Albert Pujols or Albert Einstein? by Lewie Pollis April 9, 2011 This article was originally published on WahooBlues.com. There’s no question that Albert Pujols is one of the greatest players in the history of Major League Baseball. As the active leader in wOBA (.434) and wRC+ (169), it’s not easy to come up with a superlative that sounds like hyperbole for Pujols. But a commenter on his stats page gave it a try last week: ALBERT Einstein had an IQ of 160. That means he is 60% more intelligent than the average human. Albert Pujols has a wRC+ of 177 during the past 3 seasons. That means he is 77% better at the plate than the average big leaguer. He is so much better at the plate than the average player, than Einstein was than the average human. And we all know how damn intelligent Einstein was! Even forgetting that comparing baseball skill to smarts is apples and oranges and Intelligence Quotient is an imperfect measure of mental ability—especially when the figure is just an estimation for someone who never took an official test (at least, not publicly)—this is nonsense because that’s not how I.Q.’s are scored. But that’s not to say we can’t examine this theory more systematically. I.Q. scores don’t reflect proportions of intelligence; someone with an I.Q. of 200 isn’t twice as smart as an average human. Instead, tests are scored on a bell curve of an approximately normal distribution with mean µ = 100 and standard deviation σ = 15. Retroactive I.Q. estimators are dubious, but the 160 score that this commenter used seems to be the most widely accepted figure for Einstein. That puts him exactly four standard deviations from the mean, meaning he was smarter than 99.9968% of the world’s population. In other words, 1 out of every 31,250 people is as smart as Albert Einstein. In order to put Pujols on a comparable scale, we must construct a distribution function to express his talent as a percentile instead of a proportion. Among the 242 MLB players who came to bat at least 1,000 times from 2008-10, the average wRC+ was µ ~ 106.2 with standard deviation σ ~ 19.5. That means Pujols’ 177 wRC+ over the last three seasons is 3.63 standard deviations from the mean. Assuming for simplicity’s sake that wRC+ can be accurately expressed with a normal distribution function, The Machine comes out at the 99.9858th percentile—only 1 in 7,042 people could reach that level. Viewed in this light, it’s clear that Pujols is a truly exceptional ballplayer, but a comparison to the father of modern physics is wrong. Unfortunately for Einstein, there’s one big problem that renders these results inconclusive: humongous sample bias. When we examined Einstein’s brainpower, we did so relative to the I.Q. scores of the entire human population—the mean represented John Q. Public, not the average theoretical physicist or Nobel laureate. Pujols, on the other hand, was being compared to the best baseball players in the country, if not the world; the data comes from players who were good enough not just to get to the big leagues, but to receive substantial playing time over a three-year period. If we make the generous assumption that 1 out of every 100 people on the planet is good enough to play in the MLB, Pujols jumps to the 99.999858th percentile. That’s 4.68 standard deviations from the mean—or, more dramatically, a wRC+ of 177 for every 704,225 people. In a world of 6.9 billion people, there should be 220,800 people who can match or best Einstein’s 160 I.Q. If we narrow the scope of Pujols’ competitors to 947—the number of players who had at least 20 PA’s from 2008-10—there should be 0.1345 players of Prince Albert’s caliber in the majors, or 1 for every 51.3 billion people on Earth. A hitter this good should not exist. Obviously, Einstein’s work was much more important than what Pujols has done—a game-winning homer in Game 5 of the NLCS doesn’t quite compare to E=mc2. Moreover, there are legitimate questions to be raised about the usefulness of evaluating one of the greatest geniuses of all time by an I.Q. test he never took. And these findings are as inapplicable to serious analysis as this study is unscientific. Take this all with a huge grain of salt, but relatively speaking (get it? because it’s Einstein), Albert Pujols’ ability to hit baseballs seems to be more unique than the mental capacities of one of the most influential intellectuals in human history. Lewie Pollis is a freshman at Brown University. For more of his work, go to WahooBlues.com. He can be reached at LewsOnFirst@gmail.com. Follow him on Twitter: @LewsOnFirst or @WahooBlues.