Wednesday, October 20, 2010

projecting the future

Ever do a metric butt-ton of work for a really simple conclusion? Then you'll love blogging. Today, since this week represents the halfway point of the season, we attempt to project the second half. It'd have taken about 15 minutes if I just whipped out the ol' rectal extraction tables - 5 minutes with the calculator and 10 typing the post - but I thought I'd get all scientific and use the Sagarin ratings instead.

Here's the way-too-complex methodology: Sagarin, see, assigns a rating to each team. These can be used to predict the outcomes of any game; you take the rating of the two teams, add 3.5 to the home team's rating, subtract the lesser number from the greater, and you get the point spread. UVA's rating is 64.69, Eastern Michigan's is 49.73, give UVA an extra 3.5 for being the home team, and UVA is favored, according to Sagarin, by about 18.5 points.

What that doesn't do is give you a percentage chance of winning, which is what I was really after. So I decided to make it hard on myself. I calculated the projected margin of victory (PMOV) for each of UVA's remaining games:

UVA over EMU by 18.46
Miami over UVA by 13.08
UVA over Duke by 4.61
Maryland over UVA by 1.25
Boston College over UVA by 3.46
Virginia Tech over UVA by 19.06

And then I compared those to every game played this season and their PMOVs, +/- 1 for the three smaller PMOVs and +/- 2 for the three larger so as to have a better sample size.** For example, 64 of this season's games had a PMOV between 3.61 and 5.61, the search margin for the Duke game. 49 of those ended in victory for the chalk and 15 of them ended in an upset. So I consider the Duke game to be a 77% chance of victory for UVA.***

Using that methodology, here are our chances of winning the next six games on the schedule:

Eastern Michigan: 100%
Miami: 3%
Duke: 77%
Maryland: 37%
Boston College: 22%
Virginia Tech: 0%

Nobody so far this season has pulled off an upset, when facing an 18-point PMOV. So for all intents and purposes (hey! grammar lesson: it's not "for all intensive purposes", so if I catch any of you people saying it like that I will slap you with a fish) it would take a miracle to beat VT or lose to EMU. I let the 100%s stand in the next step.

Which you ought to be familiar with: there are 16 possible outcomes from the four up-in-the-air games, and here they are:

Win all four: 0.19%

Win three, lose to BC: 0.67%
Win three, lose to Md.: 0.32%
Win three, lose to Duke: 0.06% (the least likely of all outcomes)
Win three, lose to Miami: 6.08%

Beat Miami/Duke, lose to Md./BC: 1.14%
Beat Miami/BC, lose to Duke/Md.: 0.10%
Beat Md./BC, lose to Miami/Duke: 1.82%
Beat Miami/Md., lose to Duke/BC: 0.20%
Beat Duke/BC, lose to Miami/Md.: 10.35%
Beat Duke/Md., lose to Miami/BC: 21.56%

Lose three, beat BC: 3.09%
Lose three, beat Md.: 6.44%
Lose three, beat Duke: 36.70% (the most likely of all outcomes)
Lose three, beat Miami: 0.34%

Lose all four: 10.96%

Add them all up and you get the following percentages (these include the so-called guaranteed win and loss against EMU and VT):

Chances of finishing 3-9: 10.96%
Chances of finishing 4-8: 46.57%
Chances of finishing 5-7: 35.15%
Chances of finishing 6-6: 7.12%
Chances of finishing 7-5: 0.19%

The standard caveats of rounding and adding up to 100 apply.

So there you have it: the projected finish at this point is 4-8, with a very decent chance of getting to 5-7.

Of course, if the BC game was at home it'd be a totally different story: they are ranked only 0.04 points below us, meaning that home-field advantage is the entire difference. And BC crowds have been known to be notoriously small; there probably won't be 3.5 points worth of difference at Chestnut Hill. Just one of many, many ways real life interferes with the cold, unfeeling mosaic of numbers. So take it for what it's worth to you.

**Yes, every bloody damn game. I have a special talent for deciding to do things that I think will take X time, and finding they really take X+N time, where N is a number somewhat north of twice X.

***I'm aware of the circular nature of this: these games are the sole determining factor in these ratings, so I'm applying the ratings to their own component parts. But the results were sufficiently bell-curvy, in that there were fewer upsets the greater the PMOV, so I went with it.


Adam said...

I know that was a lot of work, but I enjoyed this post. The results were right about where I expected with the BC game being the difference between 4-8 and 5-7. Let's hope their QB problems continue and they lose games coming up, ensuring a small crowd for what will most likely be a cold weather game.

Chief Wahoo said...

I love nerdiness! So here is my nerd challenge. Given the 100% chance of beating EMU wouldn't it be safe to say that out Sagarin rating would increase from that game? Also on that same note could we (by which I mean you obviously) estimate that increase? And taken even further couldn't we account fo such a scenario for the other remaining teams on the schedule? Just a thought, probably too many unknowns to make it worth while.

Also GO HOOS!!!

Brendan said...

Unfortunately nobody knows the formula behind Sagarin's numbers. A closely guarded secret, naturally.

Also, since half of the final rating includes actual margin of victory, the number would fluctuate wildly depending on whether we won by 3 or 35. It's not inconceivable that we could win and yet drop in the rankings. Same holds for the rest of the teams on the schedule.

Plus, older rankings are unavailable, probably to prevent people like me from coming up with a formula to project them.

But I did save the numbers, so I can rerun them after the game and the new rankings come out.