Geeking out on Suppan as "#1 starter"

It's official: Suppan is starting on Opening Day.

So, at least for a little while, Suppan will line up against other teams' #1 starters, and our #1 starter (presumably Gallardo) will go against guys further down in their teams' respective rotations.

This has generally provoked consternation--after all, Suppan is no one's ideal #1 starter, even for the {choose one: Royals, Pirates, Nationals, Orioles}.

However, my intuition told me this might be a smart move.  I haven't really thought through the comparison, but it's similar to the somewhat counterintuitive finding that inconsistent starters are better than consistent ones, if we're comparing guys with average performance. 

So I figured I'd drastically oversimplify the situation and run a monte carlo simulation to see what happens.

I'm going to walk through it step by step, but if you don't care about the process, just skip down to the boldface clause below.

First, let's assume that other teams line up their rotations in the typical fashion, and that our rotation lines up 5-1-2-3-4.  (It doesn't matter at all whether I have the right order of 1-2-3, as we'll see in a moment.)  Thus, every five games will look like this:

(Brewers SP vs. Opponent SP)

  • game 1: #5 vs. #1
  • game 2: #1 vs. #2
  • game 3: #2 vs. #3
  • game 4: #3 vs. #4
  • game 5: #4 vs. #5

Next, let's come up with a distribution of possible outcomes.  Again oversimplifying, let's pretend every #1 starter is equal, every 2, 3, 4 starter is equal, and every 5 starter is equal:

  • #1 starter: equal chance of 1, 2, 3, 4, or 5 runs.  (3.00 ERA)
  • #2, 3, 4 starter: equal chance of 2, 3, 4, 5, or 6 runs.  (4.00 ERA)
  • #5 starter: equal chance of 3, 4, 5, 6, or 7 runs.  (5.00 ERA)

Notice we're ignoring the effect of the bullpen.  While those ERAs may be in the ballpark, having the same bullpen every night is going to bring the end result closer together.  We're going to ignore that, because I don't want to write more than 30 lines of code.

From here on out, it's simple.  We're going to go through the 5-game sequence listed above, randomly pick one of the five possible outcomes for each of the two pitchers, and see who wins.  (Of course, there will be a lot of ties -- in those cases, we'll award half a win to each team.)

Running through the sequence 1 time (or even 1,000) doesn't give us a very good picture, since the rotation sequence doesn't have a very strong impact, and in a small number of runs, the results could simply reflect good or bad luck.

So I ran through the 5-game sequence two million times.  In both the first million and the second million (the first million, of course, was the hardest), the team that used the #5 starter in game 1 won about 50.8% of the time.

Of course, if these hypothetical rotations matched up in the typical 1 vs. 1, 2 vs. 2 fashion, each team would win exactly 50% of the time.

My friends, Macha is crazy like a fox. 

As noted, I've drastically simplified.  Of course 2, 3, and 4 starters aren't equal, and of course no team will stay exactly on schedule all season long.  (Even if they did, their 5th, 10th, 15th, etc., games wouldn't necessarily match up with ours.)  Not every team has 1, 2, 3, 4, and 5 starters equal to ours.  And of course, the Brewers will not give up exactly 3, 4, 5, 6, and 7 runs in equal numbers of Suppan's starts.

But the simple exercise gives us some insight into the result of the more complex real-world scenario.

The one thing I can think of that would negate the benefit would be the possibility that the "true" #1 (Gallardo) might end up with one or two fewer starts.  That might not be the case (depending on off days), and it might be ok (if Gallardo's innings were to be limited anyway).  But 50.8% probably means only one or two extra wins over the course of the season, and one fewer Gallardo start in favor of Suppan could well mean the opposite.

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