Thursday, March 15, 2012

Tournament Probabilities

Here are tournament probabilities based on this site's betting market rankings.  I calculated the probability of each matchup using the following formula:

Win Probability of Team A beating Team B = 1/(1+exp(-(GPFa - GPFb)/6))

I then simulated the tournament 2500 times and summarized the results by team and how far into the tournament each team made it.  These seem somewhat consistent with Ken Pomeroy's log5 predictions.

I eyeballed these probabilities against the tournament futures odds at Bovada, and the following teams are a positive ROI, according to my probabilities:
  • Ohio State - 11% ROI at 11/2 odds
  • Kansas - 71% ROI at 12/1 odds
  • Michigan State - 10% ROI at 9/1 odds
  • Syracuse - 66% ROI at 16/1 odds (this could be due to Fab Melo's absence which my modelling isn't accounting for)
The favorite/long shot bias is alive and well in NCAA futures betting, as the ROI's get very negative once you go beyond the top tier teams.

In addition, it looks like Kansas and Michigan State would be good bets to win their region, with Kansas getting 2/1 odds (19% ROI) and Michigan State getting 21/10 odds (11% ROI).  If you used the Kelly criterion for these bets, you would bet 10% of your bankroll on Kansas and 5% of your bankroll on Michigan State.  There is less "vig" on the regional futures (25% vs. 50% on the tournament winner futures).  Less variance too.

That being said, my one prediction so far hasn't panned out too well (in the rankings, I said I wouldn't be surprised if California made it to the Sweet Sixteen).  I also haven't been able to update the probabilities with the latest line moves.  This is more for my own curiosity, and I'll check back on how these bets would have performed.


  1. Great work. I have really enjoyed the college basketball posts.

    Question 1:
    How did you come up with this formula:
    Win Probability of Team A beating Team B = 1/(1+exp(-(GPFa - GPFb)/6))

    Question 2:
    Would you care to share your simulator?

  2. Thanks. I think I first saw the formula mentioned in the comments at Advanced NFL Stats. To come up with something equivalent for NCAABB, I looked at how often college basketball teams won at various point spreads (using 2005-2010 data from The Prediction Tracker). I then found that dividing the GPF differential by 6 best matched the actual winning percentage by point spread. Time permitting, I hope to share more details on that calculation (there's also a technical derivation of the formula, but the math gets a bit hairy). For the NFL, I found that dividing by 7 works best and for the NBA, 6.5 works best.

    The simulator is an ugly piece of work right now (some pasted excel values, a few formulas, and a hastily written macro). If I had time to clean it up, I would be willing to share it.