EW's Oscar Odds: a question about probability

Factual Questions
1

In the March 21 issue, Entertainment Weekly handicaps this year’s Oscar races, offering odds in the major races.

Caveats before I ask my question:
a) I am not a math whiz
b) I realize EW is doing this for fun, and not making an effort to calculate actual probabilities

Now:

I seem to remember that, when laying odds on an event, the total of the probabilities has to equal 100%. Therefore, in a given Oscar race, if everyone had an equal chance of winning, the odds on each person or film would be 5-1. (Because a 20% chance of winning = 1/5 = 5-1 odds. This could be a major misunderstanding on my part.)

If that’s the case, then EW’s odds really don’t make sense, statistically. (They may make sense from a bookmaker’s standpoint, what with having to cover the vig and all, but I really don’t know. Have I mentioned my confusion about all of this?)

For example, they handicap the Best Director race as follows:

Pedro Almodovar: 5-1, or 20%
Stephen Daldry: 15-1, or 6.7%
Rob Marshall: 3-2, or 67%
Roman Polanski: 10-1, or 10%
Martin Scorsese: 2-1, or 50%

Given those numbers, there’s a 153.7% chance that someone will win this race, when a 100% chance would be the right answer.

Am I correct in thinking EW’s bookies are mathematically challenged? If so, do I actually understand where they’ve gone wrong, or am I misremembering what probability theory I did know?

2

Well, your percentages are a little off. For instance, if someone has 1-1 odds, is that 100%? No, it’s 50%. In general, odds of x-y is the same as a probability of y/(x+y). So for instance, Almodovar has a 1/6, or 16.7%, chance. However, I still get 105% total with this method.

3

This is the kind of market a bookmaker would offer. At 105% the bookie would hold $105 to pay out $100 on each competitor. So in a two person event like me versus Mike Tyson, Tyson will be say 1 to 10 (90.9%). For the bookie to bet about 105% i must then be 14.1% or about 6/1.

4

Thanks!

Like I said, not a math whiz. So, looking at their odds for the Best Picture race:
Chicago: 1-1, or 50%
Gangs of New York: 10-1, or 9%
The Hours: 5-2, or 28.6%
The Two Towers: 20-1, or 4.8%
The Pianist: 5-2, or 28.6%

If I got those percentages right, that totals 121%. So EW is off – and not by a consistent amount from race to race. But not as badly as I’d thought.