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Implications of NCAA march madness brackets with multiplier scoring (a Stata example)

This year at our office we are again helping contribute to the great March Madness economic productivity drain. However, we are also toying with the idea of switching to a Fibonacci sequence of bracket scoring and using multiplier scoring to weight up more risky selections (particularly in later rounds). 

In prior years, we did this whole thing on paper / manually, and so to keep things simple we followed a standard scoring (pts per round) regime which was the standard espn/yahoo format (e.g., 1-2-4-8-16-32 points across the 6 rounds) .  

This year most people in our office seem supportive of a scoring scheme that incentivizes risk-taking.  So, there are essentially two changes to our scoring scheme.

First, we are changing to a 2-3-5-8-13-21 progression. With the more traditional 1-2-4-8-16-32 system, the championship game is worth 32x as much as any first-round game (which in effect makes the first round games almost mostly useless). With Fibonacci scoring, the last round game is worth 10.5x's as much as each first-round game which is much more reasonable and allows the second change of using ‘score multipliers’ have more weight in differentiating winners/losers. 

Second, we are adding score multipliers based on the seed difference. Point multipliers give ‘big upsets’ more value based on the difference in seeds and the round. For example, if you correctly pick a 10-seed to beat a 6-seed in the round of 32 (so if this has a hypothetical round multiplier of 3), you'd be awarded 12 bonus points [(10 - 6) * 3 = 12] on top of the regular points awarded in the round.  

Our planned multiplier across rounds is 1-2-2-3-3-0. The multiplier (somewhat) increases across rounds (because it is harder to make upset picks deeper into the tournament) except for the last round (Final) where essentially one player gets an automatic multiplier since there are only two teams (unless they are both 1st seed which happens about 27% of the time according to this file), so we follow a lot of other brackets that set this multiplier to zero in the last round.

To illustrate the implications of this change and allow others to toy with the scoring and multipliers I've laid out, I set up a post at the link below which has woven Stata code and output (and a .do file you can use yourself) to simulate the impacts of changing the March Madness scoring. 

The upshot of this file (as it's currently set up without any human/strategic picking) is that risk-taking pays off in most cases (>87%) in that a risk-taking player (when they win) ends beating teams that would have won via standard scoring that percentage of the time. The picking mechanism in this file is a random number generator (runiform()) and there are a lot of assumptions baked-in, but you can toggle those settings if you're interested.

Last thing, I created this woven file using Ben Jann's excellent -webdoc- (from SSC). I would have pasted the output from -webdoc- into blogger instead of putting it on our FTP but (1) blogger doesnt like the javascript for the Stata code buttons and (2) the intended audience here is mostly my coworkers at Gibson. The do file for this code is located at the bottom of the page linked above.

  Good luck picking the best of the 9,223,372,036,854,775,808 potential brackets!