Using Sagarin Ratings to Calculate Odds to Win it

[kardplayer]

I don't know how real odds makers do the calculations, but here's what I did:

1. Looked at Sagarin ratings for each team (e.g. App State = 65.77, Lafayette = 47.49).
2. Added 2.56 to the home team's rating, as per Sagarin
3. Calculated the difference in ratings
4. Calculated the odds of each team winning each game (no difference in ratings = 50%, each 1 point of difference = 2-3% additional chance of winning, e.g. a 7 point difference is about a 64% chance)
5. Calculated the likelihood of each potential second round matchup and made assumptions as to who would host (e.g. Montana @ Texas State, SIU @ App State, etc.)
6. Repeated steps 2-5 for rounds 2, 3, 4

From this, I estimated the likelihood of winning the whole thing as (percentages and odds are rounded, so they may look a bit wacky):

App State - 24.8% (4 to 1)
UNH - 14.2% (7 to 1)
Texas State - 10.0% (10 to 1)
Montana - 7.0% (14 to 1)
EWU - 6.2% (16 to 1)
SIU - 6.0% (17 to 1)
Nicholls State - 5.5% (18 to 1)
Cal Poly - 5.0% (20 to 1)
UNI - 4.5% (22 to 1)
Furman - 4.4% (23 to 1)
Hampton - 3.9% (25 to 1)
Ga. Southern - 3.8% (26 to 1)
Richmond - 3.6% (28 to 1)
EIU - 1.1% (95 to 1)
Lafayette 0.1% (981 to 1)
Colgate 0.1% (1,028 to 1)

Odds of reaching finals:
App State 44.9% (2 to 1)
UNH 27.3% (4 to 1)
Texas State 18.6% (5 to 1)
Montana 13.7% (7 to 1)
SIU 12.3% (8 to 1)
EWU 12.2% (8 to 1)
Nicholls State 11.3% (9 to 1)
Cal Poly 10.0% (10 to 1)
Furman 10.0% (10 to 1)
No. Iowa 9.9% (10 to 1)
Hampton 9.6% (10 to 1)
Richmond 8.0% (12 to 1)
Ga. Southern 7.9% (13 to 1)
EIU 3.4% (29 to 1)
Lafayette 0.5% (194 to 1)
Colgate 0.4% (238 to 1)

[Purple Knight]

Saqarin SUCK'S BIGtime.

[JohnStOnge]

Saqarin SUCK'S BIGtime.

Sagarin a number of other good power rating systems compare very well to the Vegas line in terms of anticipating winners and point spreads. If you're interested in looking at comparisons of how well different systems and the Vegas line have done, they are available at this link:

http://tbeck.freeshell.org/ (http://)

at "Results."

Even though this has been the worst year for Sagarin of those presented (1999 - 2005), its percent correct is not "significantly" different than that achieved by the closing Vegas line (p = 0.29 while, by standard convention, a "significant" difference would require p = 0.05). In other words, there is not sufficient evidence to conclude that the Vegas line is any better at identifying favorites than Sagarin's system is (and the same can be said for other good power rating systems).

While I'm not going to do it now, I'm confident that I'd get the same result in terms of evidence for differences in effectiveness if I looked at all the results 1999-2005 instead of just 2005.

It does not suck. It does remarkably well. It's amazing that you can have people betting on football, considering everything from weather to injuries to the quarterbacks' girlfriend breaking up with him, establish the lines then have mathematical models that don't "know" about any of that stuff achieve equivalent performance.

People who criticize these models either are unaware of or choose to ignore the overall results they achieve. I like Sagarin mainly because he presents his information in a good format and directly provides for prediction. But quite a few of them are very good.

[skinny_uncle]

Nice to know that AGS has a bookie.
:eyebrow:

[JohnStOnge]

My hat's off to you because if I'm thinking right there are 32,768 different possible scenarios!

[kardplayer]

My hat's off to you because if I'm thinking right there are 32,768 different possible scenarios!

There might be, but there's only 120 calculations :)

Skinny - Not a bookie, just a numbers geek...

[JohnStOnge]

There might be, but there's only 120 calculations :)

Skinny - Not a bookie, just a numbers geek...

Since you're a fellow numbers geek I'll tell you how I do it. I estimate the standard deviation of the errors as the square root of the Mean Squared Error reported at the prediction tracker site I linked above. Then I assume a normal distribution. I go ahead and use the reported bias estimate too.

So then I just take the predicted margin, divided by that estimated standard deviations, get a Z score, and use a Z table to estimate the probability. So if one team is a one point favorite by Sagarin I add the positive bias (think it's 0.73) and get 1.73. Then I divide that by 17 (the crudely estimated standard error) and get about 0.1. at Z=0.1 the probability is about 0.54. So I estimate there's a 0.46 probability that the actual outcome will be off enough in the negative direction for the favorite to lose.

I'm just looking at it as a black box...so that I'm not worrying about the characteristics of the model but just thinking of it as looking at a population of errors (observed spreads minus expected spreads).

But that's just one game. To calculate the overall odds for App State, for example, I'd have to do that for (if I'm thinking right) 64 different scenarios involving possible teams they'd have to go through in order to win the championship.

[Kill'em]

This is why I love the playoffs!

[skinny_uncle]

There might be, but there's only 120 calculations :)

Skinny - Not a bookie, just a numbers geek...
Those look like odds to me. You have potential.
:)

[kardplayer]

Once again, using Sagarin's ratings as of 11/19. I saw in one thread that all the seeds are hosting, plus Richmond. If Furman hosts, or one of the seeds gives us home field, there'd be some movement.

App. State 24.52% (4 to 1) - oddly, their percentage actually went down. My assumption is because there were no upsets in their bracket...

New Hampshire 17.13% (6 to 1)
Texas State 16.24% (6 to 1)
Cal Poly 9.66% (10 to 1)
Furman 8.91% (11 to 1)
SIU 8.72% (11 to 1)
UNI 7.42% (13 to 1)
Richmond 7.40% (13 to 1)

[eastbayaggie]

App. State 24.52% (4 to 1) - oddly, their percentage actually went down. My assumption is because there were no upsets in their bracket...


I'm confused here. Whether there are upsets in this bracket or not, the percentage for Appalachian State should increase. Help me out here, Kardplayer.

[kardplayer]

I'm confused here. Whether there are upsets in this bracket or not, the percentage for Appalachian State should increase. Help me out here, Kardplayer.

Its a good question. Here's my best guess:

The odds of winning as I've calculated them are a blended average of all the possible opponents for a team. Because SIU is a better team than EIU, App now has the harder of the two possible second round games, and their chance of winning that game is lower. Thus their odds are worse. Plus they were at 85 or 90% to win their first game, so there wasn't a lot of upside there.

Looking at the other teams... All the other teams (with the exception of UNH) were only 50-65% to win, thus their odds are much better now that they've gotten one step closer.

[eastbayaggie]

Its a good question. Here's my best guess:

The odds of winning as I've calculated them are a blended average of all the possible opponents for a team. Because SIU is a better team than EIU, App now has the harder of the two possible second round games, and their chance of winning that game is lower. Thus their odds are worse. Plus they were at 85 or 90% to win their first game, so there wasn't a lot of upside there.

Looking at the other teams... All the other teams (with the exception of UNH) were only 50-65% to win, thus their odds are much better now that they've gotten one step closer.

Oh. I see. You're using a blended average instead of a weighted average. I think if one had used a weighted average, then one would have more precise odds and would not have the Appalachian State's percentage go down.

[kardplayer]

Weighted average is actually what it was...

I don't have the numbers in front of me right now (different computer), but my memory of the UNH bracket for example is that there was a 42.5% chance that they'd play UNI, 42.5% chance they'd play EWU, a 7.5% chance Colgate would play UNI and 7.5% that they'd play EWU. This is because UNH was 85% to win and UNI/EWU was a coin toss.

App I believe was 90% to win, SIU was probably 66% or so.
That means that there was probably a 60% chance it would be App vs. SIU (.9 * .66), with App having a 60-65% chance of winning. There was a 30% chance it would be App vs. EIU, where App would have 85% chance to win.

Because their likelihood of winning the game is lower than had it been EIU, App State's numbers go down. The full equation looks something like this:

Odds of App making semifinals (all numbers are close, but not exactly what I originally had)

Pre-round 1:
Beat Lafayette and SIU - 90%*66%*60% = 36%
OR Beat Lafayette and EIU = 25%
36% + 25% = 61% chance of making second round

Post-round 1:
Beat SIU = 60%

Since 60% < 61%, chances are slightly lower now of winning the whole thing (but still very good)