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Vintage baseball on a weathered American flag

The World Series of Coin Flips

Here we go again with the annual coin-flipping ritual known as the World Series
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There is undeniably skill in professional baseball. Aaron Judge, Bobby Witt Jr., Shohei Ohtani, and Gunnar Henderson are great baseball players but they might hit 1, 2, or 3 home runs in one game and strike out just as many times in the next. For the 162-game 2024 season, they batted .322, .332, .310, and .281, respectively, which means that they made outs twice as often as they got hits.

person holding baseball ball in black leather baseball mitt

Sometimes, a batter guesses right on a pitch and hits a home run; other times, he guesses wrong and looks silly, flailing at a badly missed ball. Sometimes, a line drive goes right to a fielder; other times, a line drive goes where fielders can’t catch it. Sometimes, a weakly hit ball is caught easily; other times, a blooper drops for a base hit.

The same is true of teams. The Chicago White Sox lost three-fourths of their games this year, the worst record in modern baseball history, but they did win 41 games—including a 12–2 thrashing of the mighty New York Yankees.

The difference that luck makes

The importance of luck in baseball is why the outcomes of 3-game, 5-game, or even 7-game post-season series seem more like coin flips than true tests of ability.

Shortly before the 2019 World Series between the heavily favored Houston Astros and the underdog Washington Nationals, I wrote that,

The Astros are one of the 10 best teams this season (along with the Yankees, Tampa Bay, Minnesota, Cleveland, Oakland, Atlanta, Washington, St. Louis, and the Dodgers), but who would win a 7-game series between any two of these teams? Your guess is as good as mine — perhaps better — but it is still only a guess.

I suggested an analogy to coin flips:

Suppose that the Astros have a 60% chance of winning any single game against the Nationals and the Nationals have a 40% win probability. These probabilities are generous for the Astros because they only won 66.0% of their games during the regular season, playing against average teams, and the Nationals won 57.4% of their games… Even with this generous assessment of the Astros, it turns out that there is a 30% chance that the Nationals will be World Champions. If the Astros have a more plausible 55% chance of winning each game, the Nationals have a 40% chance of popping the champagne.

That is the nature of the beast. In a game like baseball, where so much chance is involved, … the best team often loses, and winning the World Series tells us very little about which team is really better.

I reminded readers of the great 1969 Baltimore Orioles team that lost the World Series, four games to one, to the consistently mediocre New York Mets, and the powerful 1990 Oakland A’s team that lost the World Series in four straight games to the far-less-talented Cincinnati Reds.

I didn’t predict the winner of the 2019 World Series. Who would be foolish enough to predict coin flips? My point was that predicting World Series winners is very much like predicting coin flips. As it turned out, the Nationals won the 2019 World Series, defeating the favored Astros, four games to three.

The paradox of luck and skill

Luck is even more important in the playoff series that determine the teams that will play in the World Series because only one of the playoff series is best-of-seven. The rest are best-of-three or best-of-five. Not only are the playoff series too short to tell us much, if anything, about the relative abilities of the teams but the teams are generally so evenly matched that we have the paradox of luck and skill: In any competition where luck plays an important role, the more skilled the competitors, the more the outcome is determined by luck. If the Yankees were to play my son’s high school baseball team, they would surely win almost every time. When the Dodgers played the Mets in this year’s playoffs, they won the first game 9–0, lost the next 7–3, and won the next game 8–0.

Baseball with good luck sign are on green grass

I wrote about the paradox of luck and skill in baseball before the 2022 World Series between the Houston Astros and the Philadelphia Phillies, who were a 6th-seeded wild-card team that won enough coin flips to qualify for the playoffs. The 2023 World Series was even wilder: the two teams that made it to the World Series were the Texas Rangers (which tied with two other teams for the 6th best regular-season record) and the Arizona Diamondbacks (which had the 13th best regular-season record).

The table summarizes the playoff results over the last four years (2020 was a COVID-shortened season), with the team with the better regular season record considered the favorite. (The 2023 playoff series between Texas and Houston was omitted because they had identical regular season records.) Overall, even though the favorites had home-field advantage, the underdogs won 22 of 37 playoff series and 75 of 137 playoff games. The underdogs were unusually lucky in 2023, but that’s the nature of coin flips.

                                                 Playoff Series                                  Playoff Games

                                            Favorites        Underdogs                 Favorites            Underdogs

              2021                             4                      4                              18                         18     

              2022                             4                      6                              16                         18

              2023                             2                      7                               9                          20

              2024                             5                      5                              19                         19

              Total                           15                    22                             62                         75

This year, the playoff results were perfectly balanced: the favorites and underdogs each won 5 series and each won 19 games. Despite this, the impending World Series is unusual in that the two teams that survived the coin-flipping gauntlet happened to be the teams with the best regular season records in the American and National leagues: the New York Yankees (94–68) and the Los Angeles Dodgers (98–64). On the other hand, in a best-of-five series, the Dodgers barely squeaked by the San Diego Padres, 3 games to 2, and the Dodgers’ 4–2 series with the Mets was notable for the lopsided victories by both teams — hardly consistent with scores reflecting ability.

With the Yankees and Dodgers so evenly matched, this World Series will surely reflect the paradox of luck and skill and be even more assuredly similar to a coin-flipping contest. If they played 100 times, each team would probably win close to half the games. In a 7-game series, there has to be a winner, and there will be one.

Just as surely, when the World Series is over, no matter who wins, one team will be labeled “champion” and we will be told that so-and-so “got hot,” so-and-so “came through in the clutch,” and so-and-so “choked” — when a more apt description might be that one team had more lucky coin flips than the other.


Gary N. Smith

Senior Fellow, Walter Bradley Center for Natural and Artificial Intelligence
Gary N. Smith is the Fletcher Jones Professor of Economics at Pomona College. His research on financial markets statistical reasoning, and artificial intelligence, often involves stock market anomalies, statistical fallacies, and the misuse of data have been widely cited. He is the author of dozens of research articles and 16 books, most recently, The Power of Modern Value Investing: Beyond Indexing, Algos, and Alpha, co-authored with Margaret Smith (Palgrave Macmillan, 2023).

The World Series of Coin Flips