NFL Playoff Picks 2014-15

The NFL Playoffs start this weekend, and the top seeds (NE, DEN, SEA, and GB) are appropriate (representing 4 of the top 5 teams in Pyth (the lone missing team being Kansas City, who disappointingly didn't make the playoffs)), and these teams are heavily favored.

Creating an NCAAF Model as a Function of Stadium Size

My friend roommate colleague (who's also my friend and roommate), "Stan Hooper", suggested that a decent model for predicting college football game outcomes would be rating teams based on the sizes of their stadiums.

I took the size of each team's stadium and predicted the winner of each game simply by which team had the larger capacity. I factored in home-field advantage by adding the average stadium capacity to the home team's stadium size (home-field advantage in terms of points is 3.5, which is approximately the average margin of victory by home teams (this season is 3.78)) in this equation.

On the season, the Home-Field Model predicted 60.96% of straight up winners. For comparison, my MDS Model predicted 71.71% correctly, and Vegas tabbed 75.11% correctly. Honestly I'm just relieved that a model created in 30 seconds by importing a Wikipedia page into a spreadsheet didn't beat the one I worked an entire semester on.

Kentucky is So Good They Broke My Model

The Matrix model uses a series of n x n matrices involving only wins and losses to calculate a "true" win percentage that factors in the strength of each team's opponents. There is a matrix for wins and a matrix for losses, which are then inverted, factoring in the total number of games each team has played, and then multiplied by an n x 1 vector that is each team's net wins (Note: n = number of teams (in NCAAB, 351)):

net wins = wins - losses

Each game simply is denoted by a "1". Therefore, the outputs of the win and loss matrices are bound between -1 and 1. If a team has a winning "adjusted" record, their rating is above 0; otherwise it's negative. I then standardize this rating to be analogous to win percentage, bound between 0 and 1:

i = initial Matrix rating; -1 <= i <= 1

i + 1 = i'

i' / 2 = f

f = final Matrix rating; 0 <= f <= 1

Kentucky has a rating of 1.005. As seen above, the final rating has an upper bound of 1. So the issue must be within the win and loss matrices themselves.

Kentucky's loss matrix rating is 1.000; this checks out, since they're undefeated and thus have 0 losses. The issue then is pinpointed to their win matrix: their rating is 1.010.

In their win matrix, they have 12 wins, and 12 total games (Note: only Division 1 games are included, but in this case all of Kentucky's opponents have been Division 1). This checks out too. Their strength of schedule is very high: 0.645 (0.500 is average). This is the only explanation I can offer as to why Kentucky's rating is so high: they've played a very tough slate of teams and beaten them all. Even so, it shouldn't be above 1. 

A full rundown of the Matrix method can be found here on page 31, "Least Squares Ratings", written by Kenneth Massey. 

Fluctuations in UNC's Bowl Chances Throughout the Season

Since I keep a weekly archive of my NCAAF ratings, I was able to retroactively determine how likely UNC was to make a bowl after each of their games. Obviously each win and loss greatly impacts the total probability, since a concrete "W" increases whatever pregame win probability to a 1 in the books (and conversely an "L" brings that down to a 0).

The following chart is based on simulating the rest of the season 10,000 times after each of UNC's games, using each week's archived ratings. Besides the explicit influence of each win and loss as described above, two notable changes occurred as follows:

• The 70-41 loss to ECU had a HUGE negative impact. One reason was the lopsided score itself (and only having 3 games of data at that point), and another was that this week was when I transitioned fully from my pregame rankings to using the Composite ratings that factored in only this year's data (after Week 4)
• The 50-43 loss to Notre Dame greatly improved the likelihood of 6 wins (from 13.46% to 32.03%) because it was a close loss to a good team (we performed better than expected). However, another coincident factor was that this was also the week I transitioned to fully using the Pyth ratings to predict games

Is FSU In the Top 4, Much Less #1?

Some controversy has developed in the past few weeks when the playoff selection committee ranked Oregon and Alabama (both with one loss) ahead of Florida State, the only Power 5 team without a loss.

However, the only thing that matters is that FSU makes it into the top 4 for a spot in the playoff. FSU is #1 in the AP poll, #1 in the Coach's poll, but #3 in the CFP rankings. I checked where the Seminoles ranked in more objective rating systems to see if they're underrated at #3, or whether they're overrated and should even be in the top 4 at all.

In my MDS Composite model (which aggregates wins/losses, strength of schedule, and margin of victory to estimate a complete picture of each team), FSU checks in at #11. PredictionMachine, which simulates every team against one another 50,000 times to generate rankings, ranks Florida State at #12. Kenneth Massey maintains composite rankings of a multitude of different statistical/computer models (114 to be exact), and FSU still doesn't crack the top 4: they're ranked #6. Of those 114 models, Florida State is ranked #4 or better in 51: less than half (44.74%). They're also ranked #1 in only 18: less than 1 in every 6 (15.79%).

The only model in which they rank #1 (of my MDS components) is the Matrix model, which only takes into account wins and losses and the strength of opponents (it was designed to be analogous to the BCS computers (and the implementation of the playoff selection committee was supposed to eliminate these flawed BCS systems)). Ultimately, Seminole fans should consider their team lucky to still be included in the playoff at all. The committee has left Marshall completely out of the Top 25 due to their weak schedule; Florida State's isn't all that impressive either (FSU's SOS ranks #66 in FBS per my metric, while Marshall ranks #118. For comparison, Alabama's is #17 and Oregon's is #53).

Finally, should Florida State (perhaps unfairly) make the playoff, don't expect them to win it all. Simulations of the current playoff matchups give the following results, with FSU repeating as champions about 1/10th of the time:

	Win %	National Champion
#1 Alabama	66.23%	46.19%
#4 Miss St	33.77%	18.32%
#2 Oregon	62.56%	24.82%
#3 Florida St	37.44%	10.66%