A Monte Carlo Simulation of the Big10 Race

November is shaping up to be quite the race in the Big10, I have to say, the addition of divisions and a championship game have created a great new dynamic (and makes me rethink my objection to a playoff, hmmm.)

Many sites have written about all the permutations of possible teams in the championship game, and the surprising fact that OSU is not out of it, and in fact has a very good shot at making the game. Being a bit of a nerd, I decided to play around with a “Monte Carlo simulation”:http://en.wikipedia.org/wiki/Monte_Carlo_method of the race to the championship game.

I wrote a little C program that does any arbitrary number of iterations of the rest of the season and examines the results to determine the championship game participants. The outcome of each game is determined randomly — a random number is selected from 0-1 and used as an index against the a priori probability (as made up by me) that each team would win the game. I.E., if you believe Northwestern has a 70% chance of beating Minnesota, then any random number from 0 to .7 implies a Northwestern win. I used the c rand function with a time-based seeding on each run, please no complaints about the quality of my random numbers, I am just simulating football games for gosh sakes. I toyed around with the a priori probabilities a little to see how sensitive the outcomes were. And then at the end of the season, I apply all the tiebreakers if necessary to see what teams represent the divisions in the title game. I ran the simulation 1000 times, and a few runs of 10,000 trials just for yuks. The 1000 run simulation

So — the Legends division. Not surprisingly, due to the weakness of their remaining schedule, MSU is the title game rep ~2/3rds of the time. Nebraska about ~1/3, and Michigan picks up a smattering (1%) of appearances. Since Michigan has already lost to MSU, if they ever end up tied in the standings, MSU always takes the spot. Michigan needs MSU and Nebraska to both falter (and can control the Nebraska since they have yet to play) and also needs to beat OSU, Illinois, Iowa. A tough road. This weekend’s play won’t shake things up much, the most interesting game is the Michigan-Iowa game, I would have picked Iowa a week ago but losing to Minnesota has shaken my faith in the F(erentz) Troop. The Nov 12th weekend will be more entertaining — MSU@Iowa, Michigan@Illinois, Nebraska@PSU. And then Nebraska@Michigan Nov 19th. It seems unlikely that Michigan will still be in the hunt by the time of the Ohio State game.

The Leaders division is far more interesting. PSU has the inside track, no surprise being up 2 games on everyone else at this point. They take the title game spot 30-60% of the time, depending on how you view the likelihood of them winning their remaining games. If you think they are a slight favorite in all their remaining games, then 60%. If you think they are a modest underdog, then 30%. OSU has a surprisingly good shot, 20-25%, depending on how you rate their odds against Michigan and PSU, and because they are in a good tiebreaker position having beaten Wisconsin. Wisconsin picks up the pieces and has the weakest chance due to the OSU loss. The Nov 5th weekend will likely teach us nothing as PSU has a bye, OSU has Indiana, Wisconsin has Purdue. The Nov 12th Nebraska@PSU game is one to watch, and then Nov 19th with Wisconsin@Illinois and PSU@OSU is a defining weekend. There is a very real chance that on the final weekend, all 3 teams need a win to make it to the game — OSU is at Michigan and PSU is at Wisconsin, so that should be a great day.

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