I was curious about the chances playoff teams have of getting to the Bambino Cup Finals and their chances of being crowned ABL champions. The playoff structure itself has a big impact, for example, the division champions have shorter roads to the cup. Of course, the relative strength of each team is very important, but how can that be measured?
First, let’s consider the playoff structure in isolation. Assume that all playoff teams have equal strength. If that’s the case, then the chance of winning a game or a series is 50%, a coin flip. A division champ (C-Bay or Orlando) has to win two series, so they have to flip a coin twice and have it come up heads both times. That’s one chance in four, 25%. A team with a one-game showdown to get into the lower bracket (LBI or Manahawkin) has win four series. The chance of having heads come up four times in a row is only one in 16, 6.25%. The probabilities of the 2012 playoff teams winning the ABL Championship under these conditions are shown in the table below.
Now let’s look at team strength: how to measure it, and how to use it to determine the probability of winning a game and a series. Bill James applied some statistics to the question of how to measure the probability of one team beating another in one game. He called it log5, and it uses winning percentage to measure team strength. I’ll use the ABL regular-season winning percentages for this exercise.
The log5 method works for one game, but what about a best-of-five or best-of-seven series? Well, there are formulas for that too. So now we can use these formulas to calculate the probabilities of teams reaching the finals. Three pages of scratch paper later…
Quite a spread, isn’t it?
One more series of calculations (and three more sheets of paper) gives the ultimate probabilities of teams getting their name on the hardware in 2012.
A superior winning percentage sure indicates a big advantage in the playoffs. Of course, this is simply a cold calculation based on only the playoff structure and the teams’ winning percentages. Among the factors this calculation does not take into account are:
- Home-field advantage
- Changes in team strength due to trades & injuries
- Runs scored & runs allowed
- Picther/batter match-ups
- Strength of three-man rotations
- Loaded dice