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Game-Ending Outs: Maybe A-Rod isn’t as bad at this as we thought
*July 19, 2012*

*Posted by tomflesher in Baseball.*

Tags: A-Rod, Craig Kimbrel, game-ending outs, game-ending strikouts

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Tags: A-Rod, Craig Kimbrel, game-ending outs, game-ending strikouts

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So, a friend of mine made the following comment on Facebook the other day:

## Someone has to look this up for me. Has any player, ever, made the last out for his team more often than A-Rod? He’s like the bizarro Mo.

At the time, **Alex Rodriguez** and **Curtis Granderson** were tied with 5 game-ending outs apiece for the Yankees. Since then, I thought it would be interesting to see what the average “game-ending out” looks like, at least according to Baseball Reference.

As of July 18, there were 1264 game-ending outs in the majors this year. **Aaron Hill**, **Jesus Guzman**, and **Kyle Seager** are ties for the lead with 9 apiece, with a spate of other batters tied for second at 8. Unsurprisingly, the 8th batting-order position makes the game-ending out most often; managers (of course) tend to arrange their strongest batters earlier in the lineup. By and large, game-ending outs tend to be short at-bats, with 850 coming with 4 or fewer pitches.

450 were strikeouts, with the league-leading total of 5 shared by **Edwin Encarnacion**, **Giancarlo Stanton**, and **Ryan Ludwick**. **Craig Kimbrel** of Atlanta leads the league in game-ending strikeouts, having thrown 15 of them. Kimbrel also led last year, with 31, which surprised me. **Mariano Rivera** had less than 2/3 as many, with only 20.

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Teixeira and Cano: Picking up slack?
*August 5, 2010*

*Posted by tomflesher in Baseball, Economics.*

Tags: A-Rod, Alex Rodriguez, binomial distribution, Mark Teixeira, probability, Robinson Cano, statistics, Yankees

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Tags: A-Rod, Alex Rodriguez, binomial distribution, Mark Teixeira, probability, Robinson Cano, statistics, Yankees

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Michael Kaye, the YES broadcaster for the Yankees, often pointed out between July 22 and August 4 that the Yankees were turning up their offense to make up for Alex Rodriguez‘s lack of home run production. That seems like it might be subject to significant confirmation bias – seeing a few guys hit home runs when you wouldn’t expect them to might lead you to believe that the team in general has increased its production. So, did the Yankees produce more home runs during A-Rod’s drought?

During the first 93 games of the season, the Yankees hit 109 home runs in 3660 plate appearances for rates of 1.17 home runs per game and .0298 home runs per plate appearance. From July 23 to August 3, they hit 17 home runs in 451 plate appearances over 12 games for rates of 1.42 home runs per game and .0377 home runs per plate appearances. Obviously those numbers are quite a bit higher than expected, but can it be due simply to chance?

Assume for the moment that the first 93 games represent the team’s true production capabilities. Then, using the binomial distribution, the likelihood of hitting at least 17 home runs in 451 plate appearances is

The cumulative probability is about .868, meaning the probability of hitting 17 or fewer home runs is .868 and the probability of hitting more than that is about .132. The probability of hitting 16 or fewer is .805, which means out of 100 strings of 451 plate appearances about 81 of them should end with 16 or fewer plate appearances. This is a perfectly reasonable number and not inherently indicative of a special performance by A-Rod’s teammates.

Kaye frequently cited Mark Teixeira and Robinson Cano as upping their games. Teixeira hit 18 home runs over the first 93 games and made 423 plate appearances for rates of .194 home runs per game and .0426 home runs per plate appearance. From July 23 to August 3, he had 5 home runs in 12 games and 54 plate appearances for rates of .417 per game and .0926. That rate of home runs per plate appearance is about 8% likely, meaning that either Teixeira did up his game considerably or he was exceptionally lucky.

Cano played 92 games up to July 21, hitting 18 home runs in 400 plate appearances for rates of .196 home runs per game and .045 per plate appearance. During A-Rod’s drought, he hit 3 home runs in 50 plate appearances over 12 games for rates of .25 and .06. That per-plate-appearance rate is about 39% likely, which means we don’t have enough evidence to reject the idea that Cano’s performance (though better than usual) is just a random fluctuation.

It will be interesting to see if Teixeira slows down as a home-run hitter now that Rodriguez’s drought is over.

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Quickie: 600th Home Run for A-Rod
*August 4, 2010*

*Posted by tomflesher in Baseball.*

Tags: 599 home runs, 600 home runs, A-Rod, Alex Rodriguez, Choke Index

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Tags: 599 home runs, 600 home runs, A-Rod, Alex Rodriguez, Choke Index

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**Alex Rodriguez** finally hit #600 deep to center field in Yankee Stadium on the third anniversary of his 500th home run. A-Rod hit the home run in his first plate appearance. There were 51 plate appearances since #599. He had a final Choke Index of .944, but luckily he won’t run into another milestone home run for at least a few years.

The ball landed in Monument Park, so the Yankees didn’t need to negotiate with a fan to get it back. (A security guard picked it up.) According to Michael Kaye, if the ball had landed in the stands, the Yankees would have been willing to pay for the person who caught the ball to have lunch with Alex Rodriguez and Cameron Diaz in exchange for getting the ball back, on top of an autographed baseball, hat, and bat. That opens interesting questions of valuation, much like those that came up after **Doug Mientkiewicz** attempted to keep the ball that he caught to make the final out in the 2004 World Series.

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Is A-Rod’s Performance Different?
*August 3, 2010*

*Posted by tomflesher in Baseball, Economics.*

Tags: A-Rod, Alex Rodriguez, Choke Index, OBP, p-value, probability, SLG, statistics, t-value, Yankees

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Tags: A-Rod, Alex Rodriguez, Choke Index, OBP, p-value, probability, SLG, statistics, t-value, Yankees

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In games between milestone home runs, is Alex Rodriguez’ hitting similar to other times? (This is all a very polite way of asking, “Does A-Rod choke?”) It’s difficult to answer, because there’s so little data about those milestone home runs. A-Rod, though, has some statistically improbable results and it would be interesting to look at it a bit more closely.

Over 2008-2009, Alex played in 262 games and had 1129 plate appearances with 281 hits, 65 home runs, a triple:double ratio of 1:50, an OBP of .397, and a SLG of .553. His OBP has a margin of error of .0146, so we can be 95% confident that over those years his baseline production would be somewhere between .368 and .426 and absent any time or age effect that is the range in which A-Rod should produce for any given period.

Two recent milestone home runs come to mind as examples of Rodriguez’s reputed choking. First, the stretch between home run #499 and #500 was 8 games and 36 plate appearances. (I’m intentionally ignoring extra plate appearances on the days he hit #499 and #500.) During that time, Alex had an OBP of only .306. That’s a difference of .091 over 36 plate appearances and that performance has a standard error of about .078 when compared with his regular performance, implying a t-value of about 1.16. With 35 degrees of freedom, Texas A&M’s t Calculator gives a p-value of about .127, so this difference is marginally within the realm of chance. (The usual cutoff for significance would be .05.)

A-Rod hit his last home run on July 22. Discounting the plate appearances after his last home run, he’s played in 11 games with a paltry .255 OBP and .238 SLG over 47 plate appearances. His .255 OBP has a difference of about .142 and a standard error of about .064. That implies a t-value of about 2.21, with a p-value of about .016. That is, the probability of this difference occurring by chance is less than 2%. That gives us one result as close to significant and one as probably significant.

As a side note, A-Rod’s Choke Index continues to rise. He’s gone 48 plate appearances without a home run, and at a rate of .055 home runs per plate appearance the probability of that occurring by chance is about .066. That leaves his Choke Index at .934.