Stephen Curry is a great shooter, but he ain't *that* great

Don't worry, I've got mad love for ya, Steph.

I know you're already foaming at the mouth after reading the title, but that's the only way I thought I could you lure you in for what follows. Here's a more appropriate title, but one you might have never thought twice about clicking on:

A method for predicting FG% in basketball based on small number of shots

So here's a list of the top 20 players sorted by FG% on long twos (I'm defining a "long two" as 18-23 ft). The data was acquired using the PlayIndex+ tool over at basketball-reference. Here is the exact query, if you want to see the data for yourself.

Top 20 Players by Maximum-Likelihood Estimate (MLE)

MLE is simply a statistics shorthand for "taking the straight mean" (actually, it means a lot more than that, but for our purposes, I think that's good enough).

PLAYER TEAM MLE FGA
Stephen Curry GSW 68.30% 63
Steve Novak NYK 59.50% 37
Kurt Thomas POR 53.10% 64
Quincy Pondexter MEM 52.90% 34
Joakim Noah CHI 52.00% 25
Daequan Cook OKC 51.70% 29
Boris Diaw TOT 51.20% 41
Brandon Rush GSW 50.90% 57
Jonas Jerebko DET 50.80% 61
Kevin Garnett BOS 50.20% 237
Kris Humphries NJN 50.00% 36
Yi Jianlian DAL 50.00% 32
Chris Paul LAC 49.60% 127
Michael Beasley MIN 49.30% 69
Tim Duncan SAS 49.10% 114
Kevin Durant OKC 48.80% 121
Brandon Bass BOS 48.70% 119
Anthony Parker CLE 48.60% 70
Dirk Nowitzki DAL 48.60% 175
Charles Jenkins GSW 48.00% 127

The problem we face here is that the sample sizes vary so much between players and some are really small. Is Yi Jianlian really a 50% shooter from 18-23 ft? (If he is, somebody should probably sign him already.) What about Kris Humphries? Maybe not. Conversely, Dirk shot 48.6% on 175 FGA from this range, which is a larger sample size and about where we might expect him to be. Overall, the pool of 248 players with >25 FGA from 18-23 ft had a mean FG% of roughly 38%.

What can help us "shrink" these estimates closer to the mean is taking into account the variation between players in both FG% and FGA (i.e. sample size). One way to do this is to use a multi-level model (the other is a fully Bayesian approach, which Gelman says is roughly equivalent when there are a large number of "groups" such as this). If you're interested in this type of model, I highly recommend Gelman's "ARM" book.

In R, creating the model basically takes one step:

twos.mlm=lmer(cbind(FGM,FGA-FGM)~(1|PLAYER),family=binomial(),data=long_twos)

From that, I get a list of coefficients (called random effects) which can then be converted to our new (hopefully) more predictive FG%'s.

Before I show the new list of players and their estimates, take a look at how the spread of the histogram of FG%'s shrinks when going from the MLE to the multi-level model:


Now here's the top 50 according to their multi-level estimates:

Top 50 18-23 ft FG%

The column MULTI is the multi-level estimate.

PLAYER TEAM MLE MULTI FGA
Stephen Curry GSW 68.30% 46.9% 63
Kevin Garnett BOS 50.20% 45.5% 237
Dirk Nowitzki DAL 48.60% 43.7% 175
Chris Paul LAC 49.60% 43.3% 127
Kevin Durant OKC 48.80% 42.8% 121
Tim Duncan SAS 49.10% 42.8% 114
Brandon Bass BOS 48.70% 42.8% 119
Jose Calderon TOR 47.30% 42.6% 148
Charles Jenkins GSW 48.00% 42.6% 127
Kurt Thomas POR 53.10% 42.6% 64
Pau Gasol LAL 47.30% 42.3% 129
Steve Novak NYK 59.50% 42.3% 37
LaMarcus Aldridge POR 45.20% 42.2% 208
Drew Gooden MIL 45.60% 41.9% 158
Sebastian Telfair PHO 47.50% 41.9% 101
Jonas Jerebko DET 50.80% 41.8% 61
Anthony Morrow NJN 46.80% 41.7% 109
Steve Nash PHO 47.40% 41.7% 95
Michael Beasley MIN 49.30% 41.6% 69
Brandon Rush GSW 50.90% 41.6% 57
Jamal Crawford POR 45.10% 41.5% 144
Anthony Parker CLE 48.60% 41.4% 70
Ben Gordon DET 44.30% 41.3% 158
Nick Young TOT 44.20% 41.3% 163
Darren Collison IND 46.20% 41.1% 91
Chris Bosh MIA 44.10% 41.1% 152
Arron Afflalo DEN 47.20% 41.1% 72
Klay Thompson GSW 43.70% 41.0% 158
Boris Diaw TOT 51.20% 40.9% 41
David West IND 45.60% 40.9% 90
Quincy Pondexter MEM 52.90% 40.9% 34
Russell Westbrook OKC 43.50% 40.8% 147
D.J. White CHA 45.60% 40.7% 79
Marreese Speights MEM 44.70% 40.7% 94
Carlos Boozer CHI 45.70% 40.6% 70
David Lee GSW 44.40% 40.5% 90
Jarrett Jack NOH 44.40% 40.5% 90
Kris Humphries NJN 50.00% 40.4% 36
Steve Blake LAL 47.10% 40.4% 51
Daequan Cook OKC 51.70% 40.4% 29
Jared Dudley PHO 43.10% 40.2% 109
Yi Jianlian DAL 50.00% 40.2% 32
Jason Smith NOH 43.00% 40.2% 107
DeMarcus Cousins SAC 42.20% 40.2% 147
Joakim Noah CHI 52.00% 40.1% 25
Spencer Hawes PHI 46.00% 40.1% 50
Grant Hill PHO 43.60% 40.0% 78
Jason Terry DAL 42.70% 39.9% 96
Nate Robinson GSW 43.70% 39.9% 71
Ramon Sessions TOT 43.90% 39.9% 66

Now it's starting to make more sense. Here's the bottom 50:

Bottom 50

PLAYER TEAM MLE MULTI FGA
Glen Davis ORL 24.50% 33.3% 94
John Wall WAS 29.50% 33.7% 183
Corey Maggette CHA 26.50% 33.9% 98
Dorell Wright GSW 19.60% 34.2% 46
Andray Blatche WAS 24.20% 34.3% 66
Paul George IND 22.80% 34.3% 57
Markieff Morris PHO 22.20% 34.3% 54
Ivan Johnson ATL 20.80% 34.4% 48
Daniel Gibson CLE 21.30% 34.5% 47
Antawn Jamison CLE 31.30% 34.8% 166
DeMar DeRozan TOR 32.20% 34.9% 205
Carlos Delfino MIL 24.00% 35.0% 50
Paul Pierce BOS 28.90% 35.0% 90
Josh Howard UTA 28.80% 35.2% 80
John Lucas CHI 28.60% 35.2% 77
Byron Mullens CHA 32.80% 35.3% 204
Austin Daye DET 25.00% 35.3% 48
Leandro Barbosa TOT 30.80% 35.4% 104
Tracy McGrady ATL 29.00% 35.5% 69
C.J. Watson CHI 30.00% 35.6% 80
Metta World Peace LAL 22.90% 35.6% 35
Chauncey Billups LAC 20.70% 35.7% 29
Jeremy Pargo MEM 20.70% 35.7% 29
Marcus Camby TOT 25.60% 35.7% 43
Danilo Gallinari DEN 29.40% 35.7% 68
C.J. Miles UTA 29.20% 35.7% 65
Lamar Odom DAL 23.50% 35.8% 34
James Johnson TOR 30.90% 35.8% 81
Luc Mbah a Moute MIL 20.00% 35.9% 25
Andrew Goudelock LAL 24.20% 35.9% 33
Andre Iguodala PHI 32.80% 35.9% 122
J.J. Hickson TOT 28.30% 36.1% 46
Brandon Knight DET 32.30% 36.1% 93
Wesley Johnson MIN 32.30% 36.1% 93
Jodie Meeks PHI 25.00% 36.1% 32
Norris Cole MIA 32.20% 36.1% 90
Derrick Brown CHA 29.60% 36.1% 54
Monta Ellis TOT 34.40% 36.2% 195
Dominic McGuire GSW 27.50% 36.2% 40
Tyreke Evans SAC 33.30% 36.2% 120
Tyler Hansbrough IND 32.10% 36.3% 78
Travis Outlaw SAC 28.20% 36.4% 39
Courtney Lee HOU 32.50% 36.4% 83
Earl Clark ORL 27.80% 36.4% 36
Zach Randolph MEM 24.00% 36.4% 25
Ray Allen BOS 31.70% 36.5% 63
Danny Granger IND 33.70% 36.6% 95
Jordan Farmar NJN 30.20% 36.6% 43
Josh Smith ATL 35.80% 36.6% 316
Marvin Williams ATL 33.70% 36.6% 92

Conclusions

Now, do we have any evidence that Stephen Curry is closer to a 46.9% shooter from 18-23 ft rather than truly being a 68.3% shooter according to the 63 shots he took last year? Sure we do! Just go back to 2010-11 when he shot 49.1% on 214 FGA (still great!). Or his rookie season when he shot 47% on 232 FGA (also great!). Now that 46.9% makes a lot more sense, right? (By the way, the title of this post should make some more sense right about now, too.) Stephen Curry is a great shooter, he just ain't *that* great.

Just as Stephen Curry probably isn't a near-70% shooter on long 2's, Glen Davis is probably better than a 25% player on those shots. Indeed, in 2011, Davis shot 35.8% on 226 FGA. And he was a 38.9% in 2010, but on only 36 FGA. You know, it's important to point out that just because a player takes a small number of attempts doesn't necessarily mean he'll be at the top or bottom of lists like this. Sometimes the player will "randomly" fall in the middle, too.

So, hopefully, this made some sense to you. Next time you see an analyst talking about how a player lead the league with an astronomically high FG% on 12 shots of a certain type (say in the 4th quarter of games on the road on Sundays), think about this post. Heck, maybe e-mail the guy a link to it.

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