Net Point Value (NickS, 2007)
Posted: Thu Apr 28, 2011 6:25 pm
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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
Joined: 30 Dec 2004
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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:
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(1) To be a simple linear weight that would summarize a player's total box score contributions.
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(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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NickS
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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.
NickS
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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.
Code:
(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
Joined: 30 Dec 2004
Posts: 384
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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Location: Washington, DC
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
Joined: 30 Dec 2004
Posts: 384
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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Posts: 384
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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Posts: 384
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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NickS
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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
Joined: 20 Aug 2005
Posts: 807
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
Joined: 30 Dec 2004
Posts: 384
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.