Question for Mathlete

Submitted by BILG on November 17th, 2012 at 7:16 PM

Mathlete or any other probablity expert...

At the beginning of the year, what were the chances that the two teams I hate most manage to go undefeated.  Add in that they have two overtime wins each, a bunch of other close games, and seemingly get every bounce and call during the year.

Yes, yes, I know board, both ND and OSU are good teams and good teams find a way to win, but please spare the cliche coach speak as any sports fan knows there is a lot of luck and serendipity in a "special" season.  

I do not consider either of these teams top 5 in the country, yet even if they truly are that good, what would be the chances of both going undefeated.  The football gods truly are laughing at me.  Hopefully we can ruin OSU's season next week, and Barkley gets healthy and proves that ND is a fraud



November 17th, 2012 at 7:44 PM ^

Needing overtime, officials calls, and a missed FG to beat the likes of Purdue, BYU and Pittsburgh.  Stanford is a legitimately solid squad, but ND benefited from some questionable officiating at the end of that one.  Not to mention they beat us by 7 despite being giftwrapped at least 3 of those 6 turnovers.  One impressive victory over Oklahoma doesn't have me sold. As I said, they are good (top 10-15), not great.


November 17th, 2012 at 7:30 PM ^

OSU and ND could potentially both end the season undefeated...with NEITHER having a shot to play for the national championship. That's pretty much perfect.

Young John Beilein

November 17th, 2012 at 7:30 PM ^

But accurate statistical analysis is going to require your coefficient of hatred for these two teams as well as more information on the amplitude and frequency of laughter from the football gods.  Plugging in rough estimates for these variables, your answer should be... 2.  Let me know if you got something different.


November 17th, 2012 at 8:12 PM ^

Average probablility a really good team wins a given game...I will set at like 90%.  Of course this fluctuates base on opponent, but I just put in the average win probability for the entire set of games for a year.  So thats .9^10 for 10 games.  

Thats like 35% for one team, which is extremely high...probably because the 90% for any team as an average across all games is high.  Still, if we keep that,  for both teams thats comes to like 12% they are both undefeated.  Now factor in the probablility that those would be the two teams I hate most...Not sure how to do that.

Add on top of it all the close calls they had...I mean OT games on their own must be 50/50, but for both teams to win the cumulative 4 they have played in would be .5^4 which is like 6%.

All these probabilities must compound in some way, which is an extremely complicated calculation if we do it game by game team by team for both teams.  Haven't done probabilities in a long time, but it probably requires some sort of binomial or factorial calcs.

Using history I know this.  In the past 25 years, between the two teams there has been 1 national championship and undefeated season between the two teams.  So if we use that as a baseline, the probability of one of them going undefeated at the beginning of the year, independent of the teams' actual level of play, would be 1/25 or 4%.  Both going undefeated in the same year would be .04^2 or a tenth of a percent using that logic.


November 17th, 2012 at 8:21 PM ^

When ND and Ohio State had played their first four games (I could not find my preseason notebook), my notes had the odds for Ohio State going undefeated at 5:3, or 37.5%, and ND at 13:1, or 7.14%. So, at the end of September anyway and Ohio State out of its OOC schedule, the estimated chances were not really favorable for them, but yet 12-0 was more likely for them using Massey's model than ND.