Mandatory Credit: William Perlman/THE STAR-LEDGER via US PRESSWIRE
Inspired by the recent controversy surrounding the play of former Mariner, Alex Rodriguez, I did some interesting (perhaps interesting to me, only) research on the matter. To catch anyone up, ESPN and other major media outlets love painting A-Rod as Derek Jeter's evil step-brother. Dave Cameron recently highlighted the false narrative concerning A-rod's postseason play. To sum it up, A-Rod's average postseason performance has been on par with his average regular season performance, minus the effects of extra good playoff pitching. And A-Rod's average regular season performance is hardly average, so his playoff performance flies in the face of the narrative's claim that he's an October choke artist.
Then this article came along, calling out Joe Girardi for being human, and thus prone to recency bias. To sum that one up, Girardi stayed with Raul Ibanez* in game three, instead of going with A-Rod or Nick Swisher, likely because Ibanez had hit a game-winning homerun off a lefty—Brian Matusz—just eight days before. Additionally, A-Rod and Swisher have been slumping. Now the question becomes, does a player gain some sort of confidence boost from recently good play? And on the flip side, is a player likely to continue slumping if that's what he's been doing recently? If Ibanez's homer against Matusz was predictive of another miracle, and if A-Rod and Swisher's slumps were predictive of more woes, then maybe the decision to stick with Ibanez in game three was justified. Spoiler alert: not a lot of justification coming.
It turns out that Ibanez hit just .197/.246/.246 on the season against lefties. Clayton Kershaw hit about that well, too (.207/.230/.224). In other words, Ibanez's confidence boost from hitting dingers earlier in the week would have to be mammoth to make him a respectable hitter against Phil Coke the other night. Likewise, the probability that A-Rod continued slumping would need some statistical evidence.
There is more and more evidence developing suggesting that most professional players of any sport just don't have predictive streaks. Players doing well are just as likely to fall back to their expectation as players slumping are to rise back up. But let's take a look at A-Rod specifically. Remember, this is an article about A-Rod.
To the numbers!
So here's what I did. I broke A-Rod's career down into 10-game segments starting in 1996, and I measured his batting average, OBP and ISO in each segment. If A-Rod's peaks and valleys lead to more of the same, then we'll see what we call "autocorrelation" within the 10-game segments. Autocorrelation measures whether a player's own history correlates well to his present. Positive autocorrelation could possibly show that A-Rod's streaks—good and bad—are predictive. But here's A-Rod's autocorrelation chart for ISO (they all pretty much look the same–I'll spare you the rest):
What this chart shows is the correlation between current A-Rod, and A-Rod 1, 2, 5, or 20 segments back in the past. We can probably just focus on the X-values between 1 and 5, which represent segments from 0 to 50 games in the past. Going much further back seems a little overkill. I'm not sure what happened 80 or 100 games ago is all that relevant to A-Rod's current playoff slump.
The Y-axis measures the correlation—or predicative ability for the purposes of this study. Notice that the highest correlation going back 50 games was about 0.1, and the highest on the whole chart was only about 0.15. Neither of these are high correlations. The R-squared values would max out around 0.03, which shows virtually no predictive ability.
Since autocorrelation isn't everybody's thing, I looked at this from a different perspective. Right now we're seeing A-Rod slumping. Is there evidence that specifically bad play leads to more bad play? I looked at the worst 10-game segments of A-Rods career for each of the three stats (average, OBP, ISO), and then I checked the 10-game sequence directly after those worst segments. If A-Rod is prone to long slumps, then he should continue slumping more often than not, since these are only 10-game segments. But here's what happened:
In 36 of his 246 career ten-game segments, A-Rod performed badly in batting average, relative to the nearest segments. The following 36 segments showed an average Z-score of -0.1. In other words, he nearly rebounded back to his average average.
In 37 ten-game segments, A-Rod performed badly in OBP, relative to the nearest segments. The following 37 segments showed an average Z-score of +0.05. In other words, he rebounded to do slightly better than his average OBP.
In 33 ten-game segments, A-Rod performed badly in ISO relative to the nearest segments. The following 33 segments showed an average Z-score of +0.21. In other words, he may have performed even better than his own average ability in the power department after suffering a 10-game slump.
We don't know Girardi's up-close perspective of A-Rod this past week, but we do know that A-Rod has no history of allowing poor play to compound, and there is very little evidence to claim that he underperforms in October on average. The evidence does not support mainstream media's narrative, nor Girardi's lineup decisions, but what do I know? I'm just a stat geek!
*That makes two former Mariners in this article. Sodo Mojo stamp of approval.
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Tags: Alex Rodriguez, Playoffs, Seattle Mariners, Slump
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