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September 20 2012

5:08 PM

What’s the real advantage for top seed?

Special to PGATOUR.COM

In sports, season-ending playoffs are generally structured to provide an extra advantage to the players or teams who have performed best up to that point -- for example, by pairing them with the weakest remaining team or giving them home field advantage. This is, of course, in addition to the inherent advantage you would assume they already have by virtue of being the best player or team up to that point in the season.

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It's difficult to say exactly how much of an advantage it is to a pro football team to have a bye in the first round of the playoffs, or to play at home rather than on the road, but we can quantify the advantage the top seeds in the FedExCup have entering this week's TOUR Championship by Coca-Cola.

Going into The TOUR Championship, the points each player has are set, and the points available to be won in the tournament are set, so we know what each player has to do to win the FedExCup. In particular, we know, for example, that each of the top 5 seeds controls his own fate -- if he wins the TOUR Championship, he will win the FedExCup. We also know that every player has some chance to win the Cup. But if any of the top five can win the Cup with a win at East Lake, is there really much advantage to being seeded first instead of second, or second instead of third, etc.?

To answer that, let's first take skill out of the equation. That is, one of the advantages of being the No. 1 seed is that the player who got there is the one who’s playing best right now, so you’d expect him to play well at the TOUR Championship. Instead, let's look at the advantage inherent in the seeding, rather than in skill levels.

So let’s assume every player in the field has an equal chance of winning the tournament, and in fact, that each player’s finish in the event is completely random. Of course, this doesn’t correspond with reality -- as noted earlier, some players have been playing extremely well and thus seem more likely to do well at East Lake, plus some players have track records on the course that would indicate they’re more likely to do well, etc.

But in the spirit of “in any given week, anything can happen,”  and to focus on the inherent value of the seeding, let’s assume that anything truly could happen. We’re also going to make a second simplifying assumption -- specifically, that there are no disqualifications or withdrawals, and there are no ties in the final standings at the TOUR Championship. This is also somewhat unrealistic, but shouldn’t affect the probabilities very much.

With those simplifying assumptions, we ran a Monte Carlo simulation of the event with 5,000 iterations, and looked at which seed won the TOUR Championship and which seed won the FedExCup.

Only the top six seeds have any chance to win the FedExCup without winning the TOUR Championship. The No. 6 seed has about a one percent chance to win the FedExCup without winning the TOUR Championship, the No. 5 seed’s chance is about two percent, then three percent for the No. 4 seed, five percent for the No. 3 seed, seven percent for the No. 2 seed, and 25 percent for the top seed.

So the real advantage to being the top seed going into the TOUR Championship relative to the next four seeds is the strong likelihood that, if none of the top five seeds win the tournament, it’s the No. 1 seed who’s most likely to win the Cup. That’s good news for No. 1 seed Rory McIlroy, who is playing at East Lake for the first time and is set to tee off within the hour with No. 2 Tiger Woods.

Of course, the probability of the tournament winner also winning the FedExCup is 100 percent for each of the top 5 seeds, and it drops relatively slowly from there.

For example, the No. 6 seed has a 96 percent chance to win the Cup with a TOUR Championship victory; the 10th seed could expect to win the Cup 75 percent of the time he won the tournament; and the 20th seed won about 40 percent of the time he won the TOUR Championship in our simulation. Even the 26th seed won the FedExCup more than 20 percent of the time that he won the TOUR Championship.

Several players this year could win the FedExCup by making the TOUR Championship their first victory of the season, including Louis Oosthuizen (No. 6 seed) and Lee Westwood (No. 8), but the No. 30 seed (Scott Piercy) isn’t one of them -- he won the RBC Canadian Open in July.

That said, the road to a FedExCup championship will be a very hard one for the 30th seed in any year, no matter who claims that spot. Of course, it has to start with a victory at the TOUR Championship. But whoever the No. 1 seed was in that year would also have to finish last or second-to-last at East Lake, or else that player would still have more points than the 30th seed. Also, several other players could pass the 30th seed with a good finish. Even with all that, however, the 30th seed managed, in our simulation, to win the FedExCup four times. With 146 TOUR Championship victories in the 5,000 simulated events, that means that the 30th seed could expect to win the FedExCup about three percent of the time, if he wins the TOUR Championship.

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