As a follow-up to this weekend's discussion about the Arkansas game, I figured I would do the math to figure out exactly how good Vegas thinks Arkansas is going to be in 2015. What I found is that based on the over/under values there is the implication that Vegas thinks they're the 6th best team in the country. How I determined that after the jump.
What I did boils down to the following idea: if Vegas thinks each team is going to win n games (based on their adjusted over/under*), what does the rating (i.e. strength) of each team need to be to such that based on their schedule their expected wins is n? In other words, you build a model that links team strength to probability of victory in a game (log5 method with HFA built in), such that when you sum all the game probabilities you minimize the error between modeled team wins and Over/Under projected wins.
(*) the Over/Under values I used were the 5Dimes numbers posted here and have been adjusted up or down to reflect the money line over/under odds included. If anyone wants to get into an esoteric technical discussion on how this was done or how the entire model works I'm happy to do that
The model doesn't perfectly fit the O/U data - though it's very close with a RMSE of ~0.002 and r^2 that is basically unity - so I am not claiming that the ratings produced are perfect reflections of what Vegas thinks. I suppose you could also have the discussion on the difference between what Vegas actually thinks and the lines they post due to a desire for inducing action on both/certain sides, but I won't get into that here. Having stated the caveats, the ratings included below should be close to what Vegas thinks is the quality of each team going into the season.
Tennessee comes in at 18th, which seems reasonable. Much of the rest of the top 25 is very reasonable as well, though I have to admit where Arkansas came in was a huge surprise to me. I would have definitely put them around the top 25, but #6 seems too high. However, as Vegas has them at over 8 wins (8.5 posted, but ~8.1 given the money line odds) and knowing that their schedule is absolutely brutal, they are going to need to be really good to get to that total. Probably top 10 team good.
What I did boils down to the following idea: if Vegas thinks each team is going to win n games (based on their adjusted over/under*), what does the rating (i.e. strength) of each team need to be to such that based on their schedule their expected wins is n? In other words, you build a model that links team strength to probability of victory in a game (log5 method with HFA built in), such that when you sum all the game probabilities you minimize the error between modeled team wins and Over/Under projected wins.
(*) the Over/Under values I used were the 5Dimes numbers posted here and have been adjusted up or down to reflect the money line over/under odds included. If anyone wants to get into an esoteric technical discussion on how this was done or how the entire model works I'm happy to do that
The model doesn't perfectly fit the O/U data - though it's very close with a RMSE of ~0.002 and r^2 that is basically unity - so I am not claiming that the ratings produced are perfect reflections of what Vegas thinks. I suppose you could also have the discussion on the difference between what Vegas actually thinks and the lines they post due to a desire for inducing action on both/certain sides, but I won't get into that here. Having stated the caveats, the ratings included below should be close to what Vegas thinks is the quality of each team going into the season.
Tennessee comes in at 18th, which seems reasonable. Much of the rest of the top 25 is very reasonable as well, though I have to admit where Arkansas came in was a huge surprise to me. I would have definitely put them around the top 25, but #6 seems too high. However, as Vegas has them at over 8 wins (8.5 posted, but ~8.1 given the money line odds) and knowing that their schedule is absolutely brutal, they are going to need to be really good to get to that total. Probably top 10 team good.
