Joe Girardi, Probability, and Expected Value

During last night’s Yankees-Twins baseball game, the commentators were discussing the Yankees’ increased use of defensive shifts.

A “shift” is a defensive realignment of the infield to guard against a particular player’s hitting tendencies.  For example, if a player is much more likely to hit the ball to the right side of the infield (as, say, a strong left-handed hitter might be), a team may move an infielder from the left side to the right side to increase the chance of defensive success.

Dramatic infield shifting was once a rarity in the game, employed against only a few hitters in the league.  It is now being used with increasing frequency.  “All the data is out there,” said the announcers when discussing Yankees’ manager Joe Girardi’s explanation of why he was using it more.  (Which sounded remarkably like what Rays’ manager Joe Maddon, a pioneer in increased defensive shifting, had to say when asked about it some time ago).

The essential idea is that, given the reams of data now recorded on player performance, teams have a much more refined understanding of what a player will do.  No longer is the projection “The player has a 30% of getting a hit”; now, it’s “The player pulls 83% of ground balls to the left side of the infield”.  Naturally, teams try to use such information to their advantage.

It’s good that Joe Girardi is demonstrating an increased appreciation for, and understanding of, probability.  But as last night’s game suggests, he may need to learn more about the principle of expected value.

Early in the game, the bases were loaded with two outs, and a left-handed batter came to the plate.  Girardi put the defensive shift on, responding to data on this player that suggested he was extremely likely to ground out to the right side of the infield.  But probability considerations should be only one part of the analysis.  By leaving so much of the left side of the infield undefended, a situation was created where a weakly hit ground ball that would usually be an easy out actually produced two runs for the Twins.

In short, although the probability of that event (ground ball to the left side) was low, the risk (giving up two runs) was high.  Considering both the probability and the payoff is essential to long-term success.

I’d be surprised if the Yankees’ employ the shift again in that situation.  And if the Yankees need a special quantitative consultant, I am available during the summer.

Statistically Solving Crossword Puzzles

I am lover of crossword puzzles.  I do the NYT crossword puzzle regularly, I’ve competed in the American Crossword Puzzle Tournament, and I’ve even dabbled in constructing puzzles myself.

There’s a great deal of crossover between math lovers and crossword puzzle lovers, and one example of this crossover is Matthew Ginsberg.  Ginsberg is a regular puzzle constructor, has a PhD in math from Oxford, and is an expert in artificial intelligence.

Not a huge stretch, then, that he has developed a rather effective crossword puzzle solving robot, Dr. Fill, that is now challenging the top human performers .

Ginsberg runs a company that produces software for the Air Force that helps calculate the most efficient flight path for airplanes.  Here’s the cool part:  “Some of the statistical techniques [used to calculate optimal paths of airplanes] are also handy, it turns out, for solving crossword puzzles.

Yet another example of how statistical reasoning is emerging as primary tool in modern science and society!

Superbowl Scoring

After enjoying a well-contested Superbowl that seemed to appropriately represent the teams, the season, and the league in terms of the level of play and competitiveness, I started wondering about how the big game compares to regular season play.  I wondered if teams performed better or worse, on average, given the pressure and scrutiny of the championship game.

I thought a simple place to start examining this question would be to look at Superbowl scoring versus regular season scoring.  Below is a chart showing the difference (Superbowl Score – Average Regular Season Score) for all 46 Superbowls.

At the far right, we see the results of Superbowl 46:  Giants 21, Patriots 17.  The league average in scoring this years was 22 points per game, so the difference here is 38 – 44 = -6.

It seems as though it is more common for more points to be scored in the Superbowl than in an average regular season game.  Unfortunately, there are a lot of stories one could tell about why that might be so:  better teams (and therefore better offenses) make it to the Superbowl; defenses are more susceptible to pressures of the big game; the extra preparation time gives offensive coordinators and advantage.

So how could we more rigorously explore the quantitative characteristics of the Superbowl?

Yet Another Way to Lie With Statistics

This is a nice takedown of some spurious economic analysis, courtesy of Freakonomics:

http://www.freakonomics.com/2011/03/30/how-to-spot-advocacy-science-john-taylor-edition/

Looking at the graph at the right, it’s hard not notice the negative correlation between the two given variables, and the economist in question uses that correlation to bolster his policy argument.

The graph looks a lot different, however, when you look at all the available data, not just the data between today and the arbitrarily chosen cut-off of 1990.  But that chart doesn’t support the argument as decisively.

As the author suggests, “Be wary of economists wielding short samples.”

The Year in NFL Scoring

football-in-airAs the books close on the 2011 NFL regular season, it’s time to revisit my pre-season prediction that the new kickoff rule would result in a slight decrease in per-game scoring.

The pre-season predictions on the number of touchbacks turned out to be fairly accurate.  In 2011, about 43% of kickoffs (922 out of 2151) resulted in touchbacks; in 2010, only 16% of kickoffs (359 out of 2221) resulted in toucbacks (thanks to NFL.com for the data).

Did the increase in touchbacks reduce overall scoring in 2011, as hypothesized?  No.  In 2011, around 44.4 points were scored per game in the NFL; in 2010, around  44.1 points were scored per game.  Per-game scoring actually increased slightly this year !

One issue worth mentioning, however, is the disproportionate effect the top three scoring teams have on the data.  During the 2010 season, New England was the highest scoring team in the league with 518 points total points; this was nearly 80 points more than the second highest scoring team.  In 2011, the Packers, Saints, and Patriots all scored over 500 points!  If we remove the three highest-scoring teams from each season, scoring for the rest of the league actually drops about 0.7 points per game.

It’s been fun drilling down into the data this year, and many other interesting questions popped up along the way.  And off-season changes always create new opportunities for analysis.

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