Blargh Blog

Saturday, October 02, 2004

Replacement Level President

A lot of people out there are saying that the person who they want to be president is Anybody But Bush. But what does that even mean? ABB is not a person but a category mistake. And do they really mean "anybody"? Some more contentious people might even wonder, would these people vote for Hussein and bin Laden over Bush? Would they vote for an infant? These last two questions, however, are red herrings, as Saddam Hussein, Osama bin Laden, or an infant could not even run for office if they wanted to, since the first two are not citizens of the United States and the last is under 35 years of age.

The real question is, what could ABB mean? The best answer, as is so often the case, comes from sabermetricians (sports statisticians). People interested in baseball often wonder about things like "what is the value of this second baseman?" Then the people who do sabermetrics try to come up with a way to answer them. You could compare his performance to the average performance by second basemen in the league, but even if he's below average that doesn't mean that he's worthless. After all, half of all baseball teams field below average second basemen. That's just what "average" means. A team that loses its below average second baseman may still suffer because they'd have to replace him with a player who is far enough below average that he hasn't been starting on any team.

That's why the sabermetricians came up with the idea of a replacement level player. A replacement level second baseman has the statistics that you would expect of a player who replaced your second baseman (assuming that you didn't acquire some other team's starting second baseman). Here "expect" is a technical term, meaning, roughly, that it's the average performance of all replacement second basemen. So, a second baseman's value over replacement is the number of runs that he brings to his team minus the number of expected runs that a replacement second baseman would bring. That's the general idea, at least. The precise, statistical definition can be a bit tricky to work out, but we don't have to worry about that here.

They use the "expected value" of a replacement second baseman rather than the actual abilities of the backup second baseman on that team, because they're trying to say something about the starting second baseman that is relevant for comparing him to others around the league, and for his trade value. Also, it may not be clear who his backup is, since the team could bring someone up from the minors or trade for another team's backup, and the backup might not have enough at-bats to know how good he is. So, they judge the value of a starting second baseman by comparing him to the abstraction of a replacement level second baseman rather than any particular backup second baseman.

One situation where value over replacement is a useful statistic is when one player plays more often than another. If a player is likely to miss a quarter of the season due to injuries or fatigue, is he better for your team than a slightly worse player who can play the whole season? Or, in football, how do you measure the value of a workhorse running back who gets a lot of carries?

Value over replacement has another important use. Sometimes your starter's value drops below the replacement-level value. Then you know that he's washed up, or that he's just not good enough to be starting at that level. That's a pretty clear sign that you should go out and replace him, with someone above replacement level, if possible, but with a typical replacement level player, if necessary.

And now this long set-up comes back around to politics. How do you judge a president's value? Well, one way is to compare him to the average president, or to previous presidents, but you run problems with those comparisons, since they use a small, elite comparison class. So why not compare the President to a replacement level President?

What is a replacement level President? Roughly, it's the kind of President you would expect if you were to replace the Commander in Chief with one of the politicians in a major party whose could be electable in a nationwide election. That is roughly equal to the set of 50-100 Republican or Democratic Governors, Senators, and Representatives who could have some nationwide appeal. So, a replacement level President is at the expected level of a random member of this set of politicians, a replacement level Democratic President at the expected level of a random Democrat from this set, and a replacement level Republican President at the expected level of a random Republican from this set. The definition is not very precise, but it's hard to be precise with such a small sample size of Presidents and with no good objective measures of a politician's value. The sabermetricians are far ahead of us with the statistics, but at least we can use their ideas.

So, why Anybody But Bush? Because he's worse than a replacement level President. That means it's time for him to go. And if we accept this definition of ABB then, as I suspected, we needn't worry about whether people would want to replace him with bin Laden, an infant, or Hussein, because there aren't any bin Ladens, infants, or Husseins in the replacement set.

Even if some people are not exactly excited about John Kerry, it is still pretty clear that he rises at least to the replacement level. Most people can agree, at the very least, that he is one of the 20 best Democrats in the country to have as the party's candidate for the Presidency. So, if you believe that Bush is worse than a replacement level Democratic President, as many people with Liberal leanings, and some Independents, Libertarians, and Conservatives, believe, then you should vote for ABB, who turns out to be Kerry.

There are obviously a lot of people on the Right who don't believe that Bush is worse than a replacement level Democratic President. But do most Republicans think that Bush has been better than a replacement level Republican President, or are they just choosing him because he's the incumbent? I'm genuinely curious about that question, although I don't expect many people who want Bush to be reelected to come out and say in the midst of the campaign that he is worse than a replacement level Republican.


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