The C/D Fallacy, Also Known As the Underrating of Richard Jefferson

In the world of American education, a “C” grade, ranging from 70-79.9%, is regarded as average.  Below that, and you fail; above that, and it’s a good grade.  In my experience, failure was relatively uncommon, but I was lucky to spend much of my time with smart kids.  When I was being brought up, “C’s” were bad because a “C” implied being on the verge of failure.  In the realm of the Wages of Wins and Wins Produced, being at all below average is a bad thing.  At this moment in time, playng more than a couple below-average players is somewhat inexcusable considering the sheer numbers of good players out there.  However, for that very reason, we (and I consider myself to be strongly in this camp) tend to underrate below-average players, ridiculing them as being useless.  This just is not true.

In his book Win Shares, one of Bill James’s concerns with Pete Palmer’s Linear Weights, an often-used metric at the time of the book’s publication, is that it assumed that a below-average player had negative value, and that, by extension, is worse than a player who never reached the big leagues.  While Wins Produced suffers from this to some degree-a player who is far from average as last season’s LeBron James in the opposite direction would produce -.158 Wins Per 48 Minutes-this is not the issue that I want to address.  (In fact, I have no proof in either direction; read my Mission Statement for details.)  The issue that I truly want to address is more in line with the Linear Weights issue; namely, it is our perception that any player who produces at a below-average rate is useless, rather than just any player who is a little more than one standard deviation away.  (See http://joshweil.blogspot.com for standard deviations information.)

Back to the analogy about grades, we Wins Produced people tend to view basketball players under this metric similarly to how Americans view our system of letter grades.  If we set a 75%, smack-dab in the middle of the “C” range, as being perfectly average, simple extrapolation implies that a 70%, the low end of the passing range, is a player with a WP48 of .070, assuming that a WP48 of .250 is equal to 100% and each percentage point is equal to .006 Wins Per 48 Minutes.  (Remember that the average player at each position according to Wins Produced…produces roughly .1 Wins every 48 minutes.)  As a result, a “D” would be between .010 and .070 WP48, and an “F” would be below .010.  Naturally, this completely disregards the Normal Distribution Curve, but this aligns with our perceptions more or less.  Therefore, in our view any player who produces less than .070 Wins Per 48 Minutes is not “passing” and should be quickly discarded.  And this might be feasible because of the great divide in the NBA between building the “best” team and the most productive team.  (I will again reference my article from Labor Day, “Good Can Be Bad: Production vs. Skill in the NBA.”)  However…

When the time comes that NBA teams “shape up” and start following the principles outlined in Wins Produced, creating a team with that sort of benchmark would be highly…ill-advised because of the extreme difficulty in finding replacements.  As James says in the introduction of Win Shares, “If you used Linear Weights…almost every group of players would have an average value near zero.”  The whole point of Win Shares is that below-average players have value.  By definition, only about half of the data points in any sample can be above average.  And even though my analogy has set the minimum passing rate at .070 Wins Per 48 Minutes, who really wants a “C”?  The answer is only the people who know that they cannot obtain anything higher.  And shooting for a “B” and “A” is entirely admirable, but in a situation such as the NBA, the numbers of “B’s” and “A’s” is finite, akin to a teacher who does grade on a curve.

Therefore, we have to accept that below-average players have value.  Not even improved evaluation of players from outside the current database can fix that because the average changes with every new set of data points.  Since any replacement level- or average-based system is going to fluctuate based on the strength of the sample size, nothing short of a highway robbery-level fudge factor can allow everyone to have average or above-average players.  It simply defies mathematics.  So we need to stop calling these players useless, myself most of all, and accept that, eventually if not now, those Wins Produced totals with a “0” in the tenths place are going to have mean something.  Thank you for reading, please comment, and please come back.

P.S. I mention Richard Jefferson because he has had below-average seasons in four of the last six campaigns, yet no season has dipped below a level of .050 wins.  He is often considered overpaid, and rightfully so, and washed-up, which seems to be a bit less accurate.  Interestingly, his boost from playing with the Spurs appears a good deal lower than most player’s.

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