By Kurt Bullard

Division games are an interesting beast.

Three times a year, each team in the NFL will go up a unit which it has already faced. The effect of playing a team which you have already “seen” poses some interesting questions about how the game will unfold. An offense has to decide whether to try to attack with a similar strategy as they did in the first game or try to switch it up and throw more wrinkles into the offensive gameplan.

This has serious implications for fantasy football, especially since a lot of these matchups will take place towards the end of the year, possibly in the fantasy playoffs. Take Joe Flacco, for example. He torched the Bengals for 362 yards, 2 TDs, and 1 INT earlier this season, but then struggled against the Steelers, only going for 189 yards, 1 TD, and 1 INT.

So when it comes time for the Ravens line up against Cincy and Pittsburgh, does Flacco have Cincy’s “number,” or should the results be thrown out the window?

To look at this, I looked at quarterbacks from the 2013 and 2014 seasons who threw more than four passes in each division game during a season, making the assumption that if a QB threw at least five passes, he started the game. This left me with 154 pairs of games over these past two seasons, enough of a sample size to conduct sound statistical analysis.

Since I wanted to predict performance for the second division game, I used the fantasy output in the second game as my dependent variable. I regressed the second game’s fantasy point totals against the player’s average for the season up to that game and the player’s point total from the first matchup to see whether or not knowing the outcome of the first game matters at all. I also controlled for whether the second game was on the road or at home.

These are the results of the regression:

The main takeaway is that the major consideration when predicting player performance is how they do on average, a similar finding to earlier work I’ve done, since the variable is undoubtedly significant and close to 1, meaning that all other variables held fixed, you expect the player to play more or less his average.

It also didn’t matter whether the second matchup was on the road or at home for divisional matchups; despite the large negative coefficient for the “Away” dummy variable, it was not significant. It’s possible, however, that if there were a larger sample size, the location of the game would become a significant variable, as it was in my aforementioned post where it was about a one-point bump on average to play at home versus on the road.

But nonetheless, there are some interesting findings. The coefficient for the performance for the first game was actually negative, meaning that the better someone performed in the first matchup, the worse you’d expect them to do in the second. However, although that coefficient is significant, this value could be caused by regression to the mean caused by regression to the mean than by a player being stymied because he’s being targeted more by defenses.

You can test this by seeing if the outputs in each game are independent. To see if these games are independent, I’ll be testing two hypotheses: whether a player will play above average in the second game given he played above average in the first, and whether a player will play below average in the second game given he played below average in the first matchup. Since I’ll be testing two hypotheses, I have to correct my P-value so that my true Type-I error is .05. I’ll be conservative and use the Bonferroni correction, which moves my significance level down to .025.

To look at these problems, I looked at the conditional probability of the second game predicated on the output of the first to try to get a better look at this issue. If the first game had no bearing on the second one, you’d expect that a player would outperform his average about 50% of the time. But, out of all of the players in the analysis, 74 were “above-average” in the first division matchup. Of those players, only 25 continued to outperform in the second matchup, good for only 33%. Given this result, the P-value for the hypothesis test that probability that a player should outperform twice given that he’s already done so once is .007, low enough to reject the idea that a player will outperform twice against a team given that he did so in the first matchup. It’s a very real possibility that teams focus more attention on the person who torched them last time.

The same did not hold for players who underperformed in their first game. Out of those 80, 44 players underperformed again, while 36 played above average in the rematch, numbers which are close enough to half to say that the first game doesn’t have an impact on the second game if the player underperformed in the first.

Although this analysis does shed light on some information, it still doesn’t complete the whole picture for fantasy QB performance. Another takeaway is that knowing the results of the first game and the player’s season fantasy output average only explains 23% of the variation. More than three-quarters of the variation, then, is random noise, which could be due to the flow of the game, weather, or other reasons.

So when Matthew Stafford takes on the Bears in Week 17, don’t expect him to live up to his 400-yard, 33 point performance that he put on this week against Chicago. The 11 point average is the better bet.