How many guys in the NBA are above average players?

[payitforward]

Just looking at Wp48 list, the order doesn't look right to me. Chris Paul ahead of LeBron? Kirilenko, Marion & Leonard are top 10 players? Reggie Evans, Jason Kidd & Pablo Prigioni are in the top 20? Color me skeptical regarding Wp48.

There would seem to be two goals when designing an analytical like WP48:

1. Correlate with team wins. IOW, if for every team in the league you list total WP (Wins Produced) by adding up what all a team's players produced (using each players WP48 and number of minutes played) and then list all 30 teams from highest to lowest resulting number, your list should be exactly the same as a list of the 30 teams by their record.

2. Verify that your tool actually distributes WP48 accurately among the players on the teams. Being right w/ #1 already indicates that you are doing roughly the right thing, but you do need more than that.

In re: #1, Dave Berri claims that WP48 correlates to a level of 94%. Given that the data is all public and can be checked, and that he publishes in refereed academic journals of Economics, there's little reason to doubt this (Btw, do the same thing with PER, and it correlates at @ 80%. That's enough evidence for me to jettison PER as a way of explaining how an individual player's performance contributes to team wins.)

The validity of #2 is more complex, and other than saying that a lot of regression analysis done w/ stat software was behind the way WP assigns values (positive and negative) to things players do, I can't tell you much -- you might want to read his books (which are *not* heavy w/ academic jargon but are quite enjoyable instead).

One check is provided by player movement: the data shows that players tend to produce very similar numbers (and therefore very similar WP48s) as they move from team to team -- and #1 remains valid.

Now, if we assume his metric is valid -- i.e. that it's not possible to contravene its results and no better-correlating metric is proposed in its place -- then the surprises you see are not grounds to question the metric. They just register the fact that one's intuitive sense of what makes a guy help your team win is not a reliable guide to reality... like most "intuitions."

I certainly am not surprised to see Kawhi Leonard where he is on the list. Nor Faried. Nor Drummond. And I'm not surprised to see Chris Paul at the top of the heap. I've thought of him as the best player in the league for a long time.

Someone like Reggie Evans is high on the list because he has an overwhelming skill -- rebounding. Guys who rebound extraordinarily and don't miss a lot of shots (take few and shoot a high %) have huge impact on wins.

Think about Reggie this way: every 40 minutes he got over 18 boards (!) of which 5.3 were offensive boards. He only missed 2.8 shots in that same time. Lets assume the opponent grabbed every one of those misses. In that case, lets remove 2.8 offensive rebounds from his numbers and remove those missed shots too.

That leaves Reggie Evans shooting 100% and grabbing over 15 boards every 40 minutes. Starts to be obvious how he gets so high on the list, doesn't it?

[payitforward]

Re: someone like Reggie Evans being so high on the list, one more point:

Many people have criticized WP48 for over-valuing rebounding -- usually because they are skeptical about how important it makes a guy like Reggie look.

But... the thing is, WP48 -- with that exact value for rebounding -- correlates to 94% with team wins and losses. And all the values assigned to this and that were regressed to a fare-thee-well to optimize that correlation with team wins and losses.

Lower the value assigned to a rebound and e.g. make shooting more important, and the correlation goes down.

[penbeast0]

Just a small note . . . should "above average" include a player virtually identical to the "average" player? Or should it be something along the lines of a standard deviation over the average?

[payitforward]

Just a small note . . . should "above average" include a player virtually identical to the "average" player? Or should it be something along the lines of a standard deviation over the average?

I was working w/ average or above -- on the theory that someone at "average" might be penalized by a somewhat small sample.

[Nivek]

This is a problem with your analysis method, Nivek. It's a fact that bigs almost always put up better raw numbers than wings/points. That's why wp48 adjusts for position, and it enables one to rank across positions.

Ranked by wp48, there are 155 players average or above (at 500+ minutes), of whom 34 are Centers, 30, PFs, 37 SFs, 24 SGs, 30 pgs. So 64 bigs, 61 wings and 30 point guards. Pretty even.

He ought to get "pretty even" results -- he's adjusting for position specifically to even out the position distribution. If I added in a position adjustment, I'm sure I'd get very similar results.

I don't think this is a problem with my approach, though. I think the position adjustment actually obscures an important (and unsurprising) finding from Berri's research -- namely that big guys are more important because they're more productive. What Berri has done in Wins Produced is say -- X stat contributes Y amount to wins. What he does with the position adjustment is then say, well...depending on what position you play.

I had an email exchange with David on this subject a few years ago. He wasn't convinced either.

[Zonkerbl]

No reason not to put a position interaction dummy into your regression and see if the contribution towards wins of various statistics are statistically different depending on position.

Absolutely testable. The only difficulty is defining precisely what position everybody plays.

[payitforward]

This is a problem with your analysis method, Nivek. It's a fact that bigs almost always put up better raw numbers than wings/points. That's why wp48 adjusts for position, and it enables one to rank across positions.

Ranked by wp48, there are 155 players average or above (at 500+ minutes), of whom 34 are Centers, 30, PFs, 37 SFs, 24 SGs, 30 pgs. So 64 bigs, 61 wings and 30 point guards. Pretty even.

He ought to get "pretty even" results -- he's adjusting for position specifically to even out the position distribution. If I added in a position adjustment, I'm sure I'd get very similar results.

I don't think this is a problem with my approach, though. I think the position adjustment actually obscures an important (and unsurprising) finding from Berri's research -- namely that big guys are more important because they're more productive. What Berri has done in Wins Produced is say -- X stat contributes Y amount to wins. What he does with the position adjustment is then say, well...depending on what position you play.

I had an email exchange with David on this subject a few years ago. He wasn't convinced either.

I should have said "I see this as a problem..." My bad. And you are certainly correct that WP48 should produce a pretty even spread across positions -- otherwise, it's not delivering on its goal.

There's no question bigs put up better raw WS40 numbers than wings/point guards. In general they take higher % shots and grab way more rebounds. But, somehow one still wants a way to compare players across positions -- because a GM is often in a position where he's trading across positions and for the purpose of the draft as well.

In a way, the limitation of any such method is built into it -- i.e. the attempt to come up with a single number that conveys complex information and submits to a high to low ranking w/ great accuracy. Hence, the test is not "is this the right way to understand player performance?" Rather, it's a) is this one important and effective tool to use, and b) am I using the best (i.e. most accurate) single-number metric?

There is no question that Berri's tool is better than PER, Win Shares, and a host of other tools. From your description PPA produces equivalent correlation to wins/losses. One thing that makes it hard to judge is the number of "adjustments" you've mentioned (for quality of competition, etc.). I.e. how these are made. I'll be interested to learn more when you make more public (I understand why you don't at present!).

[Nivek]

I appreciate the thoughts. Just musing on position, I still wonder about Berri's use of a position adjustment. I have a lot of respect for his work (significantly more than many (most?) of the stat goobers I interact with regularly), but I'm unconvinced that adjusting for "equality" of positions should be part of a metric. There's an underlying assumption in there that positions are created equal.

That's before getting to zonker's point that deciding what position guys play isn't an easy task.

Anyway, don't have much time for this now. I should be working on a board report.

[Zonkerbl]

Erm, regarding "somehow one still wants a way to compare players across positions -- because a GM is often in a position where he's trading across positions and for the purpose of the draft as well."

Uh, what's the problem? The win share does this.

It also finds that bigs are more productive than wings. Why is this a bad thing?

I guess the intuition is that there are certain statistics that are more relevant for some positions than others. Does a rebound from the guard position count less than a rebound from your bigs? Could a high rebound number actually indicate that your guard is not getting out and running enough, and be a bad thing? Is a high number of assists from a big a bad thing, because it's showing an unwillingness to shoot?

I suppose if I had the right database I'd do the following regression:

Dependent variable:
Outcome (win or loss) (byvariate, so you have to use the probit model)

Independent variables:
Statistics recorded by PGs: Points, assists, rebounds, turnovers, steals, blocks
Statistics recorded by SGs: Points, assists, rebounds, turnovers, steals, blocks
Statistics recorded by SFs: Points, assists, rebounds, turnovers, steals, blocks
Statistics recorded by PFs: Points, assists, rebounds, turnovers, steals, blocks
Statistics recorded by Cs: Points, assists, rebounds, turnovers, steals, blocks
(have to be careful here so you don't have an identification problem, so like instead of Statistics recorded by Cs you have totals. Otherwise you get a non-invertible matrix)

Also you want to somehow account for good defense that is not captured in the recorded statistics. Maybe add some miscellaneous, kitchen-sink type regressors:
Pace

Total points allowed

Points differential.

Problem is, those things can't be assigned to a particular player. But it would provide you a more accurate idea of the contribution of actually recorded statistics to wins.

[nate33]

I've been leery of doing position adjustments (it's one of the issues I have with Berri's Wins Produced) because I think the adjustment obscures valuable information -- namely the (unsurprising) reality that bigs are more productive and more valuable.

But are they? Yes, I imagine it's true that big men tabulate more box score stats, but does that necessarily make them more productive? Okafor posts better box score stats than Martell Webster, but perhaps Webster does some intangible things from the SF spot (like stretch the floor with his quick release and deadly accuracy) that actually help the team more than Okafor.

I'm not saying I have all the answers. I'm just a little hesitant to agree with the statement that bigs as a general rule are more productive than wings and guards.

[Nivek]

I've been leery of doing position adjustments (it's one of the issues I have with Berri's Wins Produced) because I think the adjustment obscures valuable information -- namely the (unsurprising) reality that bigs are more productive and more valuable.

But are they? Yes, I imagine it's true that big men tabulate more box score stats, but does that necessarily make them more productive? Okafor posts better box score stats than Martell Webster, but perhaps Webster does some intangible things from the SF spot (like stretch the floor with his quick release and deadly accuracy) that actually help the team more than Okafor.

I'm not saying I have all the answers. I'm just a little hesitant to agree with the statement that bigs as a general rule are more productive than wings and guards.

In my research, yes. Bigs typically produce more of those stats that correlate with winning -- hence, more productive and more valuable.

And, stretching the floor is not an intangible. Its value gets reflected in the numbers.

[payitforward]

I've been leery of doing position adjustments (it's one of the issues I have with Berri's Wins Produced) because I think the adjustment obscures valuable information -- namely the (unsurprising) reality that bigs are more productive and more valuable.

But are they? Yes, I imagine it's true that big men tabulate more box score stats, but does that necessarily make them more productive? ...

In my research, yes. Bigs typically produce more of those stats that correlate with winning -- hence, more productive and more valuable....

And yet we couldn't put a team on the floor that was all and only bigs, even though that would be the "common sense" conclusion from the numbers.

This is one of those real-world "contradictions" that point to the limits of the help you get from numbers. As well, it's one of the facts that make you want to incorporate position adjustment.

It doesn't make numbers less valuable; it just points to limits in the way they are valuable.

[nate33]

And, stretching the floor is not an intangible. Its value gets reflected in the numbers.

Shooting percentages get reflected in the numbers, but the only way "floor stretching" gets reflected in the numbers would be on/off data, and player pairs data, which is noisy.

Webster doesn't have to touch the ball on a possession to force the defense to guard him. He gets no box score credit, but Wall may get an easy layup due to the late defensive rotation.

[Zonkerbl]

But are they? Yes, I imagine it's true that big men tabulate more box score stats, but does that necessarily make them more productive? ...

In my research, yes. Bigs typically produce more of those stats that correlate with winning -- hence, more productive and more valuable....

And yet we couldn't put a team on the floor that was all and only bigs, even though that would be the "common sense" conclusion from the numbers.

This is one of those real-world "contradictions" that point to the limits of the help you get from numbers. As well, it's one of the facts that make you want to incorporate position adjustment.

It doesn't make numbers less valuable; it just points to limits in the way they are valuable.

The regression I specify above would evaluate the contribution of statistics from various positions from the reference point of a team with "average" players at the other four positions. It wouldn't be able to address the question of whether you could actually do better with five centers.

That reminds me, you could add in measurables from the combine as explanatory (independent) variables in the regression and see if they have any predictive power at all. I bet they do.

[Zonkerbl]

I've been leery of doing position adjustments (it's one of the issues I have with Berri's Wins Produced) because I think the adjustment obscures valuable information -- namely the (unsurprising) reality that bigs are more productive and more valuable.

But are they? Yes, I imagine it's true that big men tabulate more box score stats, but does that necessarily make them more productive? Okafor posts better box score stats than Martell Webster, but perhaps Webster does some intangible things from the SF spot (like stretch the floor with his quick release and deadly accuracy) that actually help the team more than Okafor.

I'm not saying I have all the answers. I'm just a little hesitant to agree with the statement that bigs as a general rule are more productive than wings and guards.

In my research, yes. Bigs typically produce more of those stats that correlate with winning -- hence, more productive and more valuable.

And, stretching the floor is not an intangible. Its value gets reflected in the numbers.

Super easy. Add 3pt% (or instead of putting in "points" as a regressor, put in "points scored from three, points scored from two, points scored from FT line) as an independent variable in the above regression.

Actually, the main work involved is collecting the data (and putting it in a format so it can be analyzed, like excel or SAS or SPSS or Stata). If someone can point me to a database where all this has been compiled I could run the regression pretty easily.

[Nivek]

Your best bet is probably basketball-reference.com. Player stats are pretty easy to download in CSV format (and other formats too). They include other useful info in their file like position and age. Not sure of their method for deciding what position a guy plays.

[penbeast0]

But are they? Yes, I imagine it's true that big men tabulate more box score stats, but does that necessarily make them more productive? ...

In my research, yes. Bigs typically produce more of those stats that correlate with winning -- hence, more productive and more valuable....

And yet we couldn't put a team on the floor that was all and only bigs, even though that would be the "common sense" conclusion from the numbers.

This is one of those real-world "contradictions" that point to the limits of the help you get from numbers. As well, it's one of the facts that make you want to incorporate position adjustment.

It doesn't make numbers less valuable; it just points to limits in the way they are valuable.

The reason you can't make up a team with LeBron, Love, and Kevin Garnett on the point/wings has nothing to do with offense, they'd be fine. It's the defensive end that would create issues and the fact that everyone drafts/values bigs more highly so they are relatively more expensive.

[Zonkerbl]

Your best bet is probably basketball-reference.com. Player stats are pretty easy to download in CSV format (and other formats too). They include other useful info in their file like position and age. Not sure of their method for deciding what position a guy plays.

Yeah, that's not gonna work. You can only download the data in little bits and pieces. In fact they have a big disclaimer that they are not in the business of handing out large datasets for free.

I would need stats like I described above for each player, for each game.