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November 25, 2009, 07:58 PM ET
The Improbability of Chris Duhon

by Kevin Pelton

I must admit being fascinated by how poorly Chris Duhon is shooting the basketball this season, a topic discussed in last week’s discussion of the Knicks. While I feel terrible for Duhon and Knicks fans who have had to suffer through his constant misfiring … I can’t look away.

After last night’s 2-for-9 outing at Los Angeles, Duhon is shooting 28.3 percent on two-point attempts (15-of-53) and an even 20.0 percent from three-point range (11-of-55). While he is not Ray Allen, Duhon has not shot nearly so poorly over the course of his career.

I wanted to look at how unlikely Duhon’s innacuracy truly is. For now, let’s consider Duhon’s SCHOENE projection his “true” shooting ability on twos (44.4 percent) and threes (39.5 percent). Though the latter might have been a tad optimistic–Duhon made a career-high 39.1 percent of his threes last year–it’s a reasonable starting point.

Duhon’s observed two-point shooting is a whopping 2.4 standard deviations below his “true” rate. Using the normal distribution, there’s about a 0.9 percent chance a player as good as we believed Duhon to be entering the season would shoot so poorly (or worse) on twos. His three-point inaccuracy is even more improbable; Duhon is a full 3.0 standard deviations below his true three-point percentage. The chances of observing such poor shooting beyond the arc? 0.16 percent. (Not 16 percent. 0.16 percent.)

Another way to look at it is the performance of past players.  Shooting 20 percent on threes is not uncommon, but Duhon’s misfiring inside the arc has relatively little recent precedent. Since the advent of the three-point line, just 14 players have shot worse than 28.3 percent on twos with at least 50 two-point attempts over the course of the season. The group doesn’t get much larger (32) if we look at players shooting below 30 percent.

Naturally, a large part of the reason this doesn’t happen very often is that while players might shoot so poorly for short stretches, they come back to normal over the course of the season. That’s really my point. While Duhon has been so bad early in 2009-10 we might have to adjust our perception of his underlying talent, the reality is there’s no way he continues to shoot so poorly.

Looking at those past examples does reveal some NBA regulars who, for one reason or another, went through a terrible slump shooting two-pointers in limited playing time (mostly early in their career) that wasn’t indicative of their actual ability. Some of the players on the list: Rafer Alston (29.6 percent in 1999-00; career 40.9 percent), Steve Blake (26.9 percent in 2004-05; career 42.3 percent), DeSagana Diop (29.9 percent in 2004-05; career 43.3 percent) and Kyle Korver (28.3 percent in 2003-04; career 42.2 percent).

(Thanks to Basketball-Reference.com’s Justin Kubatko for helping with the numbers.)

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