One weird trick to win your bracket pool

Or at least increase your odds by a very small amount

Seemingly every year, there’s a narrative that the NCAA tournament shows one league or another is overrated (or underrated). This year in the men’s tournament it’s the SEC that’s overrated (five of eight teams lost in the first round, all of which were favorites) and the ACC that’s underrated (four of five teams reaching the Sweet 16, including two underdogs).

Why could leagues be systematically over or underrated? First, the bracket is chosen by a committee that is subjective and fallible, which could definitely over or underrate leagues systematically. Second, even objective metrics could be miscalibrated due to how college basketball seasons play out: with rare exceptions, teams only pay conference opponents for the final two months of the regular season. So if several teams in the same conference get better over time, they’ll just make their opponents in the same conference seem worse; a league can’t really improve or decline in an absolute sense.

However, we also know that theories that sound true often turn out to be unsupported by the data. Are the narratives just XKCD sports commentary?

Actually, this one holds up: teams in the same league really do rise or fall together in the NCAA tournament more often than would be predicted by chance. This has some implications for winning your bracket pool. But it’s a surprisingly tricky question to analyze, so the path to get there is interesting. (See my work here—and if you think you have a better approach that shows a different conclusion, I’d love to hear it.)

Crunching numbers

I used only the men’s tournaments for this analysis, since more data is available there; data comes from BartTorvik.com.

To quantify how well a team performed in the tournament, I used Performance Against Seed Expectations (PASE), which compares how far a team advances in the tournament to how far teams of that seed go on average. A 14-seed losing in the second round gets a PASE of 0.8, because 14-seeds usually lose their first game; but a 1-seed losing in the same round gets -2.3, because 1-seeds generally go much farther.¹

So to estimate how correlated performance is within a conference, I regressed a team’s PASE on the total PASE² of all other teams in the same conference:

pase_team ~ pase_conf_minus_team

I only included conferences with at least three teams in a given year, yielding 591 team-seasons across 111 conference-seasons. The coefficient is -0.002—almost exactly no effect.

But wait! There’s a hidden bias in that analysis. The number of games in the tournament is fixed, which means if one team performs better than expected (higher PASE), the opponents it beat must perform worse than expected (lower PASE).³ If those opponents are in the same conference, that will artificially bias our coefficient down. (At the limit, if you run the same regression as a team’s PASE against the total PASE of every other team in the field, the coefficient is always exactly -1.)

You might think—as I did—that you can simply adjust every other team’s PASE by some simple factor to account for this. But this doesn’t work, because teams aren’t distributed evenly throughout the bracket (With rare exceptions, teams from the same conference can never play each other until the fourth round, when most teams are already eliminated.) So one team’s outperformance doesn’t affect others’ evenly. How can we adjust for that complex effect?

Simulating the bracket

Another tool can help: simulation. If we set up a simulation where we know league strength doesn’t affect performance at all, and measure the correlation in outcomes, we know that’s only due to bracket structure. Then, any difference between that value and what we observed above must be due to league strength.

My simulation works like this:

• Set up every bracket from 2008-23

• Simulate winners through the whole bracket using a very simple method—how often each seed has advanced in that round.

• Repeat 1000 times for each bracket

• Calculate average PASE for each team and conference across the 1000 simulations, and repeat regression (1) above on that data.

sim_pase_team ~ sim_pase_conf_minus_team

In our simulation, the coefficient is -0.042—showing there is indeed a significantly⁴ negative relationship between the rest of a conference’s performance and a team’s performance just due to bracket structure. That we found a coefficient of -.002 in reality means that the difference of +.04 is due to correlation in underlying performance. That’s not huge, but it’s not trivial either—if five conference peers each win one more game than expected in a tournament, you’re expected to win .20 more games than expected, a useful boost in the thin margins of bracket forecasting.

Implications

So to win your bracket pool, just find the league that’s underrated and pick those teams. Easy, right?

Of course not, but it doesn’t need to be. Even if you have no idea which league is underrated, you can use this to your advantage by picking a bunch of teams from any league to advance further than expected. Since leagues tend to rise or fall together, this increases your variance—which helps if your goal is to win a big pool. (It also means you’re more likely to lose big, but if you’re not near the top, nobody really cares if you’re in the middle or the bottom.)

And we can go one step further to break down why leagues outperform. At the start, I gave two theories: the committee gets things wrong, or the metrics get things wrong. Well, Torvik also has a companion metric to PASE called PAKE—Performance Above Komputer Expectations—that ignores the team’s seed and just uses computer rankings. If I rerun the first analysis on PAKE, the coefficient is -.035. That means almost, although not quite all, of the tendency to outperform is based on committee seeding; very little is based on computer rankings.

So if you’re choosing mostly based on seed—or competing against others who are—the same-conference strategy is likely to help. But if you’re using advanced metrics, it’s probably not going to do much for you.

1. Bart’s PASE numbers exclude First Four games, which shouldn’t matter in the big picture (and also made the simulation easier).

2. Total PASE works because the average PASE across all teams is 0, so adding more teams from the same conference doesn’t affect the expected total PASE. Put another way, if a conference has seven teams in the bracket that each win one more game than expected, that’s a stronger signal of league strength than if it has only one team in the bracket that wins one more game than expected.

3. Or in some cases, the opponents of its opponents, etc.

4. p=.026, if that’s your thing