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The MLB Coin-Flipping Contest

What are the chances that wild-card teams will make it to the World Series and win?

“Let me tell you sonny, how it used to be in the good old days.” Is there anything worse than what Bruce Springsteen called “boring stories of glory days”? He goes on, “I hope when I get old I don’t sit around thinking about it but I probably will.”

Well, this year’s World Series brought back memories of the glory days when there were two Major League Baseball leagues — the American League and the National League — and the regular season winners of each league met in the World Series. Now, each league has three divisions (East, Central, and West) and a complicated sequence of playoff games that involves the three division winners and three wild card teams in each league and pushes the World Series into November, so that it is possible that the Boys of Summer will be playing for the championship in near-arctic conditions.

Even worse, the teams with the best records often don’t even get to play in the World Series. As I wrote last year, there is a LOT of luck in baseball:

Batters have to decide in a quarter of a second or less whether and how to swing at a ball traveling 90+ miles an hour and possibly swerving at the last moment. Even if the ball is hit, the slightest difference in how that slender rounded bat hits that small round ball can make the difference between weak and solid hits. Even if the ball is hit solidly, it might go directly at a fielder or in between fielders. Even if the ball is hit weakly, it might be an easy popup or a bloop hit. A weak dribbler might stay fair or roll foul. Ground balls bounce off pebbles; fly balls are blown by gusts of wind.

Baseball, Life, and the Mediocrity Magnet | by Gary Smith | Medium

In short 3-, 5-, or 7-game series, we may as well flip coins to determine the winning team. In 2021, there were eleven post-season playoff series. The team with the better regular-season record won five series; the underdogs won six series. There were 40 games in these playoff series and they split evenly with the favored team winning 20 games and the underdog team winning 20 games. The year before, there were nine post-season series. One was a single-game play-off between the Red Sox and the Yankees who had identical 92–70 regular season records. In the other eight series, the team with the better record in the regular season won four series and lost four. Looking at individual games, the team with the better regular season record won 18 games and lost 18.

Here are the regular season records this year for the 12 teams that qualified for the post-season playoffs:

                                                                             Record                  Fraction Won

        American League

              East                          Baltimore                101-61                        0.623

              West                         Houston                    90-72                        0.556

              Central                     Minnesota                 87-75                        0.537

              Wild Card                Tampa Bay               99-63                        0.611

              Wild Card                Texas                        90-72                        0.556

              Wild Card                Toronto                     89-73                        0.549

        National League

              East                          Atlanta                    104-58                        0.642

              West                         LA Dodgers            100-62                        0.617

              Central                     Milwaukee                92-70                        0.568

              Wild Card                Philadelphia              90-72                        0.556

              Wild Card                Miami                       84-77                        0.522

              Wild Card                Arizona                     84-78                        0.519

One anomaly this year is that Seattle, which is in the American League with a record of 88-74 (0.543), didn’t qualify for the playoffs even though it had a better record than the Central Division winner, Minnesota.

In the “good old days,” Baltimore would have played Atlanta and the World Series winner would have been one of the best teams in baseball. Now with the seemingly interminable playoffs that have been created for no good reason other than to increase revenue, neither Baltimore or Atlanta was guaranteed to make the playoffs. That is, of course, exactly what happened. Texas, the sixth-seeded team in the American League will be playing Arizona, the seventh-seeded team in the National League.

I wondered what the chances are that wild-card teams will make it to the World Series and win the World Series. I suspected that they were high. After all, the best teams in the regular season only won a bit more than 60% of their games, and that was playing against a lot of mediocre and bad teams. When a team with a 60% winning record plays a team with a 55% winning record, it no longer has a 60% chance of winning. We are getting very close to coin flips.

I made a simple model (I will send you the details if you email me) that guesstimates the probability that a team with an X% winning record will win a game against a team with a Y% winning record. This model ignores the fact that starting pitchers have different abilities, home-field advantage (if any), and other complicating factors. Some examples of the model’s implications: A team with a 60% winning record has a 50% chance of winning a game against another team with a 60% winning record, a 55% chance against a 55% team, and a 60% chance against a 50% team.

I then used the regular season records of the 12 teams that made the playoffs in 2023 and simulated all of the playoff games using the MLB playoff structure:

               Wild Card series, best of 3

                       a. Third-seeded division winner plays third-seeded wild card team

                       b. first-seeded and second-seeded wild card teams play each other

               Division series, best of 5

                       c. first-seeded division winner plays winner of (b)

                       d. second-seeded division winner plays winner of (a)

               League Championship series, best of 7

                       winner of (c) plays winner of (d)

               World Series, best of 7

                       winners of American League and National League championship series

These are hypothetical calculations that might have been done before any of the results were known. The results were consistent with my expectations. The probability that an American League wild-card team would be in the World Series is 0.35. The probability that a National League wild-card team would be in the World Series is 0.16. The National League probability is somewhat lower because there were two really good teams (Atlanta and LA) and the wild card teams were not as good as those in the American League.

My model gave a 0.22 probability that a wild card team would win the World Series. (Of course, with Texas playing Arizona, we are guaranteed that a wild card team will win this year.) I imagine that the probabilities of wild card teams making it to the World Series and winning the World Series in any specific year are comparable to these numbers.

They say that love of money is the root of all evil. For this old timer, MLB’s love of money has turned the post-season into little more than a drawn-out series of coin flips that pretty much any team can win and has little or nothing to do with identifying the best teams that year.

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 MLB Coin-Flipping Contest