There has been a lot said recently about the playoff system in Major League Baseball, and how the two teams in the World Series are not really the best teams in baseball. Some fans enjoy the high stakes playoff games where the entire season is on the line. Other fans prefer “fairer” scenarios where each team needs to play 1,000 regular season games to get the best representation of who has the best team.
A much stranger scenario is outlined in The Science of the Playoffs by Sky Andrecheck. Complicated scenarios are created to match a team’s playoff odds with how that team performed in the regular season to create a more just playoff system. For instance, if a team has a regular season record that indicates it has a 60% chance of being better than the team they are matched up against, they should be awarded a playoff scenario where they have a 60% chance of advancing. Although the sample sizes are small and do not give an ultimate answer to which team is better, this approach offers a “fairer” post-season solution based on a team’s regular season record. I decided to take this idea and run with it by figuring out if the Kansas City Royals’ postseason run exceeded the initial probability that their regular season record demonstrated of being the best team in the AL.
To determine the probability that one team is better than the one they are facing in the playoffs, I compared each team’s win total using a binomial distribution with unknown true win pcts (p in Binomial Distribution), but known win totals (k in Binomial Distribution). If a team is the better team, then their win pct would be better than the team they are up against. The probability that Kansas City is better than another team can be found by summing all possible probabilities where Kansas City has a particular win pct and the team they are facing has a lower win pct. The math behind this method is shown below comparing Kansas City to the Oakland Athletics. The same formula was also used to determine the probability that the Royals were better than the Angels and Orioles.
Additionally, I use the impact of home-field advantage in postseason calculations as giving the home team a 51% chance of winning an evenly matched series taken from here.
Going into the wild card playoff game, the Royals had only one more regular season win than the A’s. The regular season predicted that the Royals were the better team with a probability of 51.5%, slightly better than even money. Since the Royals were given home field advantage, they were awarded a probability of advancing close to what their regular season record demonstrated. The Royals won the game, fairly confirming that they should move on to the American League Division Series.
Next up for the Royals were the Los Angeles Angels. The Angels had a regular season record of 98 wins, much better than the Royals’ 89 win total. With this disparity in win totals, the Royals only had about a 14% chance of being the better team based on both teams’ regular season records. However, taking three out of three games from the Angels, two in Los Angeles and one in Kansas City, has about a 12% chance of happening if both teams are evenly matched. So, if the Angels were better, the probability of the Royals winning all three games would be even lower. The sweep exceeded the Royals’ initial probability of being better than the Angels, once again fairly pushing the Royals forward into the ALCS.
In the American League Championship Series, the Royals played the Orioles. The Orioles won 96 games, giving the Royals only about a 20% chance of actually being the better team. The probability of sweeping the Orioles in the ALCS if both teams were evenly matched was about 6%. Here, the Royals far exceeded their regular season odds of being considered the better team.
The odds of the Royal sweeping the entire American League in the playoffs exceeded the probability that the Royals were the best team. In other words, it was totally fair that the Royals won the AL pennant.
recent Binghamton University Bioengineering graduate, avid Mets and Knicks fan.