Non-voting Explained Using... Baseball?
Originally published at Kyle Boddy dot com. You can comment here or there.
In baseball, there's an axiom that is oft-repeated by announcers, managers, players, and the common fan: Pitching and defense wins championships, or Good pitching beats good hitting. Is it true, or is it another stupid catchphrase that means nothing?
Actually, there's a modicum of truth in the statement. To explain why, you have to understand what the Pythagorean Theorem of Baseball is. It simply states that the expected winning percentage of a team can be expressed in a simple forumla:
Winning % = RS^1.83 / RS^1.83 + RA^1.83
(The actual exponent is subject to the run environment of the league, but let's just use 1.83.)
It's surprisingly accurate. For example, the 2007 Detroit Tigers scored 887 runs and allowed 797, which would give them an expected record of 89-73. Their actual record? 88-74.
Teams routinely underperform or overachieve their Pythag expected wins; this is often due to timely high-leverage bullpen support (which is subject to major fluctuations due to sample size) and/or a disproportionately high winning percentage in one-run games (which, for most teams, runs very close to .500 and is subject to quite a bit of luck). For example, the 2007 Arizona Diamondbacks had an expected record of 79-83. They actually went 90-72, which is absurdly lucky. But, over time, the expected winning percentage is a better indicator of both the team's true talent level and how they will do in the next year.
(We're getting to politics. Eventually.)
So, back to the axiom in question - does good pitching beat good hitting? Assume a team scores 800 runs and allows 800 runs. Their expected winning percentage is - perhaps unsurprisingly - 50%, or 81-81.
Winning % = 900^1.83 / 900^1.83 + 900^.183
= 254838 / 254838 + 254838
= 254838 / 509676
= .5 or 50%
Say the team in question has the choice of adding 50 runs or preventing 50 runs. Which option should they choose? I think you see where this is going.
Winning % (+50 runs) = 950^1.83 / 950^1.83 + 900^1.83 = 281341 / 281341 + 254838 = 281341 / 536179 = 52.47%
Winning % (-50 runs) = 900^1.83 / 900^1.83 + 850^1.83 = 254838 / 254838 + 229528 = 254838 / 484367 = 52.61%
That's a difference of 0.14%, or roughly a quarter of a game. Using the standard equation of 10 runs = 1 win in baseball, that's basically an increase of 2.5 runs, which could swing the difference in a few key games. Therefore, it is true - good pitching and defense is slightly more important than scoring more runs. It's not insignificant. *
Now, how do we relate it to elections? Awhile back, someone claimed that I supported Bush because I didn't vote for Kerry. When I told him he was an idiot, he insisted he was right. I then told him that I convinced at least 5 people not to vote for Bush and instead not vote, and asked him if that was good enough. He said no, unless I voted for Kerry, that I hadn't done all I could do to stop Bush from being president.
First of all, it's plainly clear to all of you with a brain that this guy is stupid. Not supporting Kerry != Supporting Bush. I won't support a candidate that does not share my critical views, ever. Keeping that in mind, have I done greater good for the world by convincing 10 people to not vote for Bush rather than convincing 10 undecided voters to vote for Kerry?
(Assume that it is impossible to convince people who would vote for Bush to rather vote for Kerry and vice versa.)
Given: 100 people are voting for Bush or Kerry, split in half. 50 will vote for Bush, 50 will vote for Kerry. That's a split of 50%, or a ratio of 1:1.
Scenario: I convince 10 people to vote for Kerry. 60 people vote for Kerry, 50 vote for Bush. That's a ratio of 6:5, or 54.54% for Kerry, 45.45% for Bush.
Scenario: I convince 10 people who would normally vote for Bush to instead vote for no one. 50 people vote for Kerry, 40 people vote for Bush. That's a ratio of 5:4, or 55.56% for Kerry, 44.44% for Bush.
By convincing 10 people not to vote for Bush, I improved Kerry's percentage win by a full point. You might say that the difference is the same in 10 voters deciding, but you'd be wrong - not only does Kerry's percentage win go up, but a lower total number of votes (90 to 100, in this case) produces higher correlation, meaning that Kerry would benefit from a better chance to win. If you don't understand that, you might want to google some basic ideas about markets and/or sportsbetting that explains lower totals producing higher correlation, or envision bags of 50:50, 60:50, 50:40 ratios of white and black marbles. If you pick 10 marbles ('deciding votes') from each bag, which ratio will produce higher correlated and higher numbers of the given marble with the edge?
So, in summary, the fact that I convince conservatives to stay home instead of voting for the Republican of choice should make liberals happier than me going out and supporting their idiotic socialistic candidate. And yes, my arguments typically only work on conservatives, because they have a higher tendency to logically understand what I'm saying.
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* If you think 0.14% is insignificant, guess what? You just proved that your singular vote (and the votes of everyone you know) is worthless. Congratulations.