The Tigers can win the division with a bad starting rotation

There are a lot of ways to rank the five teams in the American League central that are fighting it out for a division title this year. You can rank them by offense, by starting pitching, by a combination of several statistical factors, by betting odds, by Pythagorean Expectation, and so on. The following table shows how each of those teams ranks according to a few different metrics. Not surprisingly, the Royals lead the pack by the majority of measurements, and the White Sox are most frequently found at the bottom of the list.

One thing jumps out immediately: the Royals have the largest run differential, even though it's the Tigers who lead the Central in average runs scored per game. The deciding factor, of course, is that the Royals have the lowest amount of average runs allowed per game, while the Tigers are giving up the most runs per game out of any other team in the division. This does not compute, because the Royals have a division-worst starting rotation when measured by ERA or FIP. Obviously, the Royals have the best defense in MLB, but still ...

So how does a team like the Royals, with only the second best offense in terms of runs scored per game, and the worst starting rotation in the division, still end up with the highest run differential? The answer, I believe, lies in the quality of the bullpens of each team. The trouble with a statistic like ERA is that it represents the average number of runs allowed per game over nine innings. If Royals starters were always allowed to pitch all nine innings, they would be closer to allowing 4.4 runs per game, but in fact, the team leads the division in only allowing 3.6 runs per game.

How?

Because the Royals starting rotation pitches the fewest number of innings in the division.

The corollary is that their bullpen pitches more innings than any other bullpen in the AL Central, and, as everyone knows, the Royals bullpen is one of the best in all of baseball. Here is a breakdown of how much each team uses their starting rotation and bullpen.

To sum it up so far: the Royals have the worst starting rotation in the division, but the lowest usage of that rotation; the Tigers starting rotation is ranked close to second-worst in the division, and they also use that rotation longer in games than every other team except the White Sox. (At least the White Sox can claim to have one of the better rotations in the division, judging by ERA and FIP. It's their division-worst offense and defense that seems to sink them.)

We are in a position, then, to recalculate the ERA of each team's starting rotation based on how many innings the starters are actually pitching, instead of basing it on a nine-inning spread, and then factor in the affect of each team's bullpen.

And just like that, the Royals starting rotation is second-best in the division, and their pitching overall is the best in the division in terms of runs allowed per game.

As an added exercise in rounding out the numbers, we can take the cumulative runs scored per game by each team's opponents (American League only) and combine that with the pitching totals to get an adjusted average of runs allowed per game, then apply the Pythagorean Expectation formula to project a total number of wins and losses by the end of the year.

And that, apparently, is how you can win a division title with one of the worst starting rotations in your division.

Now the question becomes: do the Tigers need better starting pitching at the trade deadline, or could they accomplish the same task by strengthening the bullpen? Which position(s) can be filled more easily?