I don't post here much, but I have been lurking for the better part of a decade. I'm a two time Wyoming graduate and also a statistician! I do data analytics for a living and had some spare time so I decided to build a simple model forecasting the likelihood that Wyoming will make it to a bowl game.
Methodology
Step 1: Identify each team's Elo rank. I'm not going to try to build something from scratch so I blatently stole the fine work over at Sagarin. Strong teams have high Elo rankings, and the opposite for weaker teams.
Current Elo for MWC Teams
HomeAdvantage = 2.45
Wyo = 61.28
BoiseState = 82.40
UtahState = 64.72
Nevada = 56.56
UNLV = 57.09
SDSU = 70.30
NewMexico = 57.10
Step 2: Convert Elo into game by game win probability. I used the formula from this Reddit post and modified it slightly (m = 20 instead of 400) because that formula is based off Chess Elo which has a highest score of ~2000, whereas Sangarin uses a high score of ~100. I also factored in the home field advantage Elo modifier depending on where the games are played.
Current Wyoming win probability for remaining schedule
Nevada = 56%
Boise State = 10%
Utah State = 47%
UNLV = 55%
SDSU = 32%
New Mexico = 55%
Step 3: Assume each game is independent of one another (winning Nevada won't influence our chance to win Boise State) and run the win probabilities through a simple Monte Carlo model.
The Model
Step i. Simulate the win/loss of each remaining game using the respective probabilities in Step 2.
Step ii. Store the total number of wins from the simulated season
Step iii. Repeat Steps i and ii 10,000 times to get a distribution of probable win outcomes.
Step 4: Display the results. I present a histogram showing the most likely outcomes as well as what's called a cummulative distribution function (the line graph) that shows the probability of winning at least X number of games. My model currently shows an 82.5% probability of Wyoming winning 6+ games. Seven+ wins has a 52.2% likelihood, and eight+ has 20.5%. Nine+ wins is exceedingly unlikely at only 4.1%
Assumptions
1. The Elo rankings I took from Sagarin are accurate
2. The games are all independent from one another (no hot/cold streaks).
Hope you guys like it! If there's interest I'll continue to update this model each week. It's worth noting that prior to the Air Force win we only had a 42% chance of a bowl game. Air Force win was HUGE! After each win or loss I will update the model and the range of possible outcomes will change. I will also update the Elo ranks as they come available. (Winning Air Force both gave us a needed win AND boosted our Elo so it increased our chances of winning future games).
