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.