Probability and Emotions

by Brian on August 30, 2003

It’s well known that our intuitive approaches to probabilistic reasoning lead to fairly bizarre beliefs and behaviour in some circumstances. It can also lead to fairly odd attitudes and emotions in the right circumstances. Consider, for example, how it would feel being a fan of the various teams in the American League playoff race.

Baseball Prospectus has introduced a new model calculating the probability of each team reaching the playoffs given their current standings, their performance to date, and their upcoming schedule. I don’t know how good the model is, but let’s assume for now it’s accurate. If so, here’s the probability of each team making the playoffs as of the morning of August 30.

Yankees 91.5%
As 80.0%
Red Sox 73.0%
Mariners 51.7%
White Sox 46.2%
Twins 38.5%
Royals 18.1%

From that report you’d think Mariners fans should be at least as happy about their position as White Sox fans, maybe more so. But I suspect that’s not the case right now, because of the odd way the playoff teams are chosen.

There’s four playoff teams – the winners of the eastern, central and western divisions, and a wildcard for the best second place team. In effect the best three of the Yankees, As, Red Sox and Mariners will go through, two as eastern and western winners and the third as wildcard. And the best of the White Sox, Twins and Royals will go through as winner of the central.

Right now in the four team race for three spots, the Mariners are looking by far the weakest of the four. It’s pretty close, but it’s much easier to see the Mariners missing than any of the other three. It would be hard to feel particularly happy about your position if you’re a Mariners fan, because one of the four has to miss and you’re the most likely one to do so, by far.

The three team race for the central crown is tighter, but the White Sox have the upper hand right now. It would be easy to feel confident if you’re a White Sox fan. One of the three teams has to go through, and it’s most likely going to be you.

It should be clear what went wrong in the reasoning in the last sentence of each of the last two paragraphs. When there are many possible outcomes, you shouldn’t pay as much attention to which of them is most likely as much as to how probable each of them is. If Mariners fans did that they would think “I don’t know who we’re going to finish ahead of, but I’m still confident enough we’ll finish ahead of someone.” And if White Sox fans did that they might think “I don’t know who’s going to beat us, but it’s still a good chance that someone will beat us.” (That might be too depressing – it’s better if you’re a fan to focus on the positive sometimes. It’s possible to be too rational in sports sometimes. So let’s focus on why Mariners fans might be too depressed.)

The fallacy here, assigning too much weight to the most likely outcome, is I think reasonably common. But even once you’ve seen it it’s hard to overcome it. If I were a Mariners fan, I’m not sure I’d find the reassuring speech in the last paragraph that reassuring, even if I could (at some level) recognise the soundness of the reasoning.

{ 6 comments }

1

Elina 08.30.03 at 7:31 pm

On behalf of the UK readers I would like to … (sorry I fell asleep). Baseball – humbug.

2

zizka 08.30.03 at 10:07 pm

You have to take mojo into account. The Twins have won the World Series twice with mediocre season-long teams. They were able to do this because it’s possible to win eight or ten playoff games with only three pitchers.

They’re in the thick of the race now, once more in a very weak division. I’m a Twins fan and I love injustice when it works in my favor.

3

Doug 08.31.03 at 3:29 pm

Redundancy noted: slagging on cricket is by definition gratuitous.

Baseball, however, is the perfect game, balanced and lovely as no other, not even that funny one with the spotted ball and twenty-two guys.

4

Michael 08.31.03 at 6:58 pm

And I thought I was the only one who read Baseball Prospectus and Crooked Timber every day….

5

pathos 08.31.03 at 9:35 pm

Nope, one more who reads both.

I think the main problem, that falls vaguely on the side of “emotion” is that teams want to be able to “control their own destiny.” Seattle is in a position where they can play well, but need to rely on either Boston or Oakland playing poorly, but Chicago is in a position where if they play well, they can win.

There is more confidence (and perhaps reasonably so), when the chances of victory can be controlled by individual action, without relying on the actions of others.

6

Brian Weatherson 08.31.03 at 9:56 pm

I think pathos’s point is generally right, though in this case it’s worth noting that Seattle could guarantee themselves a place by winning out. (Especially after the Red Sox performances the last two days, but even at the time I wrote the post I think.) I agree that’s an important part of why it’s nice to be leading though, and I should have considered that in the little (psycho-)analysis.

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