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3268My version of WINVAL (my analysis of it)

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  • dan_t_rosenbaum
    Feb 24, 2004
      There are several issues to consider about these adjusted plus/minus
      statistics, but one I would hope not to spend forever on is whether
      or not I am exactly replicating what Winston and Sagarin are doing.
      I am sure that I am not, but other than the fact that they have more
      years of data at their disposal (which in this case is an important
      difference), I highly doubt what they are doing is using the data in
      a significantly more efficient manner than I am. What they are
      doing is surely different (and the results are probably quite a bit
      different due to the noisiness of this methodology), but the general
      theme of my work has to be very close to theirs.

      So let me talk about a few issues related to these adjusted
      plus/minus statistics.

      1. The single most important feature of these results is how noisy
      the estimates are. Relative to my Tendex-like index, the standard
      errors for these adjusted plus/minus statistics are 3.5 to 5.5 times
      larger. What that means is that the precision in these adjusted
      plus/minus statistics in a whole season is about equivalent to what
      you get with a Tendex-like index in three to seven games. That is
      why DeanO says in his book that they don't pass the laugh test;
      these estimates are really, really noisy.

      I should add, however, that another season or two worth of data will
      help more than adding an equivalent number of games for a Tendex-
      like index, because a new season will bring lots of new player
      combinations, which will help break up the very strong
      multicollinearity that sharply reduces the variation that can
      identify the value of these hundreds of players. There are issues
      in making use of more than one year of this type of data, but I
      suspect it will help things a lot. But at the end of the day, I
      suspect it will still be a lot more noisy than something like a
      Tendex index.

      2. So is the conclusion that something like WINVAL is completely
      useless? No. The great advantage of this approach is that IMO it
      is the least biased (in the strict statistical sense) methodology of
      gauging player value of any methodology that I have seen proposed.
      Unlike other methods that we know leave important features of player
      value, such as defense and a lot of non-assist passing, this method
      in theory captures much closer to everything that is relevant.
      (There are still things it misses, but IMO those things are second
      order relative to the things other methods miss.)

      That said, being the least biased is only part of the equation. The
      other part is how precisely can we estimate player value with this
      methodology? What is the variance of the estimates? Well, the
      upshot is that this methodology is tremendously noisy relative to
      other methods, which makes it very hard to use.

      For example, using 2002-03 data there are only about 50 players that
      using this method, we can say with the usual level of certainty used
      in statistics (a 5% rejection region) that those players are
      significantly better than the average replacement player (players
      who played less than 513 minutes). On the other hand, using my
      Tendex-like index we can say that about nearly 200 players.

      3. So how can these adjusted plus/minus statistics be used, given
      how noisy they are? With more data they might become precise enough
      to be used on their own, but I think the best way to use them is how
      I used them in the regressions at the very end of my link.

      http://www.uncg.edu/bae/people/rosenbaum/NBA/wv1.lst~

      Here I regressed these adjusted plus/minus statistics onto per 40
      minute statistics. The coefficients on these per 40 minute
      statistics are estimates of the weights that we should use in
      indexes that weight various statistics. Now I am not arguing that
      the linear weights should be pulled straight from these regressions,
      but I think we can learn some things from these regressions.

      a. The first lesson seems to be that specifications with attempts
      rather than misses seem to fit better. The second specification
      which uses two point field goal attempts, three point attempts, and
      free throw attempts has a higher R-squared that the first
      specification, even though it uses one less explanatory variable.
      (Perhaps David Berri was right about that.)

      b. It appears that rebounds have much less value than usually
      assumed (especially relative to what Berri assumed) and that steals
      and blocks are much more valuable. Perhaps these defensive
      statistics are highly correlated with other unmeasured defensive
      qualities.

      Also, even after accounting for points scored, it appears that three
      point misses are far less costly than two point misses. Perhaps
      having three point shooters on the floor spreads the floor,
      resulting in fewer turnovers and higher field goal percentages for
      other players, i.e. things that are not picked up in the three point
      players' own statistics.

      Note that I tested whether the cost of a two pointer was the same as
      that of a three pointer and the p-value for the test was 0.0024,
      suggesting that three point attempts for whatever reason are less
      costly than two points, even after accounting for the points scored
      on those attempts.

      Well, that is probably enough for now, since I suspect other things
      will come up later. I hope this was interesting.

      Best wishes,
      Dan
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