Friday, March 19, 2010

Your Team Probably Won't Win the Tournament

Your team probably won't win this year's Men's NCAA Basketball Tournament.

Mine probably won't, either.

There are 65 teams in the Men’s NCAA basketball tournament.  Only one will go undefeated for six straight games and win the national championship. Despite these odds, there are millions of us fans supporting lots of different teams and somehow convinced in our hearts that ours will be the one to cut down the nets.
Nearly all of us will be wrong, but our beliefs won’t waiver one iota until we lose.

For those teams seeded in the bottom half of their region, history says that winning is nearly impossible. But even for teams seeded 1st, 2nd or 3rd, the odds aren’t pretty.

How do I know that your team probably won’t win without knowing who you are or what team you support?   Simple probabilities.  The ones we all choose to ignore. 

This phenomenon isn’t limited to basketball, or even to sports.  An entire academic field known as behavioral finance has sprung up fairly recently to help explain the reasons and the methods we use to deceive ourselves into ignoring the odds.

We can, however, look at the last 25 years of NCAA tournament results and gain some perspective on the probabilities.  That includes 1,600 teams (if we ignore the play-in games) and 1,575 games.

Twenty-five years ago happens to be when the NCAA expanded the field to 64 teams.  Yes, there is a "play-in" game for the 65th team, but ignoring those for the last few years won't impact the statistics in any important way.

The 4 through 8 Seeds

First, let’s look at the seeds who have slightly better than a snowball’s chance. That would be the group of 20 teams seeded 4th through 8th each year.  Over 25 years, that group includes 500 teams that have won a total of three championships. The three low-seeded teams that won it all were seeded 4th, 6th  and 8th.

The success rate for this group is 3/25, or 12%, so there is a 12% chance that one of the 20 teams seeded 4th through 8th will win the tournament, based on historical results. But, the record for individual teams seeded 4th through 8th is 3 title wins per 500 attempts, so the probability of an individual team seeded in this group winning it all is about 0.06%.

The Bottom Half

4th through 8th seeds may be a long shot, but at least they have three titles.

Not one team in the bottom half of the field has won a championship in the current format.  Only four 15-seeds have even made it to the second round.  Only two teams seeded lower than 8th have made it to the Final Four (LSU in ’86 and George Mason in 2006, both 11-seeds).

No 16-seed men’s team has ever won a game.

(A 16-seed did win a game in the Women's NCAA Basketball Tournament once.)

Seeds 9 through 16 have never won a title.  Seeds 4 through 8 have won 3.  And, a whopping 88% of national titles have been won by 1-, 2- or 3-seeds.

The Top 3 Seeds

How about the top seeds, the ones who have a real shot at putting together a six game winning streak to win a championship?  Doesn’t it seem like the teams that end the regular season ranked number one in the polls win the NCAA tournament more often than not?

They don't.

1-, 2- and 3-seeds have won 22 of the last 25 championships, but 1-seeds have won 15 of those, or 60%.  The remainder have gone about equally to 2-seeds (4 titles) and 3-seeds (3 titles).  Now you know why Rick Pitino preached to his Kentucky teams that they needed a 1-seed to have a real chance of winning a championship.

But how likely is the big trophy, even if you are a 1-seed?  The NCAA only began announcing overall 1-seeds in 2004, but since 1985, only 4 of the 25 teams (16%) that ended the season ranked number 1 in the major polls have gone on to win the championshipi.  That’s about 1 in 6.

In the past 25 years of tournaments, 100 teams have received a 1-seed and 15 of those teams won the title.  The success rate for those four 1-seeds averages 15% each year.

2-seeds have won 4 of 25 championships, so the probability that the tournament winner will be a 2-seed is 16%, based on historical data.  During that period, there have been 100 teams seeded 2nd, but only 4 won titles, so the probability of your 2-seed cutting down the nets is about 4%.

If you’re a 2-seed, the challenge is potentially having to beat three 1-seeds, one in the Regional finals, one in the Final 4, and one in the championship game.  With a historical winning percentage of .536 for 1-seeds versus 2-seeds, the probability of a 2-seed, like West Virginia this year for example, winning three games in a row against 1-seeds is (0.5363)3, or slightly better than 15%, and that’s after having won the first three rounds against lower seeds.  The only team to beat three 1-seeds in a single tournament to date was 4-seed Arizona in 1997.

Of course, who’s to say that West Virginia is seeded correctly?  Maybe they should have been a 1-seed.  They think so.  And perhaps other 1-seeds will be knocked off before WVU has to play them. But seeding is just one of the reasons that the statistical favorite doesn’t win the NCAA basketball championship. 

There are new injuries, injured players who are finally healthy, lucky shooting nights (an NC State air-ball that becomes a lob pass against Houston), emotional rivalries, bad coaching decisions (Pitino not guarding Grant Hill on the inbound pass to Laettner), and fortunate calls from the officials. 

There are bad matchups. Just because Team A beats Team B and Team B beats Team C doesn’t mean Team A will beat Team C.  It just doesn’t work that way.  There is no transitive law of college sports. UK is ranked second in the nation but beat Mississippi State—who didn’t even qualify for the NCAA tournament— by one-tenth of a second in the SEC Tournament finals last week.

Probabilities can’t tell us who will win the championship, but they do tell us that the winning team, even if they are a 1-seed, will have to beat the odds. No matter how good your team is, the odds are slim that they will win the tournament. 

Probabilities also tell us that improbable doesn’t mean impossible. If you bet long-term statistical averages, which means just picking the higher seeded team, you will be right more often than you will be with any other method, but these are one-game competitions, not seven-game series.  And an individual NCAA tournament is a one-time event. 

That’s what makes the odds for even the best teams daunting.  The winner has to play near-perfect basketball for six games in a row, but it only takes one game for a lower seed to knock you out of the bracket.

While only 4 teams ranked number one at the end of the regular season went on to win titles in the past 25 years, this feat was accomplished twice as often in the past 60 yearsi

I suspect this is because the fields were smaller before 1985, meaning fewer rounds and fewer opportunities for the regular season champion to get knocked off by a lower seed.  If so, that doesn’t bode well for the expansion of the tournament to 96 teams, as has recently been discussed.

As I said, improbable outcomes are not impossible.  In 1985, Villanova was an 8-seed playing top-seeded Georgetown in the NCAA title game.  All it took to win the national championship was to go further than any 8-seed had ever gone in the tournament. . . and then to play one perfect half of basketball.

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