Neil once pointed out, that you can approximate a team’s odds of winning a game by using the point spread and the following formula:

p(W) = 1 – (1-NORMDIST(0.5,SPREAD,13.86,TRUE))+0.5*(NORMDIST(0.5,SPREAD,13.86,TRUE)-NORMDIST(-0.5,SPREAD,13.86,TRUE))

For college football games, there is research by Wayne Winston and Jeff Sagarin that the standard deviation in the above formula should be 16 instead of 13.86. One of the nice things about the SRS is that it comes very close to approximating the point spread in each game. If we give 3 points to the home team, we can then approximate each team’s likelihood of winning in their remaining games.

For example, here is a look at Oregon’s remaining schedule and their likelihood of winning each game. Note that for now, I am assuming that the Ducks host the Trojans in the Pac-12 Championship Game:

Tm | Opp | Loc | SRS Tm | SRS Opp | Proj Spread | Win Prob |
---|---|---|---|---|---|---|

Oregon | Southern Cal | Road | 65.9 | 53.9 | -8.9 | 71.2% |

Oregon | California | Road | 65.9 | 42.3 | -20.6 | 90.1% |

Oregon | Stanford | Home | 65.9 | 53.8 | -15 | 82.6% |

Oregon | Oregon St | Road | 65.9 | 55.2 | -7.7 | 68.4% |

Oregon | Southern Cal | Home | 65.9 | 53.9 | -14.9 | 82.5% |

Total | 29.9% |

Winning five games in a row isn’t easy, even for a team as good as Oregon. With four difficult games left, the odds of them going 5-0 are just 29.9%. Things are much more favorable for Kansas State:

Tm | Opp | Loc | SRS Tm | SRS Opp | Proj Spread | Win Prob |
---|---|---|---|---|---|---|

Kansas St | Oklahoma St | Home | 66.3 | 52.5 | -16.9 | 85.4% |

Kansas St | TCU | Road | 66.3 | 46.2 | -17.1 | 85.7% |

Kansas St | Baylor | Road | 66.3 | 46 | -17.4 | 86.1% |

Kansas St | Texas | Home | 66.3 | 52.1 | -17.2 | 85.9% |

Total | 54.1% |

The Big 12 has some good teams, but Kansas State appears to be an elite one. My gut tells me the SRS is underrating the likelihood of one of those teams pulling off an upset, but there’s no doubt that Kansas State would be a double-digit favorite against each of those teams right now. Of course, one thing the SRS ignores in all of these instances is the possibility of a key injury affecting any team.

Notre Dame has a history of dropping games to bad teams, but I don’t think there’s much of a chance the Fighting Irish lose any of their next three games. That means the USC game should have national title implications:

Tm | Opp | Loc | SRS Tm | SRS Opp | Proj Spread | Win Prob |
---|---|---|---|---|---|---|

Notre Dame | Pittsburgh | Home | 63.1 | 37.2 | -28.9 | 96.5% |

Notre Dame | Boston College | Road | 63.1 | 31.1 | -29.1 | 96.5% |

Notre Dame | Wake Forest | Home | 63.1 | 27.9 | -38.3 | 99.2% |

Notre Dame | Southern Cal | Road | 63.1 | 53.9 | -6.2 | 65.1% |

Total | 60.1% |

There is only a 10% chance (29.9% * 54.1% * 60.1%) that Oregon, Kansas State and Notre Dame all finish the season undefeated, at least according to the assumptions in this post. If you want to look at how all three teams got here, you can check all the NCAA game scores here.

{ 7 comments… add one }

Not splitting ends – as this is a great post, I have the same information and wouldn’t have quite figured how to do it – the stochastic element for College Football is 16 (according to Winston and Sagarin), 13.86 (or something slightly less, I think you or Neil worked it out at about 13.4 over the last 20 years) is for the NFL. This should make the % slightly higher I think.

Yep — I used 16. I think you just quickly read over that in the post.

Sorry my bad – I looked at the numbers in the tables and read the formula at the top in grey (and didn’t read the paragraph below). I didn’t think that you would miss something like that. I don’t know why I just had a gut feeling the number would be higher and figured you may have used 13.86. Good luck with the weather by the way.

Thanks.

I think the #s aren’t higher because Oregon still has two pretty difficult road games left.

Worth noting the betting lines this week.

Notre Dame is only -16.5 at home against Pittsburgh, which to me is mind-bogglingly low. Sure, the Panthers just beat Temple badly, but Notre Dame should blow them out of the water.

Kansas State is only -10 against Oklahoma State. Again, KSU seems undervalued. It’s true that the Cowboys best two games were their last two, but Iowa State isn’t very good and TCU was completely banged up. In two road games, OSU lost at Arizona and barely beat Kansas. In Stillwater this might be closer, but I expect KSU to roll.

Oregon is -7.5, which is pretty close to what the SRS predicts. But honestly, based on how frequently the Ducks have slammed on the brakes, my guess is they’re undervalued in the SRS.

Also, Alabama is 16 points better than LSU in the SRS, but “only” a 9.5-point favorite this week. Of course, Death Valley at night is a particularly difficult venue and the Tigers are coming off a bye week. To me, that line now feels about right. It opened at -7, and I liked the Crimson Tide at that line. At 9.5, I’d avoid action on either side.

One typo I noticed when lazily copy-pasting the given formula into Excel:

Above you give this formula:

p(W) = 1-(1-NORMDIST(0.5,SPREAD,13.86,TRUE))+0.5*(NORMDIST(0.5,SPREAD,13.86,TRUE)-NORMDIST(-0.5,SPREAD,13.86,TRUE))

This differs from Neil’s formula at the link you gave in that yours starts with an extra “1-“. Here’s Neil’s:

p(W) = (1-NORMDIST(0.5,SPREAD,13.86,TRUE))+0.5*(NORMDIST(0.5,SPREAD,13.86,TRUE)-NORMDIST(-0.5,SPREAD,13.86,TRUE))

It seems likely that the “1-” was intended to invert the probability so that, e.g., a spread of “3” means that a team is +3, i.e., an underdog, the opposite of how Neil’s formula treats it. However, even if that’s the case, it’s not working quite right. It needs an extra set of parentheses:

p(W) = 1-((1-NORMDIST(0.5,SPREAD,13.86,TRUE))+0.5*(NORMDIST(0.5,SPREAD,13.86,TRUE)-NORMDIST(-0.5,SPREAD,13.86,TRUE)))

You can see that the formula given in this post is off by plugging in a SPREAD of 0. Instead of getting a 50.0% chance of victory, you’ll get a 52.9% chance. The 2.9% difference for SPREAD=0 is small, and the error is probably never any larger than that, regardless of SPREAD. Still, it may matter to someone, especially if he uses the formula independently on both teams, producing two win probabilities that sum to over 100%.

Just an FYI for the other lazy copy-pasters out there. (I can’t tell whether the numbers in this post were affected, thanks to rounding and perhaps to mistakes on my part in trying to reproduce them.)

I think both formulas are right (the principle behind them anyway I haven’t copied this into Excel so I wouldn’t know if that works but they look virtually the same as what I have). I do this but do it slightly differently, and change my spread number from positive to negative and vice versa dependent on the %’s (I expect I could work out how to not have to do that but it doesn’t worry me). With a spread of 0, one formula above would essentially give you 100% – 50%, the other would give you 50% (so one is effectively Team A, the other would be Team B it’s just a question of how you would lay it out).

If you want to get into this, I’d recommend the book from Wayne Winston in the link at the top (it makes things a lot clearer – and then you could end up like me posting random queries on Excel forums when you want to take it a bit further).

Good luck.