays, or get them from 82games.
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Harold Almonte



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PostPosted: Thu May 24, 2007 7:48 pm Post subject: Reply with quote
I don't understand -(FGM*poss.). How the hell you cancel this when the other team start its (not after Reb,ST,BLK) scoring possession play?

Is it as simple as multiplying possitives by (poss)?
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94by50



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PostPosted: Thu May 24, 2007 10:58 pm Post subject: Reply with quote
NickS wrote:
Just as a note, I found that I had to create an abbreviate for missed field goals (since FGM is taken). I don't know if one is standard, but I rather like FG-.

Random interjection: I generally don't use the "M" for shots made - ergo, FG, 3pt, FT. Perhaps you could use those to avoid confusing terms.
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Mike G



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PostPosted: Fri May 25, 2007 6:32 am Post subject: Reply with quote
I hastily second 9450's interjection. These many years, I use 'FGM' when I want a column for 'FG missed'. Simple 'FG' has stood for eons as 'FG made'.
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PostPosted: Fri May 25, 2007 7:53 am Post subject: Reply with quote
Mike G wrote:
I hastily second 9450's interjection. These many years, I use 'FGM' when I want a column for 'FG missed'. Simple 'FG' has stood for eons as 'FG made'.


I'd like to agree, but there are many prominent sources using FGM for field goals made (ESPN.com, NBA.com, Foxsports.com, etc.). We can't change them, so any time I see FGM, I think field goals made. So I'd definitely suggest something different for field goals missed -- I've seen FGX before and like it better than FG- because the minus sign can be confusing.
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Mike G



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PostPosted: Fri May 25, 2007 8:04 am Post subject: Reply with quote
Well, I like Duncan a bit better than #6, and Parker I'd say is top 15 (missing from your 30). I like McGrady a whole lot more than #20, Zach and Shaq should also be top 20, it seems. Lebron and Dwight should both be about 10 spots higher; and whither Jermaine, Josh, and Chauncey?

Players I think rank too high with your new metric: Wade, Kobe, Gasol, Marion, David Lee (!), Arenas, Rashard and Ray, Redd, Amare, Baron, and Okafor.

This latter list is made up of players from bad teams, or high-paced teams. The upper list consists of players from better teams, particularly strong defensive teams, and Zach (?).

This clues me in that there's no adjustment for pace, or for scoring/rebounding differentials? I can tell you that no matter how fine you grind the raw stats, divorced from team context the players will never indicate the strength of their team.

For example, Baron Davis rebounded 5.0/40 min., while Tony Parker was at 4.0/40 . But in RebRt, the gap is narrowed to 6.8 vs 6.0 . Is Davis 25% better boarder, or just 13% better?

RebRt considers that in SA games, there were only 79.4 total Reb/G; while in GS, there were 87.3 -- 10% more. I take this a step further and factor in that GS allowed 19% more opponent rebounds than SA.

With such an adjustment, I'd unflinchingly say Davis was < 2% stronger rebounder than Parker. Head to head, they'd be indistinguishable.

Similar team-context arguments can be applied to scoring and assist rates.
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Harold Almonte



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PostPosted: Fri May 25, 2007 8:19 am Post subject: Reply with quote
NickS-
You are substracting by FGM or FTM poss. lost. When the other team put the ball in play, there must have an automatic (+)poss somewhere, for somebody or everybody. Is it a nobody's or everybody's scoring possession, or maybe the PG who put the ball on the floor?, or does it count only when is turnovered, missed or made=lost?

How do you cancel points? Are STL and BLKS the only things that avoid ponts?, other than that, isn't there any other thing?. Do the scorer shoot down himself, allways? If FTs were shot guarded and not alone, what would be the average players's FT%?

Am I being too much perfectionist with just a linear formula?
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PostPosted: Fri May 25, 2007 10:44 am Post subject: Reply with quote
HoopStudies wrote:
So I'd definitely suggest something different for field goals missed -- I've seen FGX before and like it better than FG- because the minus sign can be confusing.


I like that idea, and am stealing it. FG- has the disadvantage of looking a little bit like a type, FGX looks odd, but intentional.
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NickS



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PostPosted: Fri May 25, 2007 10:56 am Post subject: Reply with quote
Mike G wrote:
This clues me in that there's no adjustment for pace, or for scoring/rebounding differentials? I can tell you that no matter how fine you grind the raw stats, divorced from team context the players will never indicate the strength of their team.


Let me take this as an opportunity to talk a little bit about my goals for this metric.

You're correct that I'm not adjusting for pace, and that's something I absolutely *should* be doing (and may do this morning). On every other posting of the rankings I included a note that it wasn't pace or team adjusted. I didn't include it on that one just because I got tired of typing it, but it should be there.

On the other hand, I have avoided using team stats in the rating because, though they would increase accuracy, they also make it more complicated.

My goal for this line of work is not to come up with an ultimate rating system that will settle, once and for all, the debate over who is the best player in the league. I don't think that's possible, and I really don't think that's possible with a single linear weight rating.

My goal, which is both modest and ambitious, is to come up with something that's good enough to replace PER as a simple, rough approximation. Think about the fact that you see PER everywhere in the APBRMetrics world, from Roland ratings to Knickerblogger, etc . . . A big part of the value of PER is that it's easy to calculate, and that everyone knows that it's a rough approximation and don't take it too seriously.

I may be making a bigger deal out of that than I should, partially because I'm not an Excel expert, so I needed something that was simple enough for me to calculate without a lot of work.

Let me add, however, that what I really want is something that both works as a rough approximation, and is sufficiently theoretically rigorous that it's easy to increase the accuracy of the approximation as more empirical work is done. For example, I don't think anyone knows enough right now to have a value for assists that we can have complete confidence in. But if the system is set up right, it can work with a current approximation of the value of an assist and if later someone is able to come up with convincing empirical research to set the value of assists, it's easy to incorporate that without having to re-design the formula.
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NickS



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PostPosted: Fri May 25, 2007 11:11 am Post subject: Reply with quote
Harold Almonte wrote:
How do you cancel points? Are STL and BLKS the only things that avoid ponts?, other than that, isn't there any other thing?.


The one thing I am taking as set in stone is that, assuming average assist, steal and block rates, that if you have two teams play and team A beats team B by 10 points 100-90 that combined ratings of the players on team A will be 10 points higher than the players on team B.

Now, as I've shown, the crdits might look like 50-40, or their might look like 150-140, depending on whether, for example, you mostly count a missed shot as a penalty on the offense or a credit to the defense (for obvious reason, that keeps the relative scores the same, but changes the absolute values).

I don't know if that answers your question, it's a little abstract, and I'm a little confused by the question, but I think that should answer it.


Harold Almonte wrote:
Do the scorer shoot down himself, allways? If FTs were shot guarded and not alone, what would be the average players's FT%?


What does this question mean? Can you explain a little bit more?
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NickS



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Posts: 384


PostPosted: Fri May 25, 2007 11:37 am Post subject: Reply with quote
For MikeG, here's a pace adjusted set of numbers (I just used the pace values from b-r.com. I didn't calculate them myself). Tim Duncan moves past Kobe and Nash. Shaq, is #32, Chauncy #33. and Jermaine #52 just behind Jose Calderon. Perhaps amusing, Eddy Curry shows up as the league average player.

Code:
Rank Player NPV40 Rank Player NPV40
1 wade,dwyane 5.097 16 bosh,chris 3.184
2 nowitzki,dirk 5.007 17 carter,vince 3.134
3 ming,yao 4.906 18 mcgrady,tracy 2.966
4 duncan,tim 4.626 19 pierce,paul 2.901
5 bryant,kobe 4.525 20 allen,ray 2.876
6 nash,steve 4.418 21 anthony,carmelo 2.825
7 ginobili,manu 4.251 22 redd,michael 2.757
8 boozer,carlos 4.225 23 davis,baron 2.756
9 stoudemire,amare 4.003 24 lewis,rashard 2.692
10 arenas,gilbert 3.967 25 lee,david 2.677
11 gasol,pau 3.936 26 camby,marcus 2.672
12 garnett,kevin 3.871 27 okafor,emeka 2.643
13 brand,elton 3.442 28 howard,dwight 2.629
14 james,lebron 3.412 29 randolph,zach 2.497
15 marion,shawn 3.192 30 kidd,jason 2.377


Obviously, this doesn't take individual or team defense into account.
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NickS



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PostPosted: Fri May 25, 2007 2:18 pm Post subject: Reply with quote
Following Mark's request, here's a comparison of the top 10 players in each system. Because each system has it's own scale I'm not including ratings, just the rankings.

I'm a little surprised at how similar NP40 and PER are in their rankings (including having the same top 5) which is a sign both of the fact that I was probably influenced by PER when I was tweaking my parameters, and a reminder of why PER is useful -- it is not bad rating.

Code:
Player NPV PER WP48
wade dwyane 1 1 23
nowitzki dirk 2 2 15
ming yao 3 3 46
duncan tim 4 3 7
bryant kobe 5 5 30
nash steve 6 12 10
ginobili manu 7 9 11
boozer carlos 8 10 5
stoudemire amare 9 14 16
arenas gilbert 10 11 53

Player PER NPV WP48
Dwyane Wade 1 1 23
Dirk Nowitzki 2 2 15
Yao Ming 3 3 46
Tim Duncan 4 4 7
Kobe Bryant 5 5 30
LeBron James 6 14 34
Kevin Garnett 7 12 6
Pau Gasol 8 11 18
Manu Ginobili 9 7 11
Carlos Boozer 10 8 5

Player WP48 NPV PER
David Lee 1 25 32
Jason Kidd 2 30 39
Marcus Camby 3 26 42
Shawn Marion 4 15 29
Carlos Boozer 5 8 10
Kevin Garnett 6 12 7
Tim Duncan 7 4 4
Dikembe Mutombo 8 94 120*
Tyson Chandler 9 59 68
Steve Nash 10 6 12

Note that tyson chandler didn't have enough minutes to qualify on the KB list of PER but his PER falls between that of Al Harrington (119) and Andrei Kirilenko (120)


Also note that, except for Kevin Garnett and Manu Ginobili, the NPV40 ranking ends up between the PER and the WP rankings (and closer to the PER as mentioned above)

Mark



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PostPosted: Fri May 25, 2007 3:31 pm Post subject: Reply with quote
Thanks for the player ranking comparison- presented 3 ways.

Last edited by Mark on Fri May 25, 2007 10:48 pm; edited 1 time in total
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Harold Almonte



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PostPosted: Fri May 25, 2007 4:20 pm Post subject: Reply with quote
Quote:
My goal for this line of work is not to come up with an ultimate rating system that will settle, once and for all, the debate over who is the best player in the league. I don't think that's possible, and I really don't think that's possible with a single linear weight rating.

NickS- You must have started the topic with this paragraph.

What I was talking about is point diferential, counterpart, matchup. Nobody thinks that just STLS, BLKs and DRebs are the only things you need to know from a player to build a defense rating. You need points allowed, OppFG%. How do you get that, well, you can know that better than me. Do you think is not important? According to 4 factors, it could mean about a 20% of a player performance rate. That's why RolandR does a PER counterparting. If counterparting is the solution for all metrics's ills, this is the most counterparted of all (If just that plus/minus could be adjusted).
Resume: You take account scorer's points and how much possessions he lost and semi-lost at the offensive end. You must take account gained and semi-gained possessions, plus points allowed, at the defensive end.

Being the boxscore stats shortcuts about the "inter-players reality of the game", and the possession calcs, extra shortcuts; then you need to adjust to look some real. That's what WOW did.

Last edited by Harold Almonte on Wed May 30, 2007 6:45 pm; edited 3 times in total
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NickS



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PostPosted: Fri May 25, 2007 4:24 pm Post subject: Reply with quote
I disocovered an error in my spreadsheet, so new ranking, with some significant changes.

I was looking back at my formula because I wanted to make a change to how I was handling free throws and realized that I never had deducted credit from free throws to account for the penalty that I was giving to personal fouls.

Obviously my theory says that there has to be some that the total value for free throws has to be split between credit for the offensive player and debit for the defensive player. I had the thought that rather than deducting a proportion from each FT, that I would deduct from each players FTs an amount equal to a portion of the league average FT/FGA.

So, in other words, for offensive players who shoot free throws at a rate below the league average FT/FGA a higher portion of the credit for their FTs is assigned to the defender, and for players who shoot free throws at a rate above the league average will receive a higher portion of that credit.

Because I originally wasn't deducting value from free throws at all this has hurt some players that received a large portion of their value from free throws, but has helped players that are efficient in getting to the line and hitting free throws -- like manu ginobili and chauncey billups.

Code:
Rank Player NPV40 Rank Player NPV40
1 wade,dwyane 5.035 16 carter,vince 2.940
2 nowitzki,dirk 5.007 17 lee,david 2.893
3 ming,yao 4.774 18 marion,shawn 2.884
4 duncan,tim 4.682 19 howard,dwight 2.843
5 ginobili,manu 4.308 20 mcgrady,tracy 2.733
6 bryant,kobe 4.113 21 pierce,paul 2.691
7 nash,steve 4.103 22 okafor,emeka 2.652
8 boozer,carlos 4.094 23 allen,ray 2.641
9 garnett,kevin 3.782 24 billups,chauncey 2.591
10 gasol,pau 3.716 25 lewis,rashard 2.575
11 stoudemire,amare 3.650 26 randolph,zach 2.521
12 arenas,gilbert 3.554 27 redd,michael 2.504
13 brand,elton 3.446 28 kidd,jason 2.444
14 james,lebron 3.268 29 o'neal,shaquille 2.350
15 bosh,chris 3.026 30 camby,marcus 2.333
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NickS



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PostPosted: Fri May 25, 2007 4:33 pm Post subject: Reply with quote
for those surprised by David Lee's jump, let's look at his stats compared to Dwight Howard (per 40 minutes) (they play at a similar pace):

Code:
David Lee 14.4 pts (.652 TS%), 4.5 OR, 9.4 DR, 1.1st, 0.5 bk, 2.1 TO
Dwight Howard 19.1 pts (.619 TS%), 3.7 OR, 9.6 DR, 0.9st, 2.1 bk, 4.2 TO


Dwight Howard scores significantly better, but has a lower TS%, David Lee gets 20% more offensive rebounds and about the same number of defensive rebounds. Dwight Howard has 1.6 more blocks but also twice as many turnovers.

It doesn't seem wrong to me that they rank the same.

Now, that is not taking into account the question of playing against starters vs subs, something MikeG has been doing admirable work on, nor does it recognize that Dwight Howard played 80% more minutes.
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Mark



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PostPosted: Fri May 25, 2007 10:58 pm Post subject: Reply with quote
The top 30 is a group of guys nearly all paid to their max level or will when they come off rookie contract... with the case of David Lee remaining a point of interest.

The highest paid players who arent delivering star level performance by other metrics are generally pretty well known but are there any surprises by NPV?
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NickS



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PostPosted: Sat May 26, 2007 6:44 pm Post subject: Reply with quote
Mark wrote:
The top 30 is a group of guys nearly all paid to their max level or will when they come off rookie contract... with the case of David Lee remaining a point of interest.

The highest paid players who arent delivering star level performance by other metrics are generally pretty well known but are there any surprises by NPV?


Some interesting ones (remember, that this is a per minute stat):

Brian Cardinal #34
Sean May #37
Antonio McDyess #42
Nene #48
Ben Gordon #61
Dikembe #67 (he moved up in the latest change)
Donyell Marshall #72
LaMarcus Aldridge #73
Bostjan Nachbar #84
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NickS



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PostPosted: Wed May 30, 2007 1:12 pm Post subject: Reply with quote
Thanks to everyone who caught up on this thread over the weekend. I noticed that the page views increased considerably, and I'm glad that people are interested.

I've been slowing down on this a little, but continuing to think about it. I have another NPV/PER comparison that may be interesting. This is a chart comparing NPV assessment of (a selection of) rookies with PER. The columns are NPV40, PER-15, A best fit prediction of PER based on NPV for this sample, and a column showing the difference which I have multipled by 10 to make it more readable.

I did the predicted PER based on just this group rather than all values because I wanted the differences to add up to 0. I may do another comparison in which I generate a linear regression between PER and NPV for the entire data set.

I have calculated PER myself and it doesn't quite match up with the KB numbers, and may well be an error on my part. But the numbers are close enough that they should work for this comparison.

Interestingly NPV doesn't like any of the Blazer's rookies as well as PER. I know that part of this is because NPV doesn't value steals (or punish TOs) as much as PER, but I'm haven't looked closely at what's causing the differences.

List broken into groups of 5 for readability.

Code:
Name NPV PER-15 Predicted Difference
roy,brandon 0.775 2.995 0.922 -20.729
aldridge,lamarcu 0.900 2.546 1.167 -13.792
millsap,paul 2.082 2.488 3.466 9.783
balkman,renaldo 0.939 1.504 1.241 -2.627
herrmann,walter 0.894 1.492 1.153 -3.382

smith,craig 0.610 0.686 0.601 -0.843
brewer,ronnie -0.373 0.133 -1.311 -14.445
rodriguez,sergio -0.360 -0.328 -1.286 -9.586
parker,anthony -0.135 -0.422 -0.848 -4.259
boone,josh 0.344 -0.604 0.084 6.877

powe,leon 0.410 -1.164 0.213 13.773
foye,randy -0.396 -1.333 -1.357 -0.237
baston,maceo 0.235 -1.471 -0.128 13.435
rondo,rajon -0.964 -1.829 -2.461 -6.326
azubuike,kelenna -0.568 -1.941 -1.691 2.507

johnson,alexande -0.271 -2.023 -1.113 9.105
adams,hassan -1.020 -2.145 -2.570 -4.250
redick,j.j. -0.805 -2.189 -2.153 0.363
bargnani,andrea -0.464 -2.355 -1.489 8.665
udoka,ime -0.932 -2.551 -2.399 1.522

garbajosa,jorge -1.232 -2.627 -2.983 -3.552
armstrong,hilton -0.804 -2.651 -2.150 5.005
williams,shelden -0.543 -2.662 -1.642 10.197
gay,rudy -1.328 -2.738 -3.170 -4.314
williams,marcus -1.561 -3.647 -3.624 0.228

farmar,jordan -1.705 -3.937 -3.903 0.344
gelabale,mickael -2.299 -5.156 -5.060 0.968
gibson,daniel -2.002 -5.424 -4.481 9.435
morrison,adam -3.657 -7.316 -7.702 -3.866
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Mark



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PostPosted: Wed May 30, 2007 3:19 pm Post subject: Reply with quote
This gets back at how NPV and PER weight/handle each stat category and how important those differences are in the overall rating. I havent gotten around to it on my own but I would continue to read about it and perhaps comment further.

Last edited by Mark on Wed May 30, 2007 6:32 pm; edited 1 time in total
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Neil Paine



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Posts: 774
Location: Atlanta, GA

PostPosted: Wed May 30, 2007 4:57 pm Post subject: Reply with quote
Yeah, for instance, if you calculate it for every year since 1978, PER gives the following values to each action:

Code:
Category Value
---------------------------
Assists +0.67
3FG Made +1.00
FG Made +1.65
FT Made +0.90
Turnovers -1.02
FG Missed -0.71
FT Missed -0.37
Off. Rebounds +0.71
Def. Rebounds +0.32
Steals +1.02
Blocks +0.71
Fouls -0.35
---------------------------


How does NPV value each category?
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Harold Almonte



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PostPosted: Wed May 30, 2007 6:06 pm Post subject: Reply with quote
I think, no matter the natural 70/30 proportion between OReb and DReb. Once the ball is randomly in the air, The same weight you give to the effort to obtain a DReb, you must give it to OReb. They must be weighted the same in that order, and the same as a missedFG.

I think it is not the (both ends) rebounds summatory to obtain the 100 the right thing, but the sharing between the 0.70DReb and 0.30 defense to the missedFG, 0.70missedFG and 0.30 assistant teammates, 0.70OReb and 0.30 teammates influence to obtain it.

It sounds subjective no?, not for adjusted plus-minus. But, if somebody can give me a good explanation about how easy for a team is to obtain a DReb against an OReb, how spotty advantaged DRebounders are, and how metrics must reflect that, I will be quikly and easily convinced. Will it be WP?

But maybe the 70/30 must appear inside the player's rebounding total usage, not the weight.
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NickS



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PostPosted: Wed May 30, 2007 7:15 pm Post subject: Reply with quote
davis21wylie2121 wrote:
Yeah, for instance, if you calculate it for every year since 1978, PER gives the following values to each action:

Code:
Category Value
---------------------------
Assists +0.67
3FG Made +1.00
FG Made +1.65
FT Made +0.90
Turnovers -1.02
FG Missed -0.71
FT Missed -0.37
Off. Rebounds +0.71
Def. Rebounds +0.32
Steals +1.02
Blocks +0.71
Fouls -0.35
---------------------------


How does NPV value each category?


I'll need to calculate it, but that's a nice presentation. I'll get that for you.

One problem that I have is that the two aren't scaled the same (the theory behind PER is similar to that behind NPV, but I think Hollinger creates "inflation" by not debiting for made baskets, and not sharing value between things like TOs and steals).

What is the total PER for an average team? I should be able to scale to that.

Nick
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Harold Almonte



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PostPosted: Wed May 30, 2007 7:33 pm Post subject: Reply with quote
Debiting for made baskets? I think the only thing that must be debited is the assistance the scorer received. The FGA?, then you must debit all kinds of gained or lost possessions by the possibility of being or not scored in the play sequency. Sharing value between the stealer and the turnoverer? That's the summum of subjectivity, but I could accept it without much effort.
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NickS



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PostPosted: Wed May 30, 2007 7:38 pm Post subject: Reply with quote
For 2007, the numbers look like this:

This isn't scaled at all, you will notice that NPV has lower values for most things, but what really matters is their relative weights.

So if you think that (approximating), on average NPV has a value that's about 60% of the PER equivilent, it means that NPV values 3 pointers a lot more than PER does (relative to the other weights).

The reason blocks look better in NPV than steals is just that I've made a decision to weight them that way on the belief that more steals are a result of carelessness on the part of the offensive player.

I am assuming that 3pM means converting a made 2 to a made 3, whereas FGM means adding 1 to both FGM and FGA (e.g., it isn't just converting a miss to a make while keeping attempts the same).

Code:
Category NPV PER
------------------------------
Assists +0.39 +0.67
3FG Made +1.00 +1.00
FG Made +0.92 +1.65
FT Made +0.53 +0.90 (.38)
Turnovers -0.52 -1.02
FG Missed -0.55 -0.71
FT Missed -0.36 -0.37
Off. Rebounds +0.58 +0.71
Def. Rebounds +0.25 +0.32
Steals +0.62 +1.02
Blocks +0.52 +0.71
Fouls -0.09 -0.35
------------------------------
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NickS



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PostPosted: Wed May 30, 2007 7:42 pm Post subject: Reply with quote
Harold Almonte wrote:
Debiting for made baskets?


I know that sounds odd, but it a change of possession. Think about it this way, the difference between making a 2 point basket vs shooting, missing, and the other team getting the rebound is only 2 points. In both cases the possession changes, in one case the scoreboard changes, in the other it doesn't.

To keep everything scaled to points I have to say that (value of FGM) - (value of FGX + Opp Defensive Rebound) = 2.

If FGX + Opp Defensive Rebound was valued at 0, than the value of a FGM would be 2. But since there is a negative value for FGX, the value of a FGM has to be less than 2 to keep the difference between the cases at 2 points.
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Harold Almonte



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PostPosted: Wed May 30, 2007 8:08 pm Post subject: Reply with quote
My point is that the -missedFG and its bad assistance around + the DReb and its assistance around must be 0, but even if you weight only a 70% and 30% for assistance, is the same with FGM. But being FGM the end of a succesfull scoring possession, not the lost, and yes a change; when the opponent put the ball in play then, how do you credit by obtaining a neither turnovered nor rebounded scoring possession? when they convert it and then automatically punish it? when they loose it?. One change at one end cancels the other.

A FGM is just a scoring possession*points scoring prize. You only cancel points with points, there is no extra prize for rebounding, nor stealing. Points allowed is what you need to introduce in the formula to balance the offensive and the defensive (points) performance.

[Crow]

Mark



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Posts: 807


PostPosted: Wed May 30, 2007 8:42 pm Post subject: Reply with quote
Ok, multiplying the PER weights by 0.6 (following your sugestion) and comparing to NPV I can get a pretty good sense of what the differences are. Thanks.

So NPV (among other things) makes 3ptrs more valuable, all misses more costly (affecting higher usage players), rebounds more valuable, fouls less costly compared to PER. Initial reaction I am probably in agreement on the middle 2. Didnt really grasp your sentence on the 3 pt weight. I think I can see a case for the foul weight based on previous discussion about offsetting credit/debit in balance with value actually created by freethrow activity but is there more to it than that? I'd want to see that whole argument in one place to feel confident about the new weight.
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Statman



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Location: Arlington, Texas

PostPosted: Wed May 30, 2007 10:36 pm Post subject: Reply with quote
NickS wrote:
For 2007, the numbers look like this:

This isn't scaled at all, you will notice that NPV has lower values for most things, but what really matters is their relative weights.

So if you think that (approximating), on average NPV has a value that's about 60% of the PER equivilent, it means that NPV values 3 pointers a lot more than PER does (relative to the other weights).

The reason blocks look better in NPV than steals is just that I've made a decision to weight them that way on the belief that more steals are a result of carelessness on the part of the offensive player.

I am assuming that 3pM means converting a made 2 to a made 3, whereas FGM means adding 1 to both FGM and FGA (e.g., it isn't just converting a miss to a make while keeping attempts the same).

Code:
Category NPV PER
------------------------------
Assists +0.39 +0.67
3FG Made +1.00 +1.00
FG Made +0.92 +1.65
FT Made +0.53 +0.90 (.38)
Turnovers -0.52 -1.02
FG Missed -0.55 -0.71
FT Missed -0.36 -0.37
Off. Rebounds +0.58 +0.71
Def. Rebounds +0.25 +0.32
Steals +0.62 +1.02
Blocks +0.52 +0.71
Fouls -0.09 -0.35
------------------------------


I like the fact you are battling with this - I did this for quite a while a few years back....

That being said, logically (I assume that's what you are striving for), a missed FG should be worth .7 of a turnover, since a missed shot has about a 30% chance of the ball staying with the offense, while a turnover has zero % chance of the ball staying with the offense. No matter what - it seems completely illogical that a missed FG is a BIGGER negative worth than a turnover. What's worse - missing 10 shots in a game or making 10 turnovers - everything else being equal?

Your 3pt weight seems too high - a guy hitting 2 threes in 5 shots (6 points in 5 attempts) gets a full +0.52 credit more (that's the value of a turnover in your system) than a guy hitting 3 two point fgs in 5 attempts (6 points in 5 attempts).

I have some DEFINITE ideas on this (linear weights measurements & how to impliment) - there are steps linear weights people aren't taking that would just seem logical. I'll expound on this more in the future after I iron out my ideas - which I am currently working on for my very newly developed college basketball site. After I get the kinks worked out - and get all the D1 college players ranked - I'll move on to the NBA with a very similar process. The NBA will obviously be MUCH easier - since Strength of Schedule isn't nearly as tricky, and you are dealing with about a tenth of the players you are dealing with in D1.
_________________
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My current national college player rankings (and other stuff):
http://www.pointguardu.com/f136/statman ... post355594
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NickS



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PostPosted: Thu May 31, 2007 11:03 am Post subject: Reply with quote
A number of good questions, I'm glad people are still reading and thinking about this. I'll response to Statman first since he asks a couple of specific questions.

Statman wrote:
I like the fact you are battling with this - I did this for quite a while a few years back....


Thanks, I'm glad for any responses you have.

I'll say again, that I'm not nearly as invested in this specific rating system as I am in the hope that it's possible to build some clarity in the apbrmetrics community about the building blocks of linear weight systems, and what the tradeoffs are.

The whole debate over WoW inspired me to think about it because it made clear that people had intuitive responses, that hadn't been fully worked out or formalized, and part of what I'm trying to work through is just a way to explain the decisions that get made.

So talking about that is good.

Statman wrote:
That being said, logically (I assume that's what you are striving for), a missed FG should be worth .7 of a turnover, since a missed shot has about a 30% chance of the ball staying with the offense, while a turnover has zero % chance of the ball staying with the offense.


Great question, this was one of the things that struck me early one when I was working on the system that I've underplayed a little bit -- I penalize less for TOs than any other system.

This ran counter to my intuition at first, but I've come around to believing my own conclusions in this case.

The basic reasoning is this: if there were no steals I would agree with you, a TO is the worst thing that an offensive player can do, and should be penalized heavily.

But, about 60% of TOs are counted as steals.

If you count a TO as loosing a full possession, and a steal as gaining a full possession, than the difference in score between the two teams will reflect a 2 possession shift, when only one possession has changed hands.

Essentially, you can't give one player credit for a steal, and the other player a penalty for a TO on the same play, without breaking the relative scoring of the two teams.

So then it's just a matter of distributing "credit" between the two players and I give most of the credit to the person making the steal which means that the person making the TO is partially "excused."


Statman wrote:
Your 3pt weight seems too high - a guy hitting 2 threes in 5 shots (6 points in 5 attempts) gets a full +0.52 credit more (that's the value of a turnover in your system) than a guy hitting 3 two point fgs in 5 attempts (6 points in 5 attempts).


Lets run that math:

2x(FGM+3PM) - 3x(FGX) = 2x(1.92)-3x(.55) = 2.19
3x(FGM) - 2x(FGX) = 1.66

This looks all wrong, but that's because it doesn't include the entire event. The first player is generating 3 opportunities for offensive rebounds, the second is generating only 2. If you look at the difference between each player's score and their opponents score you will see:

2x(FGM+3PM) - 3x(FGX) -3x(DRB) = 2.19 - .75 = 1.44
3x(FGM) - 2x(FGX) -2x(DRB) = 1.66 - .5 = 1.16

The difference between the two players (.28) is related to the fact that the first player generates fewer opportunites for assists for his teammates and thus gets to "keep" a greater portion of the credit for his scoring. The player who shoots 3-5 is sharing more credit with the presumed assister.

Since about 60% of baskets are assisted, that difference should be 60% of the value of an assist (.24), and I suspect the remaining difference is just a rounding error in the values that I posted.
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NickS



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PostPosted: Thu May 31, 2007 11:48 am Post subject: Reply with quote
Mark wrote:
So NPV (among other things) makes 3ptrs more valuable, all misses more costly (affecting higher usage players), rebounds more valuable, fouls less costly compared to PER. Initial reaction I am probably in agreement on the middle 2. Didnt really grasp your sentence on the 3 pt weight. I think I can see a case for the foul weight based on previous discussion about offsetting credit/debit in balance with value actually created by freethrow activity but is there more to it than that? I'd want to see that whole argument in one place to feel confident about the new weight.


That's all exactlty right, and I will try to make the argument, which includes some digressions.

The first part of the argument is just understaning that what matters in a linear weight system is the relative weights of the terms. Something that values baskets at 2 points and rebounds at 1 point will end up with exactly the same relative ratings as one that values baskets at 1 point and rebounds at .5 points (assuming all the other terms are also scaled).

So what this means is that if you have a given set of values than raising the value of one term is the same as lowering the values on the other terms. Hence my use of the term "inflation" in regards to PER.

With that said, I went over the value of 3 pointers in my response to statman, so I won't repeat that. Saying that made and missed baskets and rebounds have a higher relative werights than PER is the same as saying that TOs, Steals, Blocks, and PF have a lower relative weight. The reason they all have lower relative weight is twofold:

The first reason is that I'm using a different scale for the value of possessions than PER. PER essentially uses the league average value of possessions (~1) for everything expect made baskets for which the value of a possession is assumed to be 0. This is what I am calling "inflationary". The value of a made basket is inflated which is the equivilent of deflating everything else. That decision also makes hides the problem of weighting scoring vs rebounding. If you deducted the full value of a possession from made baskets in PER all of a sudden you would find that the people it would rate very highly would be rebounders. Finding some balance between scoring and rebounding is necessary for the reason I laid out in the "two meanings of zero" post. Again, PER accomplishes that by setting a value for Rebounding, and then deflating it by adding extra value for made baskets (I realize this sounds like a completely counter-intuitive description of what's going on. I've tried to explain this point in my response to Harold Almonte). By using a lower value for possessions it reduces the value of actions that change possessions like STLs and TOs.

The second reason is that all of those are shared events. The reason why the penalty for PF is so low in my system is simply because I want to give credit to the person shooting free throws, and anything that I give as a debit to the fouler has to come out of the credit I give to the FT shooter. This is true as well of steals and blocks.
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NickS



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PostPosted: Thu May 31, 2007 12:28 pm Post subject: Reply with quote
NickS wrote:
PER essentially uses the league average value of possessions (~1) for everything expect made baskets for which the value of a possession is assumed to be 0. This is what I am calling "inflationary". The value of a made basket is inflated which is the equivilent of deflating everything else.


I realized, after posting this, that this contradicts the later argument in the post. If PER deflates the value of a possession, than I don't know whether I'm using a lower value for possessions than PER with regard to steals, blocks, and TOs. To find that out, I would need to estimate what the value of a PER posession would be if you rescaled everything to points.

I'll need to think about how to estimate that, but it would be an interesting thing to do.
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Mark



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PostPosted: Thu May 31, 2007 1:21 pm Post subject: Reply with quote
I think I am on board with your 3 pt and foul weights. I half got the 3pt explanation before but wanted to see it one more time and now see how it works with your weights and accounting system.

FG misses in NPV cost the shooter. The defender (or counterpart position assumed defender) gets no reward. Do you have any interest in taking step toward splitting the value of this jointly produce event? It is one of the main limitations/omissions of PER. Given all your other efforts, will this one get done too (as best it can today from 82games shot defense data)?
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Harold Almonte



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PostPosted: Thu May 31, 2007 3:56 pm Post subject: Reply with quote
Quote:
But, about 60% of TOs are counted as steals.

The other 40% is something called TO provoked that doesn't appear in boxscores, and you should credit to someone(s). I don't understand why you must share anything between STL and TO. It's a viceversa situation, but. What I think is all lost and gained possessions (Stolen type, rebounded type and stopped play type) have their different scoring difficulty factor, but I'm not sure whether metrics must punish by this.

I've noted the PER's regressed weights project this 70% or 2/3 of a full possession (even a FGM). That is what I call "sharing between an usager and his teammates". But I'm strangelly agreeing with the Nicks's rebounding weights, if we must to factor by rebounding difficulty (I don't know how Nick obtained his weights)

sharing * Reb. difficulty between OR-DR
(0.70) * (0.70) Off Reb
(0.70) * (0.30) De Reb
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NickS



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PostPosted: Thu May 31, 2007 4:24 pm Post subject: Reply with quote
Mark wrote:
I half got the 3pt explanation before but wanted to see it one more time and now see how it works with your weights and accounting system.


Heh, me too. I knew it worked in theory, but I was oddly happy when the numbers actually added up.

Mark wrote:
FG misses in NPV cost the shooter. The defender (or counterpart position assumed defender) gets no reward. Do you have any interest in taking step toward splitting the value of this jointly produce event?


Good question. My answer for the moment is no, because I really do want to keep it simple (or, at least, at the level of simplicity of PER). But I may change my mind and, as importantly, I don't feel protective of the ideas behind NPV. If somebody wants to steal all or part of the ideas and include that in a system that uses counterpart performance, I'd be completely happy to see that. That isn't really an answer, except to say, I think it would be interesting to see, but I'm not ambitious to do that right now.

Harold -- I'm not ignoring your questions, just thinking about how to respond. I feel like we're coming from sufficiently different perspectives that I can't really answer the questions, I can just try to explain my perspective and, hopefully, even if it doesn't convince you, you can see how it's internally consistant.
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Harold Almonte



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PostPosted: Thu May 31, 2007 5:15 pm Post subject: Reply with quote
NickS- I'm working in a theory about an uthopical totally shared basketball metric, just for fun. I'm trying to see how much I can derivate a linear formula, although I think the final integral of every linear metric is some kind of adjusted plus minus metric.

If I finally agree with you about STL-TO sharing, this part would be included more or less like this:

own STL- own TO - (α) opp STL - (α) opp TO , or
( own STL - (α) opp TO) - ( own TO + (α) opp STL)

Where (α) would be the sharing cost between the stealer and the turnoverer.

In th end, this will be: (1-α) STL - (1+α)TO
a (α) extra punishment for the stealer and the turnoverer. Uhm? I think I won't agree

Last edited by Harold Almonte on Fri Jun 01, 2007 8:44 am; edited 6 times in total
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Statman



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PostPosted: Thu May 31, 2007 7:19 pm Post subject: Reply with quote
NickS wrote:
A number of good questions, I'm glad people are still reading and thinking about this. I'll response to Statman first since he asks a couple of specific questions.

Statman wrote:
I like the fact you are battling with this - I did this for quite a while a few years back....


Thanks, I'm glad for any responses you have.

I'll say again, that I'm not nearly as invested in this specific rating system as I am in the hope that it's possible to build some clarity in the apbrmetrics community about the building blocks of linear weight systems, and what the tradeoffs are.

The whole debate over WoW inspired me to think about it because it made clear that people had intuitive responses, that hadn't been fully worked out or formalized, and part of what I'm trying to work through is just a way to explain the decisions that get made.

So talking about that is good.

Statman wrote:
That being said, logically (I assume that's what you are striving for), a missed FG should be worth .7 of a turnover, since a missed shot has about a 30% chance of the ball staying with the offense, while a turnover has zero % chance of the ball staying with the offense.


Great question, this was one of the things that struck me early one when I was working on the system that I've underplayed a little bit -- I penalize less for TOs than any other system.

This ran counter to my intuition at first, but I've come around to believing my own conclusions in this case.

The basic reasoning is this: if there were no steals I would agree with you, a TO is the worst thing that an offensive player can do, and should be penalized heavily.

But, about 60% of TOs are counted as steals.

If you count a TO as loosing a full possession, and a steal as gaining a full possession, than the difference in score between the two teams will reflect a 2 possession shift, when only one possession has changed hands.

Essentially, you can't give one player credit for a steal, and the other player a penalty for a TO on the same play, without breaking the relative scoring of the two teams.

So then it's just a matter of distributing "credit" between the two players and I give most of the credit to the person making the steal which means that the person making the TO is partially "excused."


Statman wrote:
Your 3pt weight seems too high - a guy hitting 2 threes in 5 shots (6 points in 5 attempts) gets a full +0.52 credit more (that's the value of a turnover in your system) than a guy hitting 3 two point fgs in 5 attempts (6 points in 5 attempts).


Lets run that math:

2x(FGM+3PM) - 3x(FGX) = 2x(1.92)-3x(.55) = 2.19
3x(FGM) - 2x(FGX) = 1.66

This looks all wrong, but that's because it doesn't include the entire event. The first player is generating 3 opportunities for offensive rebounds, the second is generating only 2. If you look at the difference between each player's score and their opponents score you will see:

2x(FGM+3PM) - 3x(FGX) -3x(DRB) = 2.19 - .75 = 1.44
3x(FGM) - 2x(FGX) -2x(DRB) = 1.66 - .5 = 1.16

The difference between the two players (.2Cool is related to the fact that the first player generates fewer opportunites for assists for his teammates and thus gets to "keep" a greater portion of the credit for his scoring. The player who shoots 3-5 is sharing more credit with the presumed assister.

Since about 60% of baskets are assisted, that difference should be 60% of the value of an assist (.24), and I suspect the remaining difference is just a rounding error in the values that I posted.


Well - interesting that partial credit is given for the added offensive rebound opportunity in this case - but absolutely zero credit is given for the possible offensive rebound opportunities of normal missed shots. Seriously - to have a missed shot a bigger negative than a turnover throws a monkey wrench in the whole thing for me. I understand you are giving "partial credit" for the guy that possibly got the steal (of the turnover) - BUT missed shots are by no means COMPLETELY the fault of the shooter. Just because you do not have an equivelant defensive stat to give credit to doesn't mean a missed shot is by ANY means a WORSE result than a turnover.

I look at linear weights differently. There are SO MANY other factors that are inherently tied into the stats we work with (that aren't measured) - that I think attempting to make everything somehow come out perfect to some kind of sum zero just won't work right. There are certain stats that I believe deserve more "value" than their REAL value - like steals, blocks, and assists. I gave up on the idea of having everything work out perfectly on both sides of the ball (as PER tries to do, and it appears you are trying to do now).
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My current national college player rankings (and other stuff):
http://www.pointguardu.com/f136/statman ... post355594
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Harold Almonte



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PostPosted: Thu May 31, 2007 7:57 pm Post subject: Reply with quote
α { αr (OReb - missFG - 0.44 missFT + defended opp missFG + 0.44 shooting fouled opp missFT) + (1-αr) DReb }

Where (α) is the universal sharing between an usager and his teammates, and (αr) is the possibility of a missedFG to be defensive rebounded, or the difficulty factor between a DReb and an OReb.
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Mike G



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PostPosted: Fri Jun 01, 2007 9:21 am Post subject: Reply with quote
Statman wrote:
... There are SO MANY other factors that are inherently tied into the stats ... that I believe deserve more "value" than their REAL value - like steals, blocks, and assists. ..


Agree with Dan, er, Statman. At the quantum level, we have to keep it simple to get Net=0. In the big mix, almost any registered stat has a value that is shared, amortized, randomly assigned.

Scenario: Amare dunks a missed shot.
Next trip, Duncan forces a miss, grabs the DReb, outlets, gets a dunk at the other end.
Both guys got a Reb + 2 Pts. Did one do more than the other? Since the OReb often carries the bonus of an ensuing FG, does the OReb itself need to be 2.32 times as valuable as the DReb?

If you're counting FGX as a negative, why not punish Amare's man for allowing the OReb? i.e., for missing the Reb.

I'm not really suggesting there's a proper way to iron this out. No doubt I've missed some of the explanation behind what you're doing, and I'm just trying to help. In particular, I'm not sold on the idea that OReb > DReb. Scarcity and value are unrelated.
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Harold Almonte



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PostPosted: Fri Jun 01, 2007 10:07 am Post subject: Reply with quote
Amare's offensive end:
-Amare's teammate missFG
-Amare's (weight)OReb
-Amare's (not assisted)FGM

Duncan's deffensive end:
-forces a +(weight) opp missFG
-grabs an (weight)DReb
Duncan's offensive end:
-(?)FGM

Amare saved a scoring possession and converted it in 2 points.
Duncan shot down an opponent, rebounded (he now alone gained the whole scoring possession, the defense plus the rebound). At the other end he scorers (we don't know if it was assisted or alone like Stoud.)

Amares production: 2p + OReb=missFG saved
Duncan production: Forced missFG=OReb + DReb + 2p

the difference? a DReb in the middle.
what linear metrics and boxsore didn't take account? the forced missFG, they give its credits to DRebs.

what if a Duncan's teammate forces the missFG? according to boxscore, he is not credited, and Duncan gets all the credits.
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Harold Almonte



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PostPosted: Fri Jun 01, 2007 3:05 pm Post subject: Reply with quote
MikeG
Quote:
If you're counting FGX as a negative, why not punish Amare's man for allowing the OReb? i.e., for missing the Reb.


The idea behind is, no matter who grabs the OReb., there will be only a 30% of total rebs. available to offensive players to rebound. It's a basketball game characteristic, maybe a natural law, it supposed to be the defenders's position advantage. An OReb. is a big prize given its possibilities to be accomplished, and DReb aren't the great thing, given that somebody will grab it anyway 70% of the time.
The weights could be correct, and the player's rebounding usage (the quantity of rebounds grabbed) would be what separates a skilled rebounder or a frontcourt from the rest.
It sounds logic, and I got to be convinced, not being another better logic outhere.

Of course there must be a punish by allowing your man grabs the rebound. There must be a (- oppOReb) for that player, and a (- oppDReb) to some offensive player every time the ball is not ORebounded. But, to reinvent the boxscore?, is better to reinvent the metric: adjusted plus minus!, or the easier points differential plus team adjusts.

Last edited by Harold Almonte on Fri Jun 01, 2007 7:00 pm; edited 1 time in total
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Harold Almonte



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PostPosted: Fri Jun 01, 2007 3:40 pm Post subject: Reply with quote
Quote:
Statman wrote:
... There are SO MANY other factors that are inherently tied into the stats ... that I believe deserve more "value" than their REAL value - like steals, blocks, and assists. ..

Steals and blocks stats don't have that great individual value per se, because is something a player does less than twice a game, and is not a secure thing they will end in a scoring made. But it's the inherently meaning of these stats what we must see. an above average stealer could be more than a gambler, is maybe an on the ball and on the pass hustler defender. Who knows how many assist does he avoid hustling every stealing attempt? the same the blocker (on the opponents FGA). Who knows how many missedFG does he force every blocking attempt, and how many shots does he force to be shot from long distance?
That is no boxscored, but is adjusted by some ratings.
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Mountain



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PostPosted: Thu May 29, 2008 10:07 pm Post subject: Reply with quote
Speaking on metrics... Nick, any update on NPV?


(D Sparks, the weights on page 4 may interest, including the assist weight.)
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NickS



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PostPosted: Fri May 30, 2008 1:23 pm Post subject: Reply with quote
Thanks for asking.

I have been swamped by work for the last couple of months, and have been meaning to look at the data for this year but just haven't had time.

But things are starting to slow down, and I may be able to look at this again and do 2007-08 rankings next week or the week after.

[greyberger]

Some of these recovered threads are pure gold. This one is great. You don't know what you've got 'til it's gone - I probably never would have read this if it weren't maliciously destroyed and then pulled out of the furnace.

In other words, sincere thanks to Crow!

[EvanZ]

Agreed. It made me think this morning someone should publish an APBR book.

[Crow]

Thanks greyberger. I've been focused on thread recovery so I haven't re-read all of these posts closely but I hope to. Picking up on ideas and data in the recovered thread or new ones is the goal.


Evan, I had thought about a book using material from the APBR forum (and beyond) for a few years. I thought about trying to systematize the threads by subject first, studying them hard and then trying to both boil them down and perk them up with new questions and new usages. The recovered threads here still offer a skeleton of what existed here before. Maybe more could be recovered if such a project were to pursued. The old yahoo site is another resource that should probably be recognized more, valued, protected, used.

Such a project probably could and ideally should get several hundred hours or a lot more. Most people would want to try to make some return on that investment. I can write decently or sometimes well if I work at it and re-write and refine. A better, more natural writer, more in tune with what will get read, understood, remembered and applied, and before that published and sold, might have a head up doing it, if any were interested enough to do it. A committee written book would be a possibility, but I and others haven't had too much luck in the past promoting collaborative research or action beyond the level of a specific thread.

While some fans might be interested in such a book (not sure how many), I'd say teams might also benefit from writing and reading books with a good deal of analytics (but not a monopoly). Maybe it would not be quite the same book as for a broad group of fans (though some fans would want and could handle an insider pitch and level), but it would be good to have a summary, a guide in addition to whatever ad hoc research is being done to distill and remember beliefs, principles and key findings and to promote understanding of them by the whole organization rather than just a few and to maximize the implementation effort to realize the team goals.

[NickS]

Some of these recovered threads are pure gold. This one is great. You don't know what you've got 'til it's gone - I probably never would have read this if it weren't maliciously destroyed and then pulled out of the furnace.

Thanks!

I still have those spreadsheets, and I keep thinking about going back to it and finishing up a couple of loose ends.

But I end up procrastinating because (a) it would take enough attention that it isn't something I can just pick up and do (though I could probably pull it together in a weekend if I wanted to) and (b) I never developed a definitive set of parameter weights, so it's more like a "rating system generator" than an actual rating system.

But there's a bunch of work there that I'm still quite proud of.

[DavidPerez]

This is a great statistical review about him!