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The Economist: One Swing Is All You Need


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http://www.economist.com/blogs/gametheory/2015/04/signature-significance?fsrc=scn/tw/te/bl/ed/oneswingisallyouneed

Observers familiar with the unreliable nature of baseball statistics over short time frames will surely warn that expectations for Mr Rodriguez need to be kept in check. Robert "Voros" McCracken, an early and influential quantitative analyst of the sport, once memorably wrote that any MLB hitter can do just about anything, good or bad, in a mere 60 at-bats (a little over two weeks of play). Countless players have hit four home runs in a span of 35 at-bats or less, as Mr Rodriguez has so far this year, and gone on to achieve little. In 2006 the long-forgotten Chris Shelton hit nine homers in his first 51 at-bats. He mustered just seven more longballs over his remaining 322 at-bats that season.

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 Rodriguez'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 Rodr?guez?s should fare well above average in this category over the course of an entire season.
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 batters' other line drives and outfield fly balls in that season become home runs.
Guys who are washed up just don't hit 477-foot homers. Not even once.
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I was rather shocked at the distance of the April series HR by A-Rod. I think it hit about two rows deep into the section behind the concrete, past all of the first section of LF seats, just under the overhang. He's clearly able to get good wood on the ball. His batting average was in the low .230s as of this morning. But it's a long year and it'll be interesting to see what unfolds. Just makes me wonder if he'll be healthy all year. I liked him as a Mariner, became less enamored of him as a Ranger and then completely repulsed by him as a Yankee (the swipe at the first base mitt vs. Boston in the ALCS). I admire what talent he had, but a guy so unlikeable with his willingness to throw people under the bus as he's done destroyed any good will there was left for me to offer. I think I'm not alone with this.

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