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February 6, 2009, 07:00 PM ET
Game-Winning Shots By the Numbers

by Kevin Pelton

One of the most interesting studies 82games.com’s Roland Beech has done using his exhaustive play-by-play database is one looking at player performance on game-winning, game-tying or go-ahead shots. Beech has updated his numbers, which now show LeBron James having made the most such shots dating back to 2003-04.

A couple of years ago, when this research first surfaced, I offered the following response on 82games.com:

Basically, looking at even nearly three years worth of data on game-winning shot attempts and trying to draw conclusions from them is like flipping two coins 20 times and declaring the one that lands heads more frequently to be more likely to land on heads. You just can’t tell from such a small sample size. And if three years of data is relatively meaningless, can you imagine how little one shot tells us about a player’s true ability?

Well, now we’re up to nearly six years’ worth of data, but guess what? The conclusion is still largely the same. Statistically, we can use a player’s shooting percentage and shot attempts to calculate standard deviations and construct a confidence interval for their “true” shooting percentage–not the APBRmetrics stat measuring efficiency, but the actual percentage of shots a player would make if they had an infinite number of attempts. These 95 percent confidence intervals remain enormous.

For example, let’s take Carmelo Anthony, the most accurate star player in these situations with a .481 shooting percentage. The 95 percent confidence interval for Anthony’s “true” percentage ranges from .293 to .669. Given the league as a whole shoots .298 in these situations, we can’t be entirely confident that Anthony is any better than average despite the fact that he has shot so well and has gotten a relatively high number of attempts. There are just five players (Travis Outlaw, David Lee, Eddy Curry, Carlos Boozer and Antawn Jamison) whose 95 percent confidence interval is entirely above league average and only one (Chauncey Billups, not exactly living up to his “Big Shot” label) entirely below average.

For the most part, the differences we see in players’ shooting percentages in these situations are just noise. Now, this is not the same as arguing against clutch ability or that it does not matter which player shoots in these situations. It’s just that it’s virtually impossible to draw conclusions about players’ ability from such small samples.

What does strike me as interesting is this. Both Beech and TrueHoop’s Henry Abbott, in his own discussion of the last-second numbers, argue teams and coaches are too predictable in their tactics and would be better served with greater ball movement. I don’t believe the numbers bear out this assessment. If you look at the group Beech has isolated (players who have made at least four game-winning/game-tying/go-ahead shots), the 76 players as a whole shot .353 in these situations. Using the league totals, we can deduce that players with fewer shot opportunities have shot just .232 from the field.

I can think of a couple reasons why this overstates the difference between the groups (desperation heaves are probably distributed more randomly than other late shots, and Beech’s cutoff was by shots made instead of shots attempted, meaning there are players with more attempts and a lower percentage who show up as “role players”), but it seems to me that go-to guys have actually been more successful in these situations. As to why the league as a whole scores so poorly, I think it’s a combination of heightened defensive intensity and the aforementioned prayers.

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