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    Batter up? Yes, but UCI professor’s new baseball stat shows he’s not alone
    • March 24, 2026

    There is no crying in baseball, right?

    Wrong. At some point, everybody who ever plays ball — little leaguers, high schoolers, probably big leaguers when the cameras aren’t around —sheds tears. The game is just too gut-wrenching for there to be no crying. Instead, there’s a lot of it.

    But you know what baseball really doesn’t have? Fairness.

    Line drive outs exist. Swinging bunts exist. Foul ball homers, seeing-eye singles, blown calls, sunny sky pop-ups. Hundreds of unfair things can happen in baseball games, and those unfair things often affect everything from how we regard a player’s performance to the final score.

    That’s where Michael McBride is stepping in.

    McBride is an economics professor at UC Irvine. He’s also a data guy, an expert in game theory, which is a type of math that uses numbers to predict how an event will play out when that event is influenced by more than one unknown factor. (The late UCLA mathematician Lloyd Shapley described game theory, his specialty, as the “mathematical study of conflict and cooperation.”)

    Hedge fund managers and war planners sometimes use game theory. And now, thanks to McBride, so can baseball (and softball) nerds.

    A few years ago, when he was coaching his children’s baseball teams, McBride realized game theory could help explain what really happens during a baseball game, specifically, when a run scores. It’s pretty obvious who deserves the credit when a batter hits a solo home run, but every other kind of run has several contributors. And those contributors — in McBride’s view — haven’t always been given a fair level of credit.

    Over the next few years, he developed a couple of statistical tools — Shapley Run Credits and Offensive Shapley Win Credits — to help track and recognize all the responsible parties when any run scores. And he’s written a new book based on those ideas, “Game Theory, Machine Learning, and Production in Sports: The Fair-Credit Baseball Statistics.”

    Applying higher-end math to baseball is hardly new. Branch Rickey, the general manager of the 1950s-era Brooklyn Dodgers, once hired a statistician to help him sort out why on-base percentage was a bigger deal than batting average. And sabermetrics, a term coined about 35 years ago by baseball numerologist Bill James to describe a new world of statistical reckoning for the national pastime, is now used in every big league front office and dugout.

    Someday, McBride’s ideas might be viewed as a step in that progression.

    With opening day approaching quickly, he recently talked about his book, baseball stats and why it’s fun to apply numbers to baseball.

    Q: What’s your book about?

    A: My book introduces an innovative approach to assigning credit to offensive players in baseball. In particular, I apply a concept from cooperative game theory called the Shapley Value to create new baseball statistics that satisfy several fairness properties. That is why I refer to my stats collectively as the Fair-Credit Baseball Statistics. …  One new stat — called Shapley Run Credits — fairly divides the credit among players for each run that scores, and another — called Offensive Shapley Win Credits — fairly divides the credit for winning the game by outscoring the opponent. The book provides a nontechnical introduction to what the stats are, then goes into the nitty-gritty details of their calculation and ends by showing how they illuminate our understanding of baseball. So, the book is targeted to both fans and the baseball analytics community.

    Q: Explain fairness in the context of your baseball data?

    A: When I refer to fairness, I mean that baseball stats should award credit among players in a way that accurately reflects how important their contributions were. For example, a player who contributed nothing to scoring should get zero credit, a player who contributed more to scoring than another should get more credit than the other player, and so on. Traditional stats like runs and runs batted in do not always achieve this kind of fairness, but my stats do.

    Q: I’m going to hate myself for asking this, but what is cooperative game theory?

    A: Game theory is a set of mathematical tools and concepts that are used to study social interactions. The word game can mean games like poker or backgammon, but in game theory, the word game means any interaction where an individual’s well-being is affected by another’s choices.

    Cooperative game theory is a branch of game theory that examines settings where individuals work together cooperatively to achieve some form of group production. Baseball fits in here because what one batter does directly affects a teammate’s opportunity to score, and this is relevant for my book because the Shapley Value is a concept within cooperative game theory.

    Q: Obviously, baseball is a team game. But it’s a team game based on individual performances — a hitter vs. a pitcher during an at bat, a defensive player when the ball is hit his way, a runner stealing a base or scoring a run. Why are credit statistics important? And why do credit statistics capture the essence of the game better than, or differently from, predictive statistics?

    A: It helps to think of baseball stats as falling into two broad categories. The first category includes stats that are measures of baseball skill, like batting average. The second category includes credit stats, like runs or RBI.

    Skill stats are important because they help us to predict how good a player will be going forward, but skill stats tell us less about who actually helped a team win in any particular game. Credit stats, on the other hand, can help us understand who helped the team win any particular game.

    That is why credit stats have been included in box scores for over a hundred years. Knowing a player’s season batting average helps you to know how well they have been batting but not whether they actually helped the team win in a particular game. Credit stats, such as runs and RBI, give you that information.

    Interestingly, nearly all of the advances in baseball statistics have been in the development of new and improved skill stats, so the creation of (Shapley Run Credits) and (Offensive Shapley Win Credits) is a rare exception — a meaningful advance in credit statistics for the first time in decades.

    Q: What’s unfair — or, short of unfair, what’s lacking — in traditional baseball statistics, like batting average, home runs and runs batted in?

    A: Runs and RBI can be unfair credit stats for many reasons. For one, only one player is given credit for a run and only one player is given credit for an RBI. That is a problem because scoring in baseball is so collaborative that, oftentimes, more than two players should deserve some credit. It is like runs and RBI are awarding credit only to the final leg of a relay race when everyone deserves some credit.

    Q: Do newer baseball stats, like Wins Above Replacement, do a better job of representing the game than the original baseball card numbers that dominated baseball analysis in the 20th century?

    A: Absolutely! The trend in baseball statistics over the last almost 150 years — but especially the last 50 years — is to create more complicated statistics like WAR that do a better job of representing the game. The increased complexity should be expected because it allows the new stats to account for more aspects of the game that the older stats do not account for. The downside is that new stats like WAR cannot be calculated by nonspecialists. But really, the most important thing is that you understand the stats at an intuitive level so you understand what they are telling you.

    My stats are like that because you can’t calculate them without some training. The good news is that the underlying concept — shares of runs and wins — is something any fan can intuitively grasp, even if the math behind the scenes is complex.

    Q: Who was Shapley? And why did you name your system after him?

    A: Lloyd Shapley was a mathematician who contributed to mathematical economics and game theory. He was a co-winner of the 2012 Nobel Prize in Economics for his contributions to game theory. I never met him in person, but it seemed appropriate to name the stats after him because the stats are direct applications of his idea that later came to be called the Shapley Value.

    Actually, I understand that he was a baseball fan, but he apparently never considered how this idea could be applied to baseball. Unfortunately, I did not begin on this work until after his death, in 2016, so he never got to see how his idea could actually be applied to the sport he loved.

    Q: What is mathematical fairness?

    A: Mathematical fairness refers to how fairness is defined precisely using mathematical formalism. Shapley’s brilliance is seen in his approach to creating the Shapley Value in the 1950s. He first translated our notions of fairness into mathematical language, and then, using mathematics, he was able to prove that there is one way to divide credit that is guaranteed to always satisfy all of those notions of fairness. Other ways of dividing credit will satisfy these aspects of fairness some of the time, but only the Shapley Value is guaranteed to satisfy them all of the time. His finding is very important conceptually, but it has also found many applications in business and law.

    Q: You probably played a lot of baseball. How long? What position? And how would you, as a player, fare under your new system?

    A: Yes, I played a lot of baseball, from when I was about 5 or 6 years old up through high school. My oldest memories of baseball are my father rolling me grounders in the alleyway near our house. Given the sheer volume of grounders I fielded as a child, you won’t be surprised to hear that I was an infielder in high school, mostly playing second base and third base but sometimes playing shortstop.

    I had a good eye and got on base at a high rate, so I was involved in a lot of scoring. That means I would have accumulated a good amount of SRC because I would have gotten shares of credit for lots of different runs. But I did not hit home runs, and home-run hitters are the ones who really accrue SRC because you get more credit on a home run. The career leaders in SRC — Barry Bonds, Hank Aaron, Alex Rodriguez, Willie Mays and Babe Ruth, and more —are all home-run hitters.

    Q: Explain how a player could get a negative SRC.

    A: A player can actually get negative SRC if their team would have scored if that player’s action was removed from the inning. … Only about 1% of all innings in Major League Baseball have a player who receives negative SRC, but it does happen and it’s not a fluke.

    Q: You offered an example of a guy hitting a double, and eventually scoring on a sacrifice bunt and a sacrifice fly. You noted that SRC would give all three players equal credit for that run. In other words, the guy who hit the double and the guy who bunted him to third and the guy who flew out to drive the first guy home would all get the same statistical reward, even though 150-plus years of baseball history and common sense suggest hitting the double was the tougher thing to pull off. Why not apportion lower values for actions that don’t require as much skill?

    A: Your instinct is right because hitting doubles takes more skill. But this is precisely the distinction; SRC is not a skill stat, it is a credit stat, and in that inning, the credit should be equal because the contributions to scoring were equal. …  One of the Shapley Value’s fairness properties is that it apportions credit according to the marginal impact a player has on the run scoring, and because each player’s marginal impact was the same in this inning, they each get the same amount of credit.

    If you want to measure a player’s batting skill, then you want a skill statistic, like batting average, slugging percentage, or a newer, fancier statistic. However, a player who hits a lot of doubles will tend to accumulate a lot of SRC because they will be involved in a lot of scoring. So even though SRC is not trying to measure skill precisely, players with better skill will tend to accumulate SRC.

    Q: On the one hand, the SRC model makes me a little crazy. It feels like it gives out a lot of statistical trophies just for playing. But as I think about it, SRC also reflects the notion that cooperation might be secretly more powerful than we realize, an idea that recently has popped up in a lot of seemingly unrelated areas (dog evolution, bees, artificial intelligence). Is that because of what you’ve learned in your work outside of baseball — as an economist and mathematician — teaching the use of game theory in areas like business and politics, etc.?

    A: Definitely. One thing that I have learned from economics and game theory is that there is a lot of collaboration that goes on in society that is behind the scenes, like the hidden workings of a beehive, and that is underappreciated as a result. Experienced baseball players, coaches, and fans are alert to a lot of these on-field contributions, like advancing a runner who later scores, even though they are not accounted for by traditional stats. But because they are not measured accurately, they cannot be appreciated accurately. When I created SRC, I definitely had in mind that I wanted a statistic that would accurately measure these kinds of underappreciated contributions.

    Q: Does your system reveal any hidden superstars, sort of the way on-base percentage shows that recently retired players like Joey Votto and Chase Utley (and long-retired Bobby Grich and Reggie Smith) are probably worthy of the Hall of Fame?

    A: Over the course of a long career, SRC and OSWC tend to tell a similar story as other stats. But one place where my Shapley stats reveal hidden value is in particular games or series.

    For example, Corey Seager of the Los Angeles Dodgers was selected as the World Series MVP in 2020, and there didn’t seem to be any disagreement with that selection. However, my OSWC stat reveals that Mookie Betts should have been selected as MVP.

    In fact, in my book, I show that the wrong offensive player is awarded the World Series MVP about half of the time. Hopefully my stats will be used in the future to help identify who should be given the World Series MVP award.

    Q: How far can your approach be taken in baseball?

    A: It can be taken much further. My book is just about baseball offense, but more recently, I’ve applied my ideas to pitching, that is, to assign credit more fairly to pitchers for runs allowed and outs recorded. The traditional stats like earned runs assign blame unfairly between different pitchers and between pitchers and fielders…

    I’m also working with a collaborator to explore how my new pitching stats can be adapted to bowlers in cricket. So there is still more that can be done in both baseball and in other sports.

    • Michael McBride, an economist and expert in game theory, has...

      Michael McBride, an economist and expert in game theory, has written the book, Game Theory, Machine Learning, and Production in Sports: The Fair-Credit Baseball Statistics (Courtesy of World Scientific)

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    Michael McBride, an economist and expert in game theory, has written the book, Game Theory, Machine Learning, and Production in Sports: The Fair-Credit Baseball Statistics (Courtesy of World Scientific)

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