That's an interesting new win probability graph.  I think the point spread should decay much quicker though.  By halftime the game is far enough along that the initial point spread should be virtually meaningless in the calculation of win probability.

So if you stick with a linear rate, the end of the first quarter would add on 50% of the point spread and the end of the half would add 0% of the point spread (so no points added).

Or you could play around with something like cutting the point spread in half every 5, 6, or 10 minutes.

I disagree. 14-3 against a bad team at half time should equate to 29-3 against a good team in terms of chaces of winning. The whole point is to show that the deck is stacked against the lesser team.

If Michigan had been losing 0-3 at halftime would you have felt that there was a 90% chance of winning the game?  I wouldn't have.  But that's what adding in half the point-spread would have computed.  In that scenario I would have personally put the win percentage somewhere between 1% and 51% depending on how many remotes I had thrown through the TV.

I agree that the point is to show that the deck is stacked against an underdog but I think the influence at halftime should be minimal.  At the beginning of the game, no matter how bad the opponent is, the rules mandate a tie (both teams start at 0).  By halftime if a team is losing to/tied with/barely leading a supposedly overmatched team there might be a reason for it.  The win probability should account for that.

Maybe adding 0 points at halftime is too little but I think it would be interesting to play around with the numbers.  Cutting the point spread in half every 6 minutes [or multiplying the point spread by 2^(-t/6), t in minutes] means you would add 1/32 of the point spread at halftime.  So in this game 14-3 would become 15-3.

Maybe that still decays too fast.  Then try 2^(-t/10) or 2^(-t/15), which would give us 18-3 or 22-3.  Personally I think the halftime score should be as close as possible to the real score.

We want to avoid the wild swings in win probability that occur near the beginning of a game but by halftime that shouldn't be a problem.  With a lead of 14-3 at halftime the win probability was already 87%.  I would say that's what it felt like to me watching the game.  It wasn't a perfect first half so I wasn't 100% confident, but they had started correcting problems on D and O to get that 14-3 lead.

Yes, I would have, because we were obviously the more talented team. For that reason, there is a much better chance that we outscore them by 3 in the second half. If they were up 14 at the half, I'd say that we had about a 50/50 chance of outscoring them in the second half too.

I could see maybe doing an S-curve so that the spread is taken into account more in the first half, is still 50% at half time, and trails of quickly in the second half to the point that it's almost non-existant going into the 4th quarter.

EDIT: I was probably a little hasty with the 14 point spread at the half, but if we were down by 7-10, I'd still think we had a good chance at beating EMU. So, I suppose that if you used a curve that cut the spread in half each quarter, that would work well. That would have given Michigan roughly 7-8 points at the half. If we were down 3, it would look like a 7-3 game. If the score stayed the same through the 3rd quarter, it would look like a tied game.

I rapped with a guy about this a couple of weeks ago and I tend to agree with you in that, if you're going to have a bettor's bias, it should decay as the game goes on. I actually think that bias is unnecessary, but agree that it is an interesting challenge to take on.

The problem is that we have a very poor idea regarding if the line is correct/accurate.

I think a good proving ground for this function would be games in which the underdog wins or really is a par competitor. Ohio State vs. Toledo, for example. The Rockets were a 19 point dog when that game started--way way way off the mark.

Other games: Auburn vs Utah State; Notre Dame vs South Florida; TCU's upset from week 1.

I think it makes a lot of sense to let the bettor's bias decay completely by halftime.

Mathlete does have probabilities calculated for winning specific games. Maybe the next game he could manipulate the first half numbers to reflect the work he's already done instead of a point spread.

For example, if he has our chances of winning SDSU at 85%, the first play would start at 85% Michigan and the bias would disappear like you suggest. This would get out some of the noise involved in picking point spreads, such as fanbase size, record ATS, ect.

mostly because of what you mention, the factors not related to relative strength that influence point spreads.

The danger is that errors in the model then become magnified, because you're using the model to modify the model's predictions, but I don't think that's any different than what other people have done. Models are constantly being refined anyway ... as long as the tools are all retrodictive, then it seems like a reasonable idea to me.

What worries me is that our run D is clearly way too high. They were pretty bad in the first quarter against EMU, until we realized that EMU simply could not and would not throw the ball. SDSU has a better RB and a competent quarterback. Count me as one of those people who are extremely nervous for this game, especially considering how flat Michigan has come out this year.

Western scored 7 in the 1st q and 3 in the 2nd. None in the 2nd half

ND scored 14 in the 1st Q, 3 in the second, 7 in the third and 7 w/ 30 sec. remaining

Eastern scored 3 in the first half and none after that.

I think our defense has been poor in the first quarter but, other than the last ND touchdown, has been excellent after that. I think SDSU will be a test, but I feel our defense has improved a lot since last year and will continue to get better throughout the year as we get more accustomed to this scheme and the coaches figure out which players are best and at what position.

My only concern with the defense is that our ability to create turnovers is a mirage. If we didn't lead the nation in turnover margin, our stats wouldn't look nearly as good.

'By the middle of the third quarter, the game was officially out of reach.' and yet we were still Running Denard up the middle past this time, which perplexes me.

Just curious, what happened to the predicted number of wins, conference projections, etc? Those always made me feel better.

I took his numbers from the "Projecting Michigan" diary and applied the wins to them. Without new probabilities, we have a 29.8% chance at a 9-win season and a 27.88% chance at an 8-win season. A win this weekend (85%) and next (100%) puts our chances at 31.55% and 26.97%. Northwestern was listed at 84%. So, there is a strong chance that we go into MSU 6-0.

I have to think that our chances of winning have gone up greatly against everyone except Nebraska and maybe Illinois. If that's the case, then 9-10 wins is probably what his numbers would say.

Is there any bias in the data relevant to UofMs slow starts?  I know you have to include it in the total data set, but what would we look like if we eliminated the 1st quarter, and just extrapolated out the final 3 quarters?

Basically, I am trying to see how awesome we could be if we played at ludicrous speed the whole game.

I know the team is young, and have so far rised to the occaision when called upon.  ( See BWC destroying ND linemen and being somewhat of a JAG against EMU).  Just curious to see what their potential is mathematically

Michigan in the 1st Half:

Michigan in 2nd Half:

Denard is cubic.

drop a Benjamin on SDSU +11?  Last I looked the O/U was 60.5.  I'm thinking under, and probably by a decent margin.

Like these charts: kind of a fun way to look at a game.

How far back does your data go?

Might be fun to go back and plot out the season of a number of really good teams, to see what their charts look like as a comparison point. Might also be fun to grab some teams that had "lucky" seasons (i.e., MSU last year) and see how those looked over the year.

I think you could use Tufte's ideas about many small multiples to show a bunch of these charts for a given team in a very small space, allowing for neat comparisons.

Adding point spread to a chart like this is HIGHLY mis-leading. Just chart the Appalachian game with this method. Michigan would have had very high Win percentage (probably 100% by the third quarter).

If you are going to add point spread, it needs to be based on amount of time left.

Regarding the field postion, I was fairly irritated that EMU seemed to have some kind of elite punter or something.

Wile has done much better than I anticipated but it would be nice to have the real punter back. Provided his off field decision making improves.

I like the new formulation, but as others point out you might have situations (e.g. The Horror) where Michigan's win probability stays too high throughout the game. I think you could do something very fancy, Bayes-wise, that uses the pre-game spread as a prior and the current spread as the outcome, and constantly update the projected spread based on that. I'm not smart enough to figure out the formula, though.

A simpler option is to just run the decay for 3 quarters. So if the spread is 30.5, then basically that's .5 points per minute. Rebalance across 45 minutes (3 quarters) so the initial spread would be ~22.9, so the halftime spread would be ~7.6 points. By the start of the 4th quarter you'd only be using actual in-game probabilities.

Any chance you can rerun the expected wins, and show the new graph and table?

Would like to see what the most likely outcome is and probabilites for 8,9,10 wins.