The new Gordon Beckham: binomial statistics for baseball

Watching the White Sox this year has been awful.* I have to imagine Robin Ventura wants to do this pretty much every  night. Through the end of May the Sox were hanging around .500 and then the wheels just fell off. It’s ok to lose to Detroit or Texas, but to get swept by the Cubs and Twins or drop three of four to the 4A team that is Houston** is just…ugh.

*In the interest of full disclosure, I’ve stopped watching.

** Seriously, a league-average major league player puts up about 2 WAR in a given year. The Astros have 6 players total (4 position, 2 pitchers) on pace to even sniff that mark this year. That team is baaaaaaad.

So given the state of the Sox, you can understand why I’ve spent more time checking out their stats than their games. I’ve at least found some solace there: Gordon Beckham is getting better! After a stellar rookie campaign in 2009 the shortstop-turned-second baseman soured in a big way. South siders have spent the last three summers waiting for Beckham to return to form and been largely disappointed. He has sucked. Although he’s seen limited playing time this year due to a fractured something-or-other in his left hand, the infielder has been raking to the tune of .317 – his highest average since that magical summer of ’09.

But is it all a mirage? His batting average on balls in play* is .375 – way above his career norms or league averages. Could it just that we’ve caught Gordo in the middle of a thirty game hot streak or is something else going on here?

*Rather than computing the number of at bats that result in a hit like batting average, BABIP tells us how frequently a batter reaches base on balls he does hit. It’s generally acknowledged that some players can boost their BABIP by hitting the ball squarely or running fast, but big swings in the stat are generally attributed to luck.

Turns out there might be: even though his BABIP is way up, Beckham is also hitting way more line drives when he does put the ball in play – just under 30 percent versus under 20 percent for his career average. Those line drives are more likely than fly balls or grounders to fall for hits and could explain the elevated BABIP, but now the question becomes whether that increase in LD% is real or just statistical noise. Sabermatricians, after all, love to warn of the dangers of small sample size. The good people at Baseball Prospectus have even gone so far as to calculate the point at which a given stat will “stabilize.”

In this case, however, we can do better. Using binomial statistics (what you would use for predicting the number of times a coin comes up heads in X tosses) we can test whether this version of Beckham is in line with his career numbers, and it turns out that it isn’t – which is good. We can be almost 99 percent sure that 2012 Beckham wouldn’t be putting up these numbers (at least as far as LD% goes). If we compare 2013 Gordon to his career numbers, our confidence level will only go up. Since an even closer look at his swinging habits doesn’t show much difference between this year and others, it seems safe to conclude the Beckham has just found a way to hit the ball harder. Maybe it has something to do with the mechanical changes he made at the end of last season/beginning of this one or maybe he’s just got his head in the right place right now, but either way, it's nice to have at least some silver lining in an otherwise depressing season.

Interestingly, the Baseball Prospectus people concluded that it takes nearly 1,000 batted balls – usually over 2 years – for LD% to stabilize. Using this strategy instead, we can say useful things about LD% far sooner. Baseball Prospectus's calculations rely on a cross-correlation method that is far more empirically-supported than what we’ve done here so these results should be taken with a grain of salt. Nevertheless, binomial theory is a fun, first approximation approach to questions of whether a player X’s current performance means something has changed, or if it can simply be written off as regular statistical variation.* See this post for a few more interesting examples.

*It’s especially easy if you have R-Gui (it’s free!). Just use the prop.test command.

H/T to the lovely Paras Patel for slipping me notes from Dave Sept’s fantastic Stats class. They proved invaluable during the writing of this post.

Ed Note: stats accurate as of two beer into Saturday night 6/29/13.

Ed Note II: it has since been brought to my attention that we should be using Poisson statistics since we can never know the "true talent" of Player X. In this case, the p-values change but the conclusions remain the same.