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Wednesday, April 22, 2015

The Economist: One Swing is All You Need

Hold off on the glue.

However, the sabermetric canon also includes a caveat to “Voros’s law” about the volatility of small sample sizes. Although the overwhelming majority of events that can transpire in baseball over a brief time period cannot be distinguished statistically from random variation, a handful of accomplishments are so rare that even a single game can contain impressive predictive power. Bill James, the father of modern baseball analysis, called this principle “signature significance”. In one well-known example, of the 14 pitchers who have struck out 18 or more batters in a nine-inning game during the past century, 12 were at least All-Stars, and six are in the Hall of Fame. Mr Rodríguez’s mammoth blast might well be a similar case. After all, of the 38,143 homers hit in MLB since 2007—the first year that HitTracker recorded the path of every ball to leave the yard—just 25 (0.06%, or one in 1,525) traveled 477 feet or more. ...

In order to determine how much predictive power a single deep home run can provide, I started with every batter who played between 2007 and 2014. I first discarded all their ground balls and pop-ups, since balls on those trajectories cannot become homers no matter how hard they are hit. I then measured the share of their other batted balls—the line drives and outfield flies—that turned into home runs, a standard measure of a batter’s power. If ultra-long home runs truly have signature significance, then players who hit even one ball as deep as Mr Rodríguez’s should fare well above average in this category over the course of an entire season.

As one might expect, the data were extremely noisy—using a single swing to project what will happen on as many as 300 others is a tall order. But buried within them was a powerful and highly statistically significant trend. For each foot beyond the distance of a league-average longball (usually just under 400 feet) that any individual home run travels, an additional 0.06% of that batter’s other line drives and outfield fly balls in that season become home runs (see chart).

In most cases, this amounts to a rounding error. But for the biggest of blows, those percentage points add up in a hurry. If a player about whom we had no other information—say, a recent arrival from Cuba—hit a home run of average distance in his first at-bat, we would expect him to hit about 6% more homers than an average player for the rest of the season. In contrast, if the player hit a 477-foot home run like Mr Rodríguez’s in his first at-bat, we would expect him to hit around 50% more homers than average. That is as strong an example of signature significance as one could hope to find.

JE (Jason) Posted: April 22, 2015 at 09:43 AM | 1 comment(s)
  Beats: a-rod, oldwarhorse, yankees

 

 

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