The Stat Sheet from Roy Williams for UNC-Wake Forest, 2/22/14

For last year's home game against Wake Forest,  Roy Williams sent over the official box score to the band for me at halftime, and so I analyzed some of the stat sheet to take a deeper look at some things.

KenPom Win Probability Model

I wanted to see how things like field goal droughts (which obviously correlate with less scoring) affect the in-game win probability in KenPom's Probability Graph. Unfortunately, the Wake Forest game isn't a great case study for this, since UNC's initial win probability was 90.1%. Wake Forest's longest first half FG drought lasted from 17:53-13:46, and their win probability went from 11.9% (coincidentally their highest of the game) to about 6%.

During this time, their win probability steadily dropped (as UNC's rose), until UNC went cold too. While 12% to 6% is only a 6% change, it represents a decrease by half for Wake Forest's chances.


North Carolina's longest FG drought occurred from 7:10-4:07, during which their win probability changed maybe 1%. There are two reasons for this: firstly, they were up 15 before the drought started, but more importantly, they continued to score off of free throws. However, as can be seen in the chart, this drought did allow Wake Forest to gain leverage (blue indicates the lowest leverage, purple indicates an increase).

Chance and Free Throws, 3-Pointers

The first half of this game was notable because UNC shot remarkably well from both the free throw line and beyond the arc. They went 4-5 (80.0%) from three, and 16-17 (94.1%) from the line; prior to that game, UNC was 31.02% from three and 62.30% from the line on the season.

First, the free throws: North Carolina was a notoriously bad free throw shooting team last year. They finished 62.6% for the season, which placed them 343rd out of the 351 teams in Division 1. But given that they were on fire in the first half of this game, could we theoretically conclude that the 62.30% entering the game was too low? To determine this is easy by calculating a t-value and corresponding p-score. 

The sample variance of a proportion is: s² = pq / (n - 1); p = proportion, q = 1 - p, n = sample size
So,

Thus t = 5.398, with degrees of freedom = 16. p is less than 0.0001, so based on this sample, we can conclude with an extremely high level of certainty that the team was cumulatively better than 62.30%.

However, let's look at things from another angle with regard to the threes: 5 is a very small sample size, so does making 4 of those mean we could still theoretically conclude we were a better team than 31.02%? We finished the year at 33.6%, so should we check that t-statistic too, since 80% is a very high rate?

For the pregame 31.02%, t = 2.449, and p = 0.035. At the commonly used 95% confidence level, we can conclude that Carolina actually is a better team than 31.02%.

For the season 33.6%, t = 2.32, and p = 0.041. Once again at the 95% confidence level, we can conclude Carolina was actually even better than the season average from three. 

However, this is where we should apply the "smell test". Should we really conclude that, as a team, UNC was actually definitively better than their season-long average, simply because Leslie McDonald got hot in the first half of a game against a very weak Wake Forest team (3rd to last in the ACC), went 3-3, and Marcus Paige added another and went 1-2? Wake Forest's 3-point defense was actually 38th best in the nation, but it still probably isn't accurate to conclude that Carolina was really a better team than 33.6%. There's large variance in the short-run in anything, and chance played a large role in this 4-5 stat line.

UNC's Defensive Splits on 3rd Down

On December 11, UNC fired their defensive coordinator, and it was completely justified:

First, some quick hits on how bad our defense was overall (remember, there are 125 teams in Division 1 FBS):

• UNC ranked #117 in Total Defense, measured by YPG given up
• UNC ranked #119 in 1st Downs given up
• UNC ranked #122 (4th from last) in 3rd Down Defense, measured by percentage of 3rd downs converted by the opposing offense
• UNC ranked dead last in 4th Down Defense, measured by percentage of 4th downs converted by the opposing offense

To break it down further, when you remove the Liberty game and only include FBS teams, UNC gave up 1st downs on 50% of their opponents' 3rd downs. Only three other teams in all of FBS gave up 50%+.

Being at the ECU and Clemson games in person (two games in which we got torched defensively (although you could say that about most of our games)), I noticed that we often brought in a different personnel unit on 3rd down (we gave up 70.59% and 55.56% of 3rd down conversions in these games, respectively). To me, it seemed like we would do a decent job on 1st and 2nd down, and then give up the big play on 3rd down with the new unit. I get that different units have different specialties, and you've gotta get players rest, but if the same group continuously gets burned on 3rd down, why keep putting them out there?

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.