Posted by Andy on November 6, 2007
A few days ago when I posted about run-scoring by inning, there was a cool blog post written about the length of games in extra innings. Read that one first, then come back here for some more data. To get a nice pool of data, I followed up by summing up all the extra inning games over the last 10 years (1998-2007):
Inning Games Fraction ------------------------------- 10 1998 0.468 11 1062 0.484 12 548 0.489 13 280 0.461 14 151 0.517 15 73 0.425 16 42 0.429 17 24 0.500 18 12 0.750 19 3 0.667 20 1 1.000
I got that data from the PI Team Innings Summary pages. Let's talk about the first two columns. The first one is the inning number, and the second tells you the number of games to reach a given inning. In other words, a total of 1,998 games went to extra innings from 1998 to 2007. Of those 1,998, a total of 1,062 went at least 11 innings, and 548 of those went at least 12 innings, etc. (That's a bit confusing due to the coincidence of talking about 1,988 different games and also the calendar year 1998. Also, just to be clear, the data does NOT say that 1,988 games went exactly 10 innings. It says that a total of 1.988 games went to extra innings since they went at least 10.)
Now, using data from consecutive lines means that we can determine the fraction of games that end after each inning. For example, 1,998 games went at least 10 innings, but only 1,062 went at least 11 innings. That means that of those 1,998 games that went at least 10, 936 ended in 10 innings (or during the 10th inning on a walk-off.) Dividing 936 into 1,998 tells us that 46.8% of games that went to the 10th ended in the 10th.
The third column shown us all those percentages. Looking all the way down the list, you can see that in the last 10 years, there was a 100% chance that a game that went to the 20th inning would end in the 20th inning, as no game has gone to a 21st inning.
Now, if you did your homework and read that external blog post I linked to, you'll know what I mean when I say that the length of extra innings is pretty close to being a geometric phenomenon. You can see that the likelihood of a game going one further inning is pretty constant. Taking a weighted average of the above data yields a factor of 48.4%. This means that at the start of any extra inning, there is a 48.4% chance that the game will end in that inning, and thus a 51.6% chance that the game will continue to the next inning. (These are, of course, average figures for the last 10 years' of game data.)
For a series to be truly geometric, it's necessary for the events of the series to be independent. In this case, it means that the likelihood for a team to win the game in any given inning must be independent of the likelihood for that team to win the game in the next inning. We know that in baseball, this isn't totally true. Let's suppose that a team uses its closer in the 10th inning. There's a reasonably good chance that the opposing team won't score. However, in the 11th they may be forced to bring in a middle reliever, against whom the likelihood of scoring is a lot higher. This means that the likelihood of winning from inning to inning is NOT independent, since the decision of which pitcher to use in one inning affects the decision of which pitcher to use in the next inning. It's also true that different batters will hit in consecutive extra innings, and the likelihood of scoring is not the same.
What does this all mean? Well nothing much, really. Managers still need to make good decisions about use of pitchers, pinch-hitters, pinch-runners, and possible use of sacrifices.