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I just finished reading Wages of Wins by David Berri, Martin Schmidt, and Stacey Brook. Being honest, I’m generally pretty biased against traditional economists doing performance analysis. Using economic theory, I can say that freelance writers will usually have greater incentive to do groundbreaking work, since a) most econ professors get a regular paycheck regardless of their research, and b) research on performance analysis in sports will rarely get you tenure.

But there was one concept in the book that got me thinking. The writers discuss the law of diminishing returns, and its role in analyzing individual player stats in the NBA. They used the mid-90s Bulls as an example. According to their metrics (which aren’t as well thought out as the ones Dean Oliver came up with in Basketball on Paper), Michael Jordan was worth almost 25 wins in 1992-93 to a Bulls team that won 57 games. The next year, while MJ was off trying to be Reggie Abercrombie, Chicago won 55 games. How could this be possible?

The point the authors were making is this: instead of great players like Jordan making everyone around them better, they actually lower everyone else’s production. This isn’t such a difficult concept. It doesn’t make the players “worse,” mind you, but it will limit their production in terms of points, rebounds, etc.

If you put the twelve best players in the NBA on the same team, maybe they could win 75 or more games in a season. Who knows, let’s go crazy and say they could win 82. Now let’s say you added up the “Wins Produced” for the top twelve players in the league in 2006-07 (the only pair of teammates were Shawn Marion and Steve Nash). This adds up to 229 wins, needless to say a very impressive season. Even if we just use the top twelves’ average wins produced per 48 minutes, multiply it by 5 (the number of players on the court) and then 82 (the number of games in a season), we still come out with 135 expected wins.

The point, obviously, is that there are diminishing returns after you already have a certain amount of great players. But there’s another aspect of this: if the stat gives you 135 expected wins in an 82 game regular season, you’re probably using the wrong stat.

Now how does this apply to baseball? Offensive stats work pretty well within this realm. Only in really extreme cases (i.e. Barry Bonds 2004) could you find a way to make the expected number for of wins added for a hypothetical team go over 162 (based on VORP, or any other measure that only takes into account one side of the run equation).

But with fielding this is still a major issue, and I think this is the biggest problem with most defensive stats out there. Baseball Prospectus’s DT translations have Andruw Jones at 43 runs above replacement in centerfield for the Braves in 1998, and Omar Vizquel at 36 runs above replacement at short for Cleveland. Had they been playing on the same team in ‘98, can we really say that the two of them combined would have been 79 runs above replacement? What if you add up all the other top defensive players’ totals from that year, or any other year really?

This is a problem that needs to be solved. Yes, there has been a lot of progress made on defensive stats. And it’s great that more and more systems agree on who is good and who isn’t. But how can we really evaluate players without knowing how much their contribution on defense, good or bad, is really worth? And we need to stop rewarding and/0r penalizing players based on who their teammates are.

One key is more regression to the mean. I’m picking on the DT cards only because they’re easily available. But there are many extreme examples that hurt their credibility . They have Cal Ripken at 24 fielding runs above average in 1986. The next three seasons: -7, -5, +22. This just doesn’t work.

We’re not sure how the DT’s are calculated, but I’m willing to bet they’re similar in theory to defensive Win Shares: find out how the team as a whole did, and break that performance down into components after making adjustments. I have a hard time believing there’s a great deal of regression to the mean, if any. This leads to flukish one-year performances and generally unreliable year-to-year results.

Again, I’m just using the DT’s as an example. Most defensive systems have this problem, and until it is fixed, we’re left guessing how much each player is really worth in the field.

Feedback? Write a comment, or e-mail the author at shawn(AT)squawkingbaseball.com

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  1. on October 16th at 05:17 pm
    Omar Vizquel said:

    I totally agree. I think the system is flawed. When you give the example with Vizquel and Jones it really brings it into question. Thanks for all the hard work!

  2. on October 16th at 11:05 pm
    David said:

    Outstanding site, found you through Deadspin. The inside numbers and analysis of baseball (and all other sports) is absolutely fascinating. Keep up the great work.

  3. on October 17th at 01:08 am
    Griffin Caprio said:

    You kind of miss the point with regards to diminishing returns and win score. You can’t simply take 12 random players, put them on the same team and add their win scores. Win score isn’t a simple measurement, it’s a calculation of efficiency produced within a certain situation, in this case a given team.

    If you change the entire makeup of a team, then you’re changing the situation that produced the original win score. In fact, given your point that you can’t have all of those all stars put up their normal win scores within the limit of an 82 game season proves the law of diminishing returns. Despite all of the players being all stars, sacrifices will have to be made because there is only one ball.

    - Griffin

  4. on October 17th at 02:16 am
    dbg said:

    While I was reading your thoughts on Wins Produced I kept thinking “who cares?”. I mean you’re never going to have that much talent on an NBA team. The real test for that stat is if it does its job in the real world. I’m not saying it does or doesn’t cause I don’t know. But, if you do find that a team is projected to win 200 games in an 82 game season, I think you can safely say they’re gonna be AWESOME!!!!

  5. on October 17th at 04:28 am
    Flint said:

    I think you misunderstand the argument Berri is making, as Griffin said. The paragraph staring “the point, obviously…” contradicts itself. What you say in the second sentence makes no sense given what you acknowledged in the first sentence, i.e. that the law of diminishing returns applies. That is not a problem with WP. .