## What's The Best Statistic For Evaluating Player Value?

Great discussion topic and research from blacknoiseNW.

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Friday the 13's Truehoop content included a link to the following writeup by Zenon Zygmont:

Underrated Statistics and Underrated Players

Zygmont addresses a Tyler Cowen response to this question: "Which is the most underrated statistic for judging the value of an NBA player?"

Cowen doesn't actually address the question specifically, but rather says that we overvalue high-producing players on bad teams, and undervalue players contributing to good teams. The simple premise is that good teams keep good players, and bad teams let good players go.

Zygmont posts this axiom as :

Player statistics are tracked to separate a player from his teammates. This is necessary because we can see which teams are successful. What decision-makers need to do is determine which players were responsible for the team outcomes observed.

For such a simple, straightforward thesis - there is endless debate. Zygmont goes on to use Wages of Wins (which invokes the Wins Produced composite metric) to weigh in on the discussion.

He produces two top 10 lists: one for best players on losing teams, another for least productive players on winning teams.

Martell Webster made the second list. Chris Paul made the first one (along with Bosh, etc.) Zygmont goes on to the following conclusion:

Again, stats are supposed to separate a player from his teammates. And when we make this separation, we do discover that good players can be found on persistent losers. In other words, team outcomes are really not an underrated stat.

This is all just a set up, of course - for what really interests me. What stat really is the best for evaluating player value?

All sorts of stats are available for us, from PPG to APG to RPG to eFG%, TS%, and +/- to the composite stats such as the well-known Player Efficiency Rating (PER), Net PER, Win Shares (WS), Wins Produced (WP), Wins Above Replacement Player (WARP), etc. Each of these composite stats distills measurable statistics into a single number than then can be used to compare players. Each system uses weights contributing measurables differently - and some have better data quality than others.

Ultimately, the relative utility of a composite stat is measured by its correlation to winning. Add up all the WP for the players on a team, and does it account for how many wins were actually produced by that team?

This is a tougher question to answer than first appears - but not impossible. More to the point - it is the critical question to answer if you want to use composite stats in discussion on this blog. I tend to use composite stats in discussion for simple convenience. Individual metrics are unwieldy and prone to personal bias (not in interpretation of the individual stat, such as TS% - but in the tendency to use these stats in isolation). No player can be defined by a single statistic. We can, however, start with a composite statistic and then drill down to isolate individual player weaknesses/strengths. In terms of efficient discussion in an online forum, I favor this approach.

After the jump, I link to another Wages of Wins (WP-focus) article specific to the Blazers and discuss its implications. I then compare the quantitative basis for the article (WP) with WS to see if they agree.

-- Jump --

On July 31, 2010 - Burzin Daruwala posted the article Can the Blazers Move from Promise to the Promise Land? as part of the Wages of Wins Journal 2009/2010 team reviews series.

Burzin focuses on the discrepancy between the Blazers' regular season performance and their playoff performance from the last two seasons - seeking to determine if there is any particular basis for optimism or pessimism.

He uses WP for his analysis - which is where I get really interested. Not to sell Burzin's analysis short - I think his topic is interesting - but injuries make any positive conclusions pretty difficult. However, the WP data he posts from Andres Alvarez's automated WP site says some very interesting things about the Blazers:

1. Pendergraph is one of the 8 above average players on the Blazers.
2. LMA is not (2009/2010 regular season)
3. Camby is really good
4. Oden can be great
5. Batum is on track to be very special
6. Miller and Bayless weren't that good in the playoffs
7. Bayless wasn't that good in the regular season
8. Bayless and Miller weren't that good in the post season
9. LMA is a below average Center
10. Cunningham stepped it up in the post season
11. Fernandez may have been better in 2010 than anyone gives him credit for
12. Fernandez was really good in 2009
13. Fernandez, along with Webster, Cunningham and Camby - was one of the four best playoff performers in 2010 (but still below average)
14. Webster is a below average player

This WP composite is very interesting - it supports the LMA and Bayless naysayers, supports the idea that Roy was the MVP over Miller, supports the Batum propaganda, and lets us know that picking up Camby for Outlaw/Blake was an even better trade than we may have suspected.

Picking one particularly polarizing player as an example (looking at you LMA) - how does WP compare to other available composits? Both stats say that LMA is one of the primary contributors to wins - but WP says he does it based on total production, rather than effective production. WS says LMA is an above average player (.145 WS48 vs. 0.074 WP48). Both WS48 and WP48 set average at 0.100.

So which one is right (or, at least better?)

The calculation method for WS is here:

The calculation method for WP is here:

The answer is - they arrive at the same conclusion when compounding individual player performances and correlating those to team actual wins.

WP has a average difference of 2.5 calculated wins produced versus actual wins. WS has an average absolute error of 2.74 wins - basically identical.

The difference is how individual players are credited with contributing to the actual wins. LMA gets more credit in the WS system, less in the WP system. Miller gets a lot more credit in the WP system, and a lot less in the WS system. Roy is the top player in both.

Conclusion? A little more work is needed to find out why one system favors a player more than another system. The overall results are good - but I don't have a firm handle on the specific weights that benefit particular players. However, I suspect that WP values blocked shots and assists higher than WS - which would at least partially account for the one system favoring LMA (WS) and the other favoring Miller (WP). LMA's low blocked shots totals don't bring him down as much in WS, and Miller's assists totals boost him in WP.