# Momentum in Baseball: Do Ninth Inning Rallies Carry Through Extra Innings?

by Ben Blatt

In January, John published on our HSAC blog ‘Momentum in College Basketball: Do Late Rallies Carry Over to Overtime?’. As you can probably tell by the title of this post, I was inspired by his research to see if the statistically elusive concept of momentum could possibly apply in baseball. Specifically, do teams that come back to tie the game in the ninth inning do better than expected in extra innings?

All games between 1980 and 2010 in which the game was tied in the ninth inning, a total of over 2300 games, were included in the data set. When the home team blew the lead in the ninth, it won in extra innings 53.1% of the time. When the home team came back in the ninth, it won in extra innings 53.8% of the time.

Just looking at those summary statistics does not give us enough information to confirm or dismiss the notion of any extra inning ‘momentum’. The individual game probabilities would need to be known. Luckily, fellow HSAC members have already looked into this problem in the paper ‘Predicting Overtime with the Pythagorean Formula’ which was published in the Journal of Quantitative Analysis in Sports in 2010.

The paper uses the concept of Pythagorean expectation, usually used to predict the number of wins over the entire course of a season based on runs scored and runs against, and applies it to individual extra inning games while making appropriate adjustments for home and away games (the paper also covers NFL and NBA overtime games). Using the values that were found in the paper, a probability of the home team winning each game once it reached extra innings was calculated.

The game probabilities were then used to simulate the games in question a total of 100,000 times, more than enough to get an accurate distribution of how many games the team with ‘momentum’ would be expected to win. The median of the simulation showed that the team with ‘momentum’ should have won 1157 of the games while in reality they won 1167. However, the simulation showed this difference was not nearly enough to be statistically significant at the .05 or even .1 level. Therefore, we cannot reject the null hypothesis that momentum does not exist in baseball showing yet another example where momentum in sports is most likely non-existent.

#### harvardsports

View all posts

• Interesting. Would you have that broken out by deficit overcome/lead relinquished?

• Ben Blatt says:

Over 60% of the games were only one run leads and a bit over 10% were games where the lead was three of more. I ran the simulation again on games where the lead was at least two and then once more on games where the lead was at least three. In both these cases, the results still showed the difference was not significant.

• How did you simulate the games in question? And why not run more than 100k sims?
vr, Xeifrank

• Ben Blatt says:

Thanks for the questions!

Each game’s individual odds were found based on the factors of team runs scored, runs against, and home/away. Finding these odds are explained explicitly in the paper ‘Predicting Overtime with the Pythagorean Formula’.

Once these individual probabilities are found, the simulation is virtually like simulating a series of coin tosses. Simulating each game and then summing the amount of ‘wins’ for the team with ‘momentum’ was one trial. Simulating 100k trials is arbitrary, although I just ran it again with 10k trials and the most that either the 5th,25th,50th,75th,or 95th quantile differed from the original simulation was one game. This suggests that 100k is more than sufficient to form an accurate distribution.