January 22, 2016

BP Unfiltered

How Greinke vs. Arrieta vs. Kershaw Played Out

by Tom Tango

This is Part 2 of my analysis of the IBA voting. Readers are encouraged to read Part 1 first.

When we have two strong candidates, a first-past-the-post system likely makes the most sense. We don't want a system that allows the much lesser candidates to have additional voting impact. We saw this with the Trout-Donaldson race, where any individual voter could decide to give these two players a small gap in points, or a large one, by simply omitting a player from the ballot altogether. Each vote did not count the same. For those interested, I go into more details of this on my blog.

Sometimes, when you have three strong candidates, a first-past-the-post system might not work out the best. There might be a situation where Candidate A is preferred to B who is preferred to C who is preferred to A. You can get into a situation of near deadlock, and the tight race that knocks out the (slightly) least of the three transfers a great deal of support to one of the other two. While we didn't get that in the NL Cy Young, it did have that potential.

You might think of Trump, Cruz and Rubio on the current political scene, where in a head to head, Trump might be preferred to Kasich, Kasich to Rubio, and Rubio to Trump (just a potential illustration). Depending which of the three you knock out, it'll give us a different winner.

First, I'll present the first-past-the-post, with the instant-runoff method I discussed in Part 1. Only four candidates were named on at least 50 percent of the ballots. Here was how often they finished in first place, after we knocked out all the other candidates:

• 131 Kershaw
• 126 Arrieta
• 75 Greinke
• 3 Scherzer

Scherzer gets knocked out, and his 3 votes go to Kershaw (1, now at 132) and Greinke (2, now at 77). First-past-the-post is 168 votes. Therefore, the 77 votes of Greinke becomes the key. Where did they go? 51 went to Arrieta and 26 went to Kershaw. The final tally:

• 177 Arrieta
• 158 Kershaw

In a clear head-to-head battle, Arrieta was preferred over Kershaw, getting 53 percent of the votes.

How about if we looked at Kershaw and Greinke? In that case, it was 184-150 Kershaw over Greinke, for 55 percent of the votes for Kershaw. Finally, how about Arrieta and Greinke? That one was lopsided 213-121, with Arrieta getting 64 percent of the votes.

If we did have a situation of Arrieta beating Kershaw beating Greinke beating Arrieta, then we'd simply average out their head-to-head results. While we don't find this kind of paradox among these three pitchers, we'd likely be able to find it among another set of three pitchers or players elsewhere on the ballots. It's fascinating to consider the different kinds of ways to rank votes, when the number of candidates is more than two.