Albert Pujols would be very happy if we all just forgot about the last month of baseball.
Pujols signed a 10-year, $240M contract over the winter with the Los Angeles Angels of Anaheim*. The statistically-minded balked at the deal, which would pay him $30m in 2021, when Pujols will be 41 years old. Still, it wasn't hard to imagine that the deal could still be worthwhile, so long as Pujols crushed in the first half of the deal.
...Whoops. Pujols, projected by FanGraphs to hit 28 home runs this season, is still waiting for his first homer some 107 plate appearances into the season. That's the longest drought of the season, and naturally, everyone's asking, "What's wrong with The Machine?"
First, let's see if the drought is that unusual. For his career, Pujols has hit a home run in just under 6 percent of his plate appearances, which means that, in any given plate appearance, there's a 94% chance he won't leave the yard. As we've discussed, Pujols is up to 107 PAs on the year, so the probabililty of him not hitting a homer in that stretch is
P(no homer in PA 1)*P(no homer in PA 2)*P(no homer in PA 107) = (.94)(.94)...(.94) = .94^107 = 0.15%**
That's really unlikely (the odds are something like 670 to 1), but remember: Pujols has been in the league a long time, and has amassed more than 7,500 PAs, so yeah, a 100+ PA drought could happen purely by random chance.
Let's dig a little deeper. FanGraphs also provides us with Pujols' advanced stats, and none of them seem especially out of whack. His fly ball rate is down a tick (37% this year vs. 40% career), but his line drive rate is actually higher than usual (25% vs. 19%). So it's not like he's making weak contact.
More worrying for Angels fans? Pujols' strikeout rate ("13% vs. 9.5%) is up while his walk rate (5.6% vs. 13%) is way down. To back this up, let's look at his O-Swing%, defined as the number of pitches he swings at outside the strike zone. For his career, Pujols has been right around league average in this stat, chasing 21.8% of pitches out of the zone. But so far this year, Pujols has seen 151 pitches off the plate and gone after 40.8% of them.
More bad news: this one ain't necessarily random. Using a one-proportion z-test, you can figure out that the probability of seeing that many swings in a random sample is 5.6 standard deviations away from the mean. The probability of that happening is more than 128 million to one. They have a word for that in Pujols' birthplace: improbable.
Now, you could argue that Pujols has gotten less selective over the years, and that's true: in his last three seasons with the Cardinals, Pujols' O-Swing% went from 23% to 28% to 32%. Still, even by that standard, the 41% he's chasing this year is an outlier: repeating the one-proportion z-test with 32% as the "true" percentage, this year's performance is 2.4 standard deviations above the mean for a probability of 114 to one.
It passes the smell test, too: Pujols just signed a $240 million contract, might be (understandably) feeling the pressure to earn that contract in a new city, and is pressing, going after pitches he normally would lay off, causing more strikeouts when he misses and a little weaker contact even when he connects. But let's not bury Pujols just yet. After all, another Dominican slugger -- David Ortiz -- opened the 2009 season without a homer in his first 161 PAs, then went another 80 PAs before hitting his second on June 5. He finished the season with 28 home runs.
*-Or, as Baseball Prospectus' Kevin Goldstein calls them, "The The Angels Angels".
**-Granted, this assumes each PA is independent (that is, P(no homer in PA 1) has no effect on the other probabilities), but this is a blog post, not my thesis, and this is The Machine we're talking about, so let's go with it.