March Madness Bracket Scoring
There are a variety of scoring systems in NCAA pools. The most common is to double the points for each round: 1-2-4-8-16-32. This puts a lot of emphasis on the championship, making the early rounds largely irrelevant. The other extreme is to make all points the same: 1-1-1-1-1-1. This has the opposite effect of making the championship largely irrelevant. I wanted to find a mathematically ideal balance. I discovered that Fibonacci scoring or something similar was the best fit.
To start with, I pulled National Bracket data from ESPN to get a measure of the variation in how people pick their brackets. I compared it to the actual tournament results dating back to 1985 when the field was expanded to 64 teams.
Using those two pieces of data, I was able to calculate how much of a spread there is in the number of correct picks people have:
Most people get 22 or 23 picks right in the first round, with a standard deviation of 2.4.
In the second round, most people get 9 picks right, with a standard deviation of 1.9:
Most people get 3 of the 8 games right in the third round, with a standard deviation of 1.4:
The best way to ensure that each round is equally valuable is to scale each round so the standard deviations are approximately equal. In trying to balance that with keeping a points system with simple, whole numbers, the solution I came up with was:
This gives each round roughly equal weight. If you’re 2 standard deviations above average in the second round, it sets you ahead of average by 12 points. Then if you’re 2 standard deviations below average in the third round, it’ll set you back 12 points.
I could have dialed it in tighter, but I wanted to keep the numbers simple. For example, 4-5-7-11-19-32 fits great, but is cumbersome. Below is the standard deviation data for each round, if you want to come up with your own.
Among common scoring systems, the concept that best fits this approach is using a Fibonacci sequence: either 1-1-2-3-5-8 or 2-3-5-8-13-21. Both of those options turn out be good matches. Most online leagues aren’t fully customizable to the point that you can choose any point value for each round, so if you’re setting up a league where Fibonacci scoring is an option, that would be my recommendation.