The WGOM

Sharks vs. Piranhas Part II

August 12th, 2007 by GreekHouse

For any of you who have not yet read part I of the story, I recommend reading it first. I won't bother to reintroduct the two teams here, so you will need to at least look at part I before reading this. I had intended to include slumps in part 2, but in an effort to keep this a reasonable length, I will make that part 3 of this article. There is still plenty here for discussion!

As mentioned in part I of the article, the Sharks will win 54% of the time. This includes winning 48% of the time without going to extra innings. A little over 10% of the games will be tied at the end of 9 innings and go into extra innings. Conventional wisdom would suggest here that the Piranhas would hold a slight edge in these extra inning games due to their non-reliance on the long ball. Not so! If you understand the basic concepts from part I, it should be clear that the Sharks will hold an edge here as well. Not only do they hold the edge in extra innings, but they will win a whopping 60% of extra inning games! The Piranha's problem is exacerbated here. Their distribution of runs is even worse since they still are scoring too many of their runs in bunches. The Sharks will fail to score in about 63% of all inning. So as you might expect, we would prefer to score a single run at the expense of having bigger innings. The Piranhas will fail to score in about 75% of all innings. Because of this difference, the Sharks will have a dominant edge in extra inning games.

But these are Piranhas after all, what if they decide to start playing some small ball? Unfortunately, they never double, so hitting a leadoff double and bunting the runner to third is out of the question. The only strategical decision they can make is to try and bunt the runner over to second after a leadoff single. Let's say that the Piranhas adopt the strategy of bunting the runner over after a leadoff single and because they're proficient at bunting, they will be able to move the runner to second this way with a 90% success rate. Further, we will assume that when they fail, they will fail in the best way possible--by ending up with a runner still at first and 1 out. We will ignore the minute possibility of a bunt single since the Sharks will be expect a bunt in this spot and ignore the possibility of a double play because of the Piranha's speed.

It turns out this is a reasonable strategy for the Piranhas, but it's not good enough. This will drop the Shark's winning percentage from 60% to just under 58%. It is also worth noting that this strategy reduces the Piranha's run expectation from 4.5 R/9 to 4.0 R/9--making it a terrible early game strategy. What the Piranha's are able to do with this strategy is to smooth their distribution of runs slightly at the expense of overall expectation. The most consistent way to score runs however is by simply hitting the ball over the fence.

The key point to be made here is that the Sharks are playing baseball in a way that optimizes their distribution of runs scored. In extra innings, we really only need to score one run to win and the Sharks are playing baseball in a way that maximizes the ability to do so. Now consider any other team that scores 4.5 R/9. If the team does not score 100% of it's runs off of home runs, it will occasionally leave runners on base. Because they are leaving runners on base, they will have to compensate by having more high scoring runs than the Sharks. Thus, it doesn't matter what a team does. If it is not scoring 100% of its runs on home runs, it can never perform as efficiently as the Sharks and will never be able to win more than 50% of the games against them. This applies not only to sacrifices, but to extra base hits, stolen bases, or anything else you can think of that do not increase overall run expectation.

It is possible to come up with a distribution that can beat the Sharks. One such distribution would be a team that scores either 0 or 1 runs per inning each with a 50% probability (we'll call this an ideal team). However, such a distribution is outside of the bounds of what is possible in a baseball game. The Sharks distribution is optimal in this sense. The worst possible distribution that a team could have would be if it generated all its runs from walks. They would need 4 walks in an inning before they started scoring runs. This is the theoretically worst distribution since it maximizes the number of runners left on base (although in practice this team would be very good at wearing down the opposition's pitching staff).

Below are some tables of how the different teams match up. (Percentages listed are the winning percentages of the teams on top)

All teams (with the exception of the bunting piranhas) average 4.5 R/9. The results are exactly as you would expect. The teams that leave fewer runners on base do better. The bunting piranhas tend to do slightly better in single inning (extra inning) contests due to their ability to sacrifice some run expectation in exchange for a flatter distribution, but they get killed in 9 inning games for the same reason.

This entry was posted by GreekHouse on Sunday, August 12th, 2007 at 11:03 pm and is filed under GreekHouse, MLB, Minnesota Twins. It is one of 44 entries by the author. We are no longer accepting Letters to the Editor on this post.