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Talent Is Nice, but Luck Is Vital

The college basketball fan in your life, unless she went to Florida or Virginia Commonwealth, undoubtedly thinks the draw her team received in the men’s N.C.A.A. tournament was fair at best — and a gross miscarriage of justice at worst.

This will make her exceptionally annoying to talk to for the next 96 hours or so. So here’s a guide as to whether she actually has a credible case.

The draw, undoubtedly, can make a huge difference. For instance, Ken Pomeroy’s ratings — which are better at predicting the outcome of tournament games than the Ratings Percentage Index formula used by the tournament’s selection committee — regard Washington as the 15th-best team in the country and Florida as the 19th best. Our tournament projections, however (based in large part on Pomeroy’s ratings and others like them) give Florida a 3.3 percent chance of winning the national championship, but Washington just a 0.4 percent chance. That’s almost a tenfold difference based solely on where the teams were placed in the bracket.

Washington’s road to the Final Four is especially bumpy because of geography. For their first game, the Huskies fly across the country to face Georgia in Charlotte, N.C. — 169 miles from Georgia’s campus in Athens, but 2,281 miles from Seattle. If the Huskies win that game, they will probably face North Carolina, also in Charlotte. Up next? Probably Syracuse. In Newark, where the stands will be as orange as the basketball.

That’s as close as it gets to playing three road games in the tournament. And if Washington wins them, its reward will probably be a game against the country’s best team, Ohio State.

Florida, by contrast — despite being blown out in the Southeastern Conference title game and having a Pomeroy rating that suggests it should be a No. 4 or No. 5 seed rather than a No. 2 — will get U.C.-Santa Barbara in its first game, followed by either U.C.L.A., over-seeded at No. 7, or an underachieving Michigan State. If the Gators win those games, they will probably face No. 3 Brigham Young, which has struggled since losing one of its top players, Brandon Davies, because he violated the university’s honor code.

The cases are not completely comparable, however. Florida was lucky twice: first, by getting a No. 2 seed when it probably deserved lower, and second, by getting an exceptionally favorable draw for a No. 2. (In fact, it was lucky in a third way as well: its first two games will be played in Tampa.)

Washington, on the other hand — while it got an incredibly difficult draw for a No. 7 seed — probably cannot complain much about its seeding.

Here is where we need to introduce a distinction between merit and talent. Washington, Pomeroy’s ratings suggest, is a rather talented team. The Huskies’ 10 losses came by an average of just 5 points, whereas their 23 wins came by an average of 21. There is abundant evidence that in the long run, those things tend to even out. Washington really was not that far from going into the tournament with a 27-6 record instead of 23-10.
But close doesn’t count for the seeding committee, which prefers not to consider margin of victory. And Washington didn’t lose six games; it lost 10 in a mediocre Pacific-10 Conference.

By the committee’s standards, in fact, Washington is seeded generously. Its R.P.I. is just 32, which usually corresponds to a No. 8 or No. 9 seed. According to another formula, the “Elo Chess” version of Jeff Sagarin’s ratings — which also does not account for margin of victory but is designed more sensibly than R.P.I. — Washington had just the 42nd-best performance among the 68 tournament teams, which would be more in line with a No. 11 seed.

Here’s a thought experiment that I’d like to attempt. Suppose that the teams are seeded based on what we’ll call “merit”, the measure for which is Sagarin’s ratings. So Washington, for instance, is seeded as a No. 11 in our experiment, while Florida — which is ranked 17th by Sagarin — is either a low No. 4 or a high No. 5.

Once the seeds are set, a team gets a fair draw relative to its seed. So Washington gets an average draw for a No. 11, rather than a tough one for a No 7.

Next, we need some way to measure success in the tournament. I propose the following formula: a team gets 1 point for winning its first-round game, 2 points for winning its second-round game, and so forth. A team that won the national championship would get 1+2+3+4+5+6 points, which is 21. We’ll call this measure Tournament Success Points, or T.S.P.s.

The idea is to compare the number of T.S.P.s that a team is expected to receive based on its actual draw – we derive these numbers from our tournament forecasting model — to that under this hypothetical situation. When we run a regression analysis on the actual tournament draw, we find that both a team’s seed and its talent level predict its number of T.S.P.s. This allows us to decouple these components: we can estimate how far a team would advance if it maintained its talent level, but were given a fair seed.

In Washington’s case, we find its score with a fair draw is 1.97 points. That’s compared to 1.36 points given its actual draw. So even if you buy that Washington was overseeded based on merit (and that case is debatable), they were still very unlucky — their actual draw, as a No. 7 seed, is much tougher than the typical draw for a No. 11 team.

So Washington wasn’t the unluckiest team in the tournament. That distinction belongs to Nevada-Las Vegas. U.N.L.V. received a No. 8 seed. But it ranked 22nd in Sagarin’s formula and 25th in R.P.I., which implies that it ought to have been a No. 5 or No. 6 seed.

There is a big difference between being a No. 5 (or 6 or 7) seed and a No. 8 (or 9) seed, because the latter two have to face a No. 1 in their second game, usually in an unfriendly arena. U.N.L.V. is no exception, having to face Kansas — perhaps the second-best No. 1 seed — in Tulsa, Okla. That’s if the Rebels get past their first game against Illinois, a team that, like Washington, has underachieved but has quite a bit of talent. On talent, rather than merit, our formula ranks Illinois 14th in the country, so this is tantamount to facing a No. 4 seed.

Ohio State, despite being the tournament’s No. 1 overall seed, also ranks high on the list of teams with tough draws. The Buckeyes’ weekend matchup, against either George Mason or Villanova, could be challenging, and their prospective third game against Kentucky is a major obstacle. Although the No. 2 seed opposite them, North Carolina, is not extraordinarily strong, it could get No. 3 Syracuse instead, a tough game since it would be played in Newark.

Other tough draws include Wisconsin and Texas, both No. 4 seeds; Utah State, which deserved a higher seed than its 12; and sixth-seeded St. John’s, which will travel to Denver to face a good No. 11, Gonzaga. Connecticut, also, was unlucky on balance and just missed the list.

But other teams were extremely fortunate.

Florida tops the list, and probably has one of the luckiest draws in the history of the tournament: a combination of weak opponents, favorable geography and overseeding.

San Diego State, despite having an argument that it could have been a No. 1, made out well as a No. 2. The reason is mostly geography; although the Aztecs could potentially face Connecticut and Duke in the regional final, they would do so in Anaheim, Calif. They also should get a fairly soft second game against either Temple or Penn State.

Pittsburgh is somewhat fortunate to be a No. 1 seed, and very fortunate to be in the weakest overall bracket.

Among lower seeds, Gonzaga and Michigan State qualify as lucky by being in the softest subsection of the bracket. Michigan State might have helped itself by not advancing further in the Big Ten tournament. If it had beaten Penn State on Saturday, it might have been bumped up to a No. 8 or No. 9 seed and played a No. 1 seed in its second game. Instead it received a No. 10 — probably an easier draw in a top-heavy field like this one.

Nate Silver is the founder and editor in chief of FiveThirtyEight.