Super Bowl Statistical Arbitrage
This is not intended to be gambling advice, rather a conversation about risk pricing.
I took a peek at the money line odds for the NFC and AFC Championship games this weekend. Some quick math suggests the following probabilities of Super Bowl match ups:
- NE vs ATL 48%
- NE vs GB 26%
- PIT vs ATL 21%
- PIT vs GB 12%
(A quick study will note that the total adds to 107% when it should 100%. The 7% is the sports book profit margin on the bets. I didn’t make an assumption on how to adjust this in the probability of outcomes.)
I looked at the odds to win the Super Bowl and something seemed amiss. The current odds are as follows:
- NE 7/5
- ATL 13/5
- PIT 4/1
- GB 4/1
(A quick study will notice these odds total 109% when it should be 100%. It has been my experience a sports book has a higher margin on future bets.)
- First observation. PIT and GB are too high. The money line odds of either winning their respective conference championship are 37% (GB) and 32% (PIT). To win the Super Bowl they have to win their conference championship first. If the market assigns a 20% probability (4/1) of winning the Super Bowl, then their odds of winning the Super Bowl game imply 62% (PIT) and 54% (GB). Too high!
- Second observation. If PIT and GB Super Bowl odds are too high AND one cannot short (or bet against) a team, then one team must be too low. At 13/5 to win the Super Bowl, this suggests ATL would be a 41% chance to win the Super Bowl IF they won the NFC title. This seems to make sense. What does not make sense is NE at 7/5. This suggests if NE wins the AFC title they would be a 58% favorite to win the Super Bowl. Based on point spread variances over time, this would suggest NE would be a 2.5/3 point favorite.
If NE plays in the Super Bowl, I expect them to be a 4–7 point favorite against ATL or GB. A 4–7 point favorite suggest a win probability between 62–72%. If you do not believe NE would be a 4+ point favorite against ATL or GB, then you will disagree with this analysis.
How to play?
- Before the AFC title I would buy NE to win the Super Bowl at 7/5. Based on the above, I expect a 4–14% edge. (Note there is risk of loss. Think of this as counting cards at the blackjack table. Overtime these probabilities work in your favor.)
- If NE wins the AFC Championship I speculate they are a 4–7 point favorite. Thus the money line for the Super Bowl underdog would be around +200 (bet $100 to win $200 + your initial $100). Before the Super Bowl I would bet the money line on the underdog.
Three possible outcomes based on a $100 bet:
- NE loses the AFC title (~30% probability). You are out $100 (bummer).
- NE Wins the AFC title AND the Super Bowl. You win $140 from the futures bet and lose the $100 you bet on the Super Bowl underdog. Net winner $40.
- NE wins the AFC title AND loses the Super Bowl. You lose the $100 futures bet, but you win the $200 money line bet. Net winner $100.
The expected outcome is +$12.70 (per $100). It is in one’s interest to play positive expected outcomes. (Assuming $100 bet, ~70% NE wins AFC title based from the Vegas odds and a 65% chance NE wins the Super Bowl if they play in the Super Bowl.)
Good luck!
