Sunday, March 30, 2008

The Fallacy of Accurate Predictions

Heard this on the radio this morning - a website,, has picked the Brewers to finish fifth in the National League Central. Fifth!

Like many in the national media, they do not see the Brewers winning the National League Central. But fifth???

Let's take a closer look. Here is how they (they - not me) see the National League (they only give you the wins - I filled in the other two columns):

New York 91 71 --
Philadelphia 87 75 4
Atlanta 81 81 10
Washington 80 82 11
Florida 74 88 17

San Diego 88 74 --
Colorado 87 75 1
Arizona 86 76 2
Los Angeles 82 80 6
San Francisco 73 89 15

Chicago 84 78 --
St. Louis 84 78 --
Cincinnati 84 78 --
Houston 83 79 1
Milwaukee 82 80 2
Pittsburgh 72 90 12

Wow. Quite a pennant race it's going to be. Then a three-way playoff for one division and another one-game playoff for the wild card spot. Yeah, ok.

Do you see something else? They've got 12 teams finishing .500 or better. In fact, according to their predictions, the National League will go a combined 1318-1274; an astonishing 44 games over .500. They must not think much of the American League, hey? The only way such a lopsided result could occur is if the NL owns the AL in inter-league play. Let's check:

New York 95 67 --
Boston 92 70 3
Toronto 84 78 11
Tampa Bay 74 88 21
Baltimore 66 96 29

Los Angeles 90 72 --
Seattle 90 72 --
Texas 73 89 17
Oakland 67 95 23

Detroit 95 67 --
Cleveland 89 73 6
Chicago 84 78 11
Minnesota 74 88 21
Kansas City 69 93 26

If you do the math, you see they've got the American League also playing over .500 (1142-1126). There's obviously no way that can happen, and if you try to fix it, you pretty much need to change your prediction for every team.

In a couple of weeks, I am going to unveil a program I wrote to estimate each team's chance of winning their division title given their current win-loss records. One of the main principals that strikes you when using such a system, or really any system of predicting outcomes of events, is that you must balance both sides of the equation. The percentages must add up to 100%. The wins must equal the losses. This seems like a simple principle, but it's amazing how many people get it wrong.

If you are reading this, you probably think that the Brewers are going to win the NL Central. Let's say that you think that their chances of doing so are about 60%. Then what chance do the Cubs have? 40%? They can't - that wouldn't leave anything for any of the other teams. 30%? That would not only mean that you think there is only a 10% chance that the division winner will be either the Cardinals, Reds, Astros, or Pirates, but it also means that you think the Brewers chance of winning is double that of the Cubs. See the problem?

If you actually go through the exercise of dividing up 100% among the six teams in the NL Central and want to be as accurate as you can and be fair to every team, using all of the information available to you, you will probably be forced assign a number less than 50% to every team. Try it. But what that means is that every team in the division is more likely to not win than they are to win. It also means that if you try to predict a winner, you are more likely than not to be wrong - no matter who you pick.

Call me a wuss or call me an astute mathematician, but this is why I stay out of the predictions game.

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