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I’m a lifelong baseball fan, and so today is one of the most exciting days of the year for me: Major League Baseball’s Opening Day. Many people feel the same way, including countless writers, scientists, economists and other academics who are also fans of America’s national pastime. I have often wondered why baseball fandom seems so prevalent within certain professions. Perhaps baseball simply attracts folks with a certain cast of mind. Maybe it’s the reverse, that baseball trains the brain to operate in certain ways. Perhaps both are true.
Sports fans have long noticed fundamental differences between baseball and other spectator sports, with baseball characterized either positively or negatively, depending on the fan’s vantage point. (If you haven’t seen it, watch George Carlin’s classic routine [ [link removed] ] contrasting the nomenclature and objectives of baseball with football.) Baseball is often derided for its slower pace and sporadic activity by those who prefer that sports deliver more continuous action (like basketball), or that they more closely replicate physical combat (like American football).
The pleasures of baseball, by contrast, reside as much in the thinking that occurs between pitches as in observing the graceful physical action. It’s a sport for people who share Socrates’ distaste for the “unexamined life”—those who aspire to be fully aware of what is going on even as it’s going on. This requires sufficient pauses in the action for the mind to notice, to wander and to analyze. To those who would disdain these contemplative aspects, Brooklyn Dodgers announcer Red Barber had his answer: “Baseball is dull only to dull minds.”
Stories from Numbers
I attribute many of the analytical instincts I deploy as a professional adult studying economics to my childhood experience as a baseball fan. From the moment I first became aware of baseball players, they came prepackaged with a catalogue of numbers—presented on the backs of baseball cards, blaring on stadium scoreboards and dotting the pages of guidebooks. The young fan instinctively inspects these numbers for clues to players’ essences. Without trying, he or she quickly learns what the great baseball analyst Bill James has noted: “Baseball statistics can tell stories.”
Being a young baseball fan is for many people their first experience with detecting meaningful patterns in numerical data and seeing how that data can conjure vivid pictures. This process develops so unconsciously that even those immersed in it don’t notice it is happening. To borrow a type of illustration from James, if you show virtually any fan the backs of two baseball cards, one of which describes a player with a .237 batting average, 31 home runs, 137 strikeouts and zero stolen bases, and the other a player with a .329 batting average, 7 home runs, 11 triples and 53 stolen bases, the fan will envision two very different players. If asked which of them is the first baseman and which is the center fielder, which one is 24 years of age and which is 36, which one batted leadoff and which batted seventh, no fan would hesitate in answering. From baseball, we learn to derive impressions from tables of numbers as reflexively as we do from descriptive words.
Some of my earliest familiarity with the poetry of numbers came from staring at the backs of baseball cards—not looking for anything in particular, just looking, in the way kids do. (As Yogi Berra put it, “You can observe a lot by watching.”) Certain number patterns, especially those associated with small data samples, appeared over and over. If a pitcher had, say, four decisions, there were only five possibilities for his winning percentage: .000, .250, .500, .750 or 1.000. Especially intriguing were the frequently encountered patterns of repeating decimals. For example, any number of wins achieved in nine decisions produced a winning percentage of a single digit endlessly repeated (.111… for one win or .888… for eight wins, rounding to .889). The pattern associated with 11 decisions was similarly striking. Baseball thus familiarized me with division, repeating decimals and rational numbers long before school did.
Long walks home from the corner store where I bought baseball cards were of sufficient duration for such insights to sink in, as were the breakfasts during which I studied the backs of 3-D cards fished from boxes of Kellogg’s Frosted Flakes. Without intending to, I memorized the three-digit decimals associated with every possible outcome in any number of at-bats or decisions up to a dozen, as well as with many larger numbers.
By the time school got around to instructing us in long division, I had more intimate familiarity with the recurring patterns of decimals than I had with the names of people in my extended family. Trips to the ballpark became opportunities to exercise these nascent powers. The scoreboard would display a player’s batting average and his number of hits on the season, but tantalizingly omit the third number in the equation—his at-bats. I noticed I could calculate the at-bats by silently dividing his hits by his batting average, after which I could add the result of his recent at-bat to calculate his updated average before the next time he stepped to the plate. Long division to three or four places became second nature to me, as automatic as reciting the Pledge of Allegiance. And while I know that few kids were as absorbed by the mathematics of baseball as I was, there’s no doubt that the sport inculcates in nearly all its fans a greater comfort with numerical reasoning.
Numbers reign supreme in baseball in a way they do not in football or basketball. It simply is not as informative—or absorbing—to compare the statistical records of two quarterbacks as two batters. A good part of the reason for this is that baseball statistics are far more descriptive of an individual player’s profile, conveying his relative power and speed, the accuracy of his strike zone judgment and how aggressively he swings the bat. Another reason is that individual performance is more isolable in baseball than in other sports: No quarterback can generate statistics without the direct participation of his team’s receivers and offensive line, whereas a baseball player bats alone. And each batter’s individual statistics tell us a great deal, independently of who’s on base ahead of him or who waits on deck behind him.
The Limits of Knowledge
What we can learn from the mathematics of baseball goes much deeper than what we can calculate. Baseball also teaches early lessons in uncertainty—that one lives in a world of unpredictable events, that good decisions can still lead to bad outcomes, and that one should not assign much importance to any single data point. The lessons are stamped all over the sport. The best team typically loses more than one-third of its games; the worst team typically wins more than one-third of its games. Even if a manager makes the absolute right decision, it might not work out. On any given swing, the worst hitter might hit the ball on the nose, whereas the best hitter might foul a ball straight back into the stands or miss entirely. On any given day you don’t know who on your team will get the most hits, but more often than not it won’t be the team’s biggest star.
Anyone whose suppositions about life are that we can control events, that bad outcomes prove bad decisions, and that past results govern future performance will be utterly unable to understand baseball. Even relative to other sports, baseball is relentless in teaching these lessons. Alabama’s college football team may crush one opponent after another, but no baseball team is ever so certain to win—not a game, not a series, not even a pennant race. Tendencies are proved over the long run, but any given day might produce a great surprise.
Appreciating life’s unpredictability can’t help but carry forward into one’s professional decision-making, relationships, investments and attitudes about public policy. It certainly has for me. Baseball teaches that while there are ways to maximize your chances of success, there will also always be factors outside your control, and you are better off thinking in terms of probabilities than predetermined outcomes.
Baseball leads its fans through various aspects of mental skill development—pattern recognition, numerical calculation, correlation, inferencing, understanding of uncertainty, probability, risk and reward. It also teaches that a little knowledge is a dangerous thing. In baseball as in other fields, as soon as we master received wisdom, we tend to assume we know more than we do. It’s one thing to be conversant in a field, but it’s entirely another to grasp the limits of one’s own understanding. Baseball has taught me many times that I’ve been quite wrong about something, after I had been utterly convinced by my detailed knowledge that I must be right. Expertise does not automatically confer wisdom, or even correctness.
Whenever we belatedly recognize the limits of our understanding, we look back with embarrassment on our earlier ignorant certitude. Unless and until that point is reached, the enthusiastic learner can be insufferable. Memorizing information, performing calculations and deriving results are all skills readily mastered by the immature mind. These tasks might all be performed correctly and yet still prompt faulty conclusions. We grow not merely when we correct these specific errors, but when we extend our newfound humility to reasoning about other things.
We all go through this learning process, but I recall multiple instances of baseball making it especially explicit. In the baseball stat lines I encountered in youth, the final entry on the right was always batting average (for hitters) or earned run average (ERA, for pitchers). I assumed these numbers were placed in these prime locations because they equated to overall quality. It seemed to make sense; after all, a batter is attempting to hit, so it stood to reason that the more frequently the batter succeeds in doing so, the better he must be. Similarly, the fewer earned runs a pitcher allows every nine innings, the better he must be doing. Or so it seemed.
Of course, there were always hints that these particular statistics weren’t all-illuminating, even if I suppressed my awareness of it. Watching a game, I’d see a fielder flub a difficult play, after which everyone in attendance waited for the scorer to determine whether it constituted a hit or an error, which in turn determined whether a run was earned or unearned, and thus whether it affected the pitcher’s ERA. Similarly, I noticed that my beloved Pittsburgh Pirates comfortably led the league in scoring but not in batting average—and that Gene Clines, who spent more time in the dugout than on the field, had a higher average than Willie Stargell, who led the league in runs batted in. Nevertheless, I persisted in ranking hitters by batting average—and in believing that because I knew every player’s average, I knew more than others about who was better.
But baseball helped me to see the vast difference between possessing information and understanding it. One of the delights of a 1970s childhood was the proliferation of tabletop games re-creating with uncanny accuracy the real-life performances of major league players: Strat-O-Matic [ [link removed] ], APBA [ [link removed] ] and even the basic All-Star Baseball [ [link removed] ], which reduced each player’s profile to simple arcs of various lengths around the circumference of a spinner. My friends and I would confidently “draft” players for our tabletop teams according to their batting averages, then watch in befuddlement as the players hit just as they did in real life, and yet the teams whose players had the highest batting averages somehow didn’t win.
From Anecdotes to Science
These mysteries were not resolved until graduate school, when I discovered the writings of Bill James. James revolutionized a generation’s understanding of baseball, and his scientific approach led, slowly but inexorably, to major league teams overhauling their competitive strategies in deference to the analytical methods he pioneered. For me—a poor graduate student who had spent his entire meager monthly entertainment budget on James’ 1985 Baseball Abstract—reading James was a revelation of a magnitude younger fans are unlikely to understand.
Here, finally, was a baseball writer who wasn’t interested in parroting the shibboleths recited during Game of the Week telecasts, but in testing whether dominant theories of the game were actually true. Among other things, James developed methods for measuring the extent to which each player’s actions contributed to his team scoring runs, or prevented the other team from doing so, and thus how much each player contributed to winning.
James’ writings proved there was a market composed of countless people like me—fascinated by baseball and wanting to understand better how it worked. However, he also rubbed other people the wrong way, primarily for two reasons. First, he challenged what many believed they knew for certain, something people never take kindly to. Second, he wielded mathematical methods as part of his arsenal, annoying those who don’t like math and who are suspicious of those who use it. In this respect, James remains misunderstood. James has never been solely about math; he is simply willing to use it where it helps to explain things. James relies equally on other ways of learning: He himself is a voracious reader of baseball history, as eager to understand what can be conveyed through words as by numbers. Indeed, if there is a better living baseball historian than Bill James, I don’t know who it would be.
Reading James changed my relationship with baseball. He inspired me to develop a precursor of a fantasy baseball league as a side business in grad school, one that used sabermetric methods [ [link removed] ] to simulate nine-inning games between the managers’ chosen lineups, rather than compiling statistics in arbitrary categories as most fantasy leagues do. I began to read baseball’s scholarly journals and occasionally published in them myself, a practice I continued into my early professional life.
In a 1995 piece, I analyzed Don Larsen’s perfect game [ [link removed] ], an event unique in baseball history because a.) it occurred in a World Series game, and b.) Don Larsen was far from an all-time great. I concluded that the pitcher most likely to have accomplished this was Sandy Koufax at the peak of his powers in 1965, whereas 1968—when Bob Gibson and Denny McLain each had three starts in the same World Series—was the year such a feat was most likely to have occurred.
Ultimately, I wasn’t able to keep up as a sabermetrician. James inspired an entire generation of up-and-coming analysts, many of whom built upon his foundation to develop new analytical systems. Major league teams found they benefited from applying these methods to everything from personnel changes to defensive positioning to setting up pitcher-batter matchups. When “Moneyball” first became a bestselling book [ [link removed] ] and then a hit movie [ [link removed] ], the popularization of sabermetrics was complete. Every ambitious professional (investment bankers were reportedly especially taken by the book) wanted to apply similar methods to gain a competitive edge, while every major league team, broadcaster and fan base routinely cited findings of the new analytics. I found it challenging enough to follow developments even as a fan, and remaining ahead of the pros was out of the question.
Nothing New under the Sun
Understanding of baseball has come a long way in recent years—among fans, major league teams and members of the media. A modern manager and franchise would have an enormous informational advantage over the teams of just a few decades ago. At the same time, certain cognitive shortcomings remain every bit as prevalent today as they ever were. It does fans little more good today to memorize which players have the most wins above replacement [ [link removed] ] (WAR) than it did for young me to memorize the players with the highest batting averages, if they don’t understand how WAR is calculated, what it really means, and how it might diverge from a player’s true value to his team. Simply memorizing numbers and citing authoritative sources does not embody understanding. To the extent that today’s fans uncritically recite a different set of statistics than yesterday’s did, we’re not any smarter.
In baseball or in any other field, the truth is always out there, beyond the reach of any scientific model we develop. The algorithms we develop to simulate baseball are intended to represent reality, but no matter how accurate they appear to be, they are not reality. We should be continually hunting for places where we are undoubtedly missing something.
Nor should we neglect other routes to knowledge. I happen to like spreadsheets and mathematical models; they serve the ways I find easiest to think. But the “Moneyball” portrayal of a fundamental dichotomy—scientific number-jugglers with a close tie to reality on one side, the irrational Old Guard mired in groupthink and superstition on the other—is misleading. There are many elements of reality that number-crunchers can lose sight of, whereas a good manager needs social skills and good intuition just as much as he needs familiarity with the analytics. There is still tremendous information to be gleaned from the recorded impressions of observers throughout baseball history, none of which is diminished by the emergence of mathematical models.
Finally: Don’t blame analytics for ruining the game. Instead, the game ought to be adapted to keep pace with the accumulation of knowledge. For example, I disagreed with MLB’s 2023 decision to ban infield shifting. Instead of blaming teams’ analytical departments for figuring out that the best winning strategies weren’t necessarily the ones most exciting to watch, baseball should have changed the playing conditions (outfield fences, scope of fair and foul territory, balls and bats) so that winning strategies were more entertaining.
Such environmental changes could easily reduce the relative advantage of power hitters, increase the utility of putting the ball in play, increase the benefit of outfield speed, reduce the numbers of strikeouts, foul outs and walks, render pitching more strategic and reduce the number of pitches per at-bat. In short, teams shouldn’t be penalized for deducing what wins. Rather, MLB should work to create conditions conducive to more exciting baseball—the new pitch clock being one successful example—and let teams innovate within them.
In the end, baseball is a competition, and one of the great things about competition is that it ultimately rewards those who figure things out. The fact that in baseball it often takes decades to do so reminds us that in life what may seem obvious to us today wasn’t always so clear, and that there are countless things we remain ignorant of that future generations will know. Baseball is that rare athletic competition that engages our aesthetic sensibilities at the same time it stimulates deep reasoning and boundless curiosity. Whether you’re a jock, a poet, a nerd or a little bit of each, there’s always a new way to play the game.

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