# Tigers Run Distributions

One of my favorite exercises is to examine run distributions. With the All Star Break it gives me a chance to look at where the Tigers rank in terms of runs scored and runs allowed by game.

First up we’ll take a look at the offense and runs scored per game.

To explain the graph, the column height represents the total number of games in which the team scored x amount of runs. The orange represents the number of games the team won and the blue is the number lost. The yellow line shows the cumulative percentage of games played at that run level.

This pretty much reiterates what we already know. The team is rarely shut down completely, and frequently puts a pounding on teams by scoring more than 5 runs in 59% of their games. MLB as a whole has only topped 5 runs in 46% of games.

But what you’ll also notice is that the Tigers need all those runs. Even when scratching out 3 runs, the team only won 4 o f 14 games.

For some context here is the same chart for all of MLB in 2007:

The flip side of course is runs allowed. Here is the Tigers distribution:

Now the other thing we can do with this is look at the distribution, compare it to the winning percentage at various run levels for MLB, and come up with expected win totals.

Working with the run scored distribution and multiplying by the expected winning percentage we see that the Tigers expected record given a normal runs allowed distribution would be 50.1-35.9. That’s pretty close to their actual 52-34 record.

Now of course the Tigers runs allowed distribution isn’t representative of MLB. Performing the same exercise with runs allowed, one would expect the Tigers to have a 42.6-43.4 record given normal run support. So essentially without the strength of their offense they’d be a .500 team. This is hardly earth shattering news in that the bats have clearly been the strength of this team. But it does help to highlight the magnitude that the different components have contributed to the resulting record.

The other thing to note is that on both counts the Tigers record is shy of their actual record. So one could conclude that the team has been a little lucky given the way that things have shaken out. I want to emphasize the little part of luck. If you look at their pythagorean record, they are right on pace with their actual. So this isn’t to say they are doomed or aren’t a good team. I also wouldn’t call this predictive, but simply a record of what has happened so far.