When 15th Is Better Than 8th: The Math Shows the Bracket Is Backward

[CloneAggie]

Interesting (but long) blog post on the seeding of teams.

When 15th Is Better Than 8th: The Math Shows the Bracket Is Backward - NYTimes.com

Suppose that, lucky you, you’re the coach of a team given a No. 8 seed in the N.C.A.A. tournament bracket.

This is a less-than-ideal position: provided that you win your first-round game, you’re due to face the No. 1 seed in the second round.

But a friend of yours — another coach who owes you a favor — calls you with a “Let’s Make a Dealâ€￾ proposition.

His team is seeded No. 10 in another regional. He offers to swap with you: you get his No. 10 seed and he gets your No. 8. The teams in each region are otherwise about as strong as one another.

Are you better off switching?

The answer is almost certainly yes: the No. 10 seed is intrinsically a better position than the No. 8 seed. So, for that matter, is the No. 11 seed. The 12th seed is also better than the No 8. As are the 13th and 14th seeds. And possibly even the No. 15 seed, depending on your objective.

I found this chart interesting:

 

[Hugs4ISU]

I do not understand part of the graph. Offhand, you would think it would be based on prior data on how many games each seed has one, and in particular how many times each seed has made the Sweet 16. But then, no 16-seeded team has EVER one an NCAA tournament game, so how can that chance be higher than zero if it is based on prior data?

 

[CloneAggie]

I do not understand part of the graph. Offhand, you would think it would be based on prior data on how many games each seed has one, and in particular how many times each seed has made the Sweet 16. But then, no 16-seeded team has EVER one an NCAA tournament game, so how can that chance be higher than zero if it is based on prior data?

In the blog, he says:

Let me be very clear about what this chart means. It is not the chance that a No. 1 seed, for example, will win its first round game. Instead, it is the chance that a decent team with a power rating of 85 would win the game if it took the place of the No. 1 seed in the bracket — the “Let’s Make a Dealâ€￾ Scenario.

In other words, all teams have a "power rating" from 0 to 100. If we hold that power rating constant (in this case, at 85), it is better to be seeded 10th through 15th than to be seeded 8th or 9th if your goal is to reach the Sweet 16. And given that the difference in power rating between 8/9 and 10/11/12 is historically not very much (as seen by another graph in the blog post), it would actually be better to be 10/11/12 than 8/9. Historically, the power ratings do start to drop off more after 12 though.

 

[azepp]

Very interesting. I do like his radical solution about just seeding the top 6 in each region.

 

[theshadow]

1985-2010, Seeds making Regional Semis ("Sweet 16")
Sorted by 1st/2nd round pods

#1 - 91; #8 - 9; #9 - 4; #16 - 0

#2 - 67; #7 - 18; #10 - 19; #15 - 0

#3 - 53; #6 - 37; #11 - 12; #14 - 2

#4 - 44; #5 - 38; #12 - 18; #13 - 4