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Entering Game 7: Wyoming has an 82.5% chance of making it to a bowl game

F

Flexo

Member
Hi!

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.
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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).
 
Just to highlight how important beating Air Force was: take a look at our chances from before the AF game. That victory DOUBLED our bowl chances!
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Dude! This is amazing.......you've got me really curious

Sent from my XT1585 using Tapatalk
 
If we had beat EMU then there would be two adjustments to the model.

1. The entire distribution would be shifted one win to the right (82.5% chance to win 7+ games, 97.2% chance of 6+

2. Our Elo ranking would be a bit higher. I'm not going to delve into the details of exactly how Elo works, but the effect would be a higher Elo would translate into a higher chance for us to win future games.

Put 1 and 2 together and you would be 97.2%+++ chance for a bowl game (the exact +++ depends on Elo adjustment).

Make sense?
 
Very interesting. And cool.

I felt all the remaining games besides Boise and SUDS were 50/50. Be curious to see how the lines compare to your model.
 
No numbers matter right now. If Wyoming beats Nevada the UW/Boise game is generational. So huge. THE day you want to be in Laramie WY USA
 
What a coincidence. I was about to post a very similar analysis I worked up myself, but you beat me to the punch. The main difference was I used crayons and the back of napkins. Good stuff, very interesting.
 
Like the stats.

Here is a link to ESPN's chance to win each remaining game based on their FPI ranking system. It has been nice to see that % steadily rise through the season. Prior to the season I think our forecasted finish was 2-10 up to 6.4 - 5.6 now.

ESPN Wyo projection week 8
 
Expat_Poke said:
Like the stats.

Here is a link to ESPN's chance to win each remaining game based on their FPI ranking system. It has been nice to see that % steadily rise through the season. Prior to the season I think our forecasted finish was 2-10 up to 6.4 - 5.6 now.

ESPN Wyo projection week 8
Click to expand...

I think they only had one conference game above
50% for us to win


Sent from my iPhone using Tapatalk
 
Crazy how the rolls seem to be reversed for the Cowboys and Wolfpack this year. Nevada had a respectable season coming into Laramie last year and got beat. I hope we can avoid a similar let down.

We should be able to run the ball on Nevada. When we can run the ball effectively we are damn hard to beat.
 
BeaverPoke said:
So what you're saying it we're going bowling!
Click to expand...

Not out of my mouth, a lot of football left. I won't be saying that until Cowboys get win #7, and before that, they need to get wins #6 and #5. 6-6 makes Wyoming bowl eligible. While a 6-6 team likely goes bowling, it does not guarantee a bowl game.
 
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