An effort to create a efficiency/volume public-friendly stat

[crsofa]

Hi everybody! This is Mario, from Spain, first post here! What I'm going to try to "sell" you here is a stat that tries to work as a trade-off between efficiency and volume, and does so in a "mainstream" way. I'm trying to find a way to introduce something that the non-analytic public can grasp, so is more informative than groundbreaking.

Usually, the points per possession, TS%, etc. leaderboards are hard to sell, because people can't put them in perspective and don't like them when they find a 6-8 points per game guys on top, and of course, nothing wrong against them, but I think it's more valuable if a guy scores 25, even if the efficiency is a little smaller.

So, enter here POSAP, Points Over Same-Usage Average Player? Possession? (first name that came to mind). The concept is quite simple, and tries to answer the questions, "How many points more would this player score over an average one, that season, given the same number of possessions?". The leader this season is Kevin Durant at 299 total POSAP, or 4.04 per game, which means that he scores 4.04 points more than someone shooting (and turning over) the ball as much as him, at the league average rates of "success". I really think that this can have some potential in the media to introduce who has been efficient, with something tangible ("He's giving you X! points per game more") and the "no-name" players mixed with the top dogs. here is this year leaderboard:



Even though it doesn't appear too much "efficiency" oriented, as the top scoring guys all appear there, some of them have negative POSAP's, here is the ranking for the top scorers



The formula is pretty simple, is just

Total Points-(League Average Points per Possession*Number of possessions used)



and can be kept really simple, but I made a couple of adjustments that made sense to me. I wanted it to just measure scoring and to be somewhat simple, because once again, I think of it as a "communication" tool, but I change two things in the typical FGA+0.44*FTA+TO part of the equation.

One, is the use of OReb in as EvanZ does in nbawowy.com, where he multiplies each field goal missed by 0.73 to account for the chance of the ball being rebounded. I use this, but instead of 0.73, I use as a coefficient the Season Total OReb/Season Total REB. This year is 73.4% so far, so it would be perfect, but slowly declines over time, and ends in 66% in 1980. Once again, it wouldn't be a problem to use a constant through the years, but I think is an easy adjustment to make.

And the second one, and probably the most "controversial" would be the use of turnovers. Using "Total turnovers" in the equation made the rating hard on the PG's and good-passing type of players, and I wasn't planning to give any credit for assists on this to make up for it. Yet, I will concede, that more passing and playmaking, brings more turnovers, so what I did was trying to separate "shooting" turnovers of "passing" TO. I just used a simple linear regression model, with total shooting possessions (FGA+0.44 FTA) and AST as the explanatory variables, and Total TO as the dependent variable. The coefficients for this year are [0.105810699673, 0.176459796916] and what I do is trying to find the Total Number of Estimated TO, and scale both contributions to the actual number. For example, for Durant, 1628 shots, 329 assists, 256 turnovers, using the coefficients on the shots and the assists we have 1628×0,105810699673+329×0,176459796916=230 estimated TO, 172 from "shooting", 58 from "passing". We scale them to get to 256 total, and Durant ends up with 191 "shooting" turnovers.

R² for this season is 0.91, and as you can see in the graphic, the estimated possessions total are pretty close to the actual ones



I know that is a cumbersome part, considering that every player has the same proportion of turnovers depending on the play, and I would be more than glad to receive more suggestions on how to "separate" them, but I think it works good enough keeping it that simple. Also, I wouldn't mind to not considerate turnovers, just shots(turning POSAP into... POSAS? ), or count them in full, acknowledging that some players are underestimated.

So that's it. Obviously, taking those "passing TO" out make the average possession better (from 1.04 or so points to 1.09 points this season) and this is taken into account, as the average is the global league one, counting only league-wide "shooting" turnovers.

The model can be extended (using a per position average instead of the whole League one, taking into account distance of shots and rebounding rates as a function of that...) but I prefer to have something easy. You only need to take care of three factors (rebounding rate and the two LR coefficients) for a whole season, and it's quite easy to explain to everyone.

This would be the year-by-year leader of POSAP



And this is the all-time (since 1978) Top 25



as for the bottom...



And I leave you the link to a spreadsheet with POSAP calculated for every player and every season from 19789 (first with turnovers) until now. I hope to receive feedback on whether you find the idea potentially interesting or if is there any other metric already doing this job.

[deepak]

Sounds like a good stat, thought may need a simpler name if you hope for it to become used in the media.

The issue I see is that a player who's high usage but just under league-average efficiency which will a lower rating than a player who's very low usage and similarly just under league-average efficiency. It doesn't seem right to me. Shouldn't a high usage player with a .53 TS% have a higher efficiency/volume rating than a very low usage player with a .53 TS%? You may consider using something less than league-average efficiency for the baseline.

[crsofa]

The name is "whatever"... xD This discussion reminds me of a very recently article in the Baseball community about using the replacement player level instead of the average player baseline (http://www.fangraphs.com/blogs/index.ph ... ent-level/) and is definitely something to consider.

What I like about the average in the NBA, is that is supposed to be at the line where you "win", .500, the last Playoff ticket level. Using the average then generates negative values: it emphasizes that you might be hurting the team taking shots from better players, whereas a "replacement level" is not as dramatic in the sense, that everyone looks good (maybe not good "enough"), except for the really terrible ones. But, maybe, somewhere in the middle...

Thank you for your input!

[DSMok1]

What I like about the average in the NBA, is that is supposed to be at the line where you "win", .500, the last Playoff ticket level. Using the average then generates negative values: it emphasizes that you might be hurting the team taking shots from better players, whereas a "replacement level" is not as dramatic in the sense, that everyone looks good (maybe not good "enough"), except for the really terrible ones. But, maybe, somewhere in the middle...

Thank you for your input!

A player with high usage and slightly below average TS% is a well above-average offensive player. This has been verified a number of times--the most simple way would be to regress onto a long-term APM dataset's offensive ratings.

In my own ASPM model, I use a term of the form USAGE*(TS% - Threshold), where threshold was found empirically and is below NBA average.

[Neil Paine]

The big trap this falls into is thinking that the efficiency level the league average player "would have" scored at is constant across players of all usage levels. That's just not going to be the case -- the mythical league-average player is going to find it much tougher to maintain a 53.5 TS% at Kobe Bryant's usage level vs. somebody like Steve Novak's. The way the formula is set up now, it assumes it's just as easy to hit that 53.5 at 30% usage as it is at 10%. You need to build in a trade-off where the "league average" goes up with an easier workload and down with a harder one.

[crsofa]

I updated the formula changing the "average" for a "replacement" level. With 38864 games in 36 seasons, I looked for a number that made every team 10 wins worse than their total (on average), so the Wins (I used the relationship 1 point=2.645 wins) add up to 29184 (75% of the played games/real wins).

That number, the one I multiplied the "League average points per scoring possession" is 0.888055. The figure is higher than the 0.83 that WARP uses to define replacement, which is the one I hoped to find, or at least get close to, and probably the translations of points to wins has something to do with it.

What I get changing the average threshold, is that the "replacement scoring player" is more or less Willie Green in 2007, 11.3 points per game, 45.8 TS%, 10.4 TOV% or Sly Williams in 1985, 12.3 points per game, 48 TS%, 15.2 TOV%.

Now, this correction makes higher usage players better than the more efficient/less used ones.

2013 leaderboard looks now as follows:



Now no player scoring less than 10 points per game is in the Top 25 (Novak falls from 11th to 51th, for example), and higher scoring players shoot up (Westbrook from 178th to 25th). I think that the trade-off efficiency/volume is now leaning towards volume, but then again, winning leans toward volume too.

Now the Top 25 scorers this season. Some of them had a negative value with respect to the average in the previous version, but now only Love, who played 18 games has it. But still, players like Rudy Gay, Monta Ellis and Jrue Holiday rate poorly.



Year-by-year leaderboard also changes a little bit, once again, higher usage guys goes up (Dana Barros is replaced by Robinson in 1995, Rice by Jordan in 97, Allen by LeBron in 2009...)



Top 25 now has Jordan ruling them all


And the worst seasons with 41 games played at least are here:


A replacement player, using the same number of possessions than 2007, 36.3 TS%, 19.8 TOV%, Speedy Claxton would have scored 6.9 points per game instead of 5.3

Now, no 20 points per game player has a negative POSRP value (the worse, with +0.7 per game is Antoine Walker in 2003). Do you think that this is correct quantitavely? That a 20 ppg player shooting 46.7 TS% with 13.4 TOV% still adds a (small) positive value over replacement when it comes to scoring? The most used scorer that rates under replacement level is 1996 Jason Kidd (16.6 ppg, 46.8 TS%, 18.6 TOV%, -0.2 points over same usage replacement player) so more or less, that's the place where the line is drawn now.

Comparing with the ASPM 2011 leaderboard, this is looking a little bit "generous" (Tyreke Evans, 17.8 ppg is just at the line with +0.1 points per game over replacement whereias in ASPM "Offense" rates -1.06, for example), but they are different...

And, what do you think about the "scoring turnovers" and "passing turnovers" separation? Any thought on that?

Thank you all for your input.

[crsofa]

The big trap this falls into is thinking that the efficiency level the league average player "would have" scored at is constant across players of all usage levels. That's just not going to be the case -- the mythical league-average player is going to find it much tougher to maintain a 53.5 TS% at Kobe Bryant's usage level vs. somebody like Steve Novak's. The way the formula is set up now, it assumes it's just as easy to hit that 53.5 at 30% usage as it is at 10%. You need to build in a trade-off where the "league average" goes up with an easier workload and down with a harder one.

The way is set up now does that. Getting a +1.0 POSAP is easier (needs a smaller TS%) scoring 30 points per game than 6.

For example, to get the same +1.0 POSAP, Player A, who scores 32.5 points in 30 possessions, needs an efficiency of 1.083 points por possession (League average 1.05). Player B, that uses 6 scoring possessions, needs to score (6*1.05+1) 7.3 points to have the same POSAP. Then Player B efficiency (7.3/6=1.217) needs to be much higher.

And now, with the new adjustment the gap is wider in total numbers. To have the same POSRP than a "Kobe" that uses 25 possessions at league average (let's say again, 1.05), which is 25*1.05-25*1.05*0.888=+2.9, a guy that only uses 5 possesions needs to score 2.9+1.05*0,888*5=7.6 points, 1.52 points per possession, way higher than league average (which nobody does, Novak is at 1.4, for example). If the 5 possessions guy scored at a league average rate, his POSRP would be 0.6, smaller than the 2.9.

Now, we can argue if that proportion is the right one, but the trade-off now is there when you shoot over the "replacement level".

[v-zero]

I would like to posit that the usage interaction only exists for wing scorers, and in general usage does not self-interact. I.e. guys who have high usage but play in the paint shouldn't get any kind of usage trade-off, but wing scorers should.

[EvanZ]

I would like to posit that the usage interaction only exists for wing scorers, and in general usage does not self-interact. I.e. guys who have high usage but play in the paint shouldn't get any kind of usage trade-off, but wing scorers should.

Ok. But Tyson Chandler.

[v-zero]

Ok. But Tyson Chandler.

...Only has 13% usage. Plus, he gets a lot of good looks around the rim/at the rim thanks to great floor spacing from wing scorers (obviously led my Melo), and he also gets a decent number of rebound scores thanks to those same wing scorers.

[crsofa]

I tried to find the value for the threshold in a different, not-related to "wins" manner. I just looked at the team-level POSRP, and find the threshold that produces the biggest correlation with the "raw" offensive rating (points per shooting possession as a team). The threshold is 0.8945 times average, really close to the 0.8881 using "wins over replacement", and even though it rises the "replacement level" slightly, barely changes anything. I like to see that two different methods yield a similar result, even both could be wrong, though

[deepak]

I would like to posit that the usage interaction only exists for wing scorers, and in general usage does not self-interact. I.e. guys who have high usage but play in the paint shouldn't get any kind of usage trade-off, but wing scorers should.

Ok. But Tyson Chandler.

Wilt Chamberlain also comes to mind. In 66-67, his FG% goes up to 68% when he dramatically reduces his shot attempts. In his last 2 seasons, when his shot attempts dramatically reduce for the second time in his career, his FG% again jumps to near 70%. I have to think its related.

[EvanZ]

Ok. But Tyson Chandler.

...Only has 13% usage. Plus, he gets a lot of good looks around the rim/at the rim thanks to great floor spacing from wing scorers (obviously led my Melo), and he also gets a decent number of rebound scores thanks to those same wing scorers.

Right, you seem to be contradicting your earlier point, or I'm not understanding you.

Isn't your point that big men do *not* have a USG/efficiency tradeoff?

[v-zero]

I suppose my reply was rather ham-fisted. I believe the actual tradeoff exists for wing scorers, and I believe that the benefactors of their work are interior players, as such as you are correctly pointing out you should be penalised for not being a wing scorer, just as you should be rewarded for being one. However, you don't need to directly penalise the bigs, you can merely reward the wing scorers and hence the bigs will be naturally penalised by distribution of credit.

[DSMok1]

I suppose my reply was rather ham-fisted. I believe the actual tradeoff exists for wing scorers, and I believe that the benefactors of their work are interior players, as such as you are correctly pointing out you should be penalised for not being a wing scorer, just as you should be rewarded for being one. However, you don't need to directly penalise the bigs, you can merely reward the wing scorers and hence the bigs will be naturally penalised by distribution of credit.

I disagree that there is a significant difference simply by position--each player has their own tradeoff level (Novak at 30% usage would be horrible, as would Chandler), but all 13% usage players are different and some could perhaps elevate their usage without as huge a hit in TS%.

I think the current 0.89 or so threshold is a good number on average. Good job!

There is also an interaction with AST%, but that would complicate matters (ASTs are sort of like usage in that there is an interaction with TS% & USG%).