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If you play fantasy football like me, then you likely read NFL stats and watch videos of the prognosticators’ picks-of-the-week. I am not in a high-stakes league with money, so my motivation is purely one of personal enjoyment. Yet, I am the reigning league champion and so I take it as seriously as a working graduate student can. Keeping up with inside tips helps me maintain my competitive edge. At least I thought that it did.

It is not uncommon to hear a fantasy football expert make the following statement:

Start PLAYER X because the opposing team is not very good against the RUN/PASS.

Watch the following video and listen to the predictions made by Yahoo’s Brad Evans. Note how he uses NFL stats to bolster his claims to “start” or “sit” a particular player.

Here are the two big picks that Brad Evans makes (summarized):

1. Matt Schaub is going against a Tennessee Titans team that is allowing 278 passing yards per game this season. Play him.
2. You don’t want anything to do with Jay Cutler! He is going against one of the most aggressive defensive lines in the league in the Philadelphia Eagles. They have limited opposing passer to just 1.6 touchdowns per game. Jay Cutler is going to be swarmed over!

I recently began exploring the mathematical realities behind fantasy football experts’ predictions for a seminar course on mathematical problem solving. Why? The topic interests me in a Moneyball-type of way, and I think that there is the potential to connect NFL data to an emerging personal line of research: creating engaging modeling activities for K-12 students. Plus, I might be able to eventually make my own informed decisions about fantasy football roster decisions!

My exploration into the mathematical realities of so-called fantasy football experts use of NFL stats arose from an observation: I listen to what they say, their advice seems plausible and informed, and I act upon their statements by changing my fantasy football lineup. Yet, more often than not, my decisions don’t pan out and my final point total for the week is lower than not making a change. At least that is the way that it seems to me when I lose- and, honestly, I only begin to question the experts when I fall to an opponent. Last week I lost.

Taking my loss in stride, I began wondering whether or not mathematics might be more informative than the experts. For example, does a quarterback like Matt Schaub actually throw for more yards when playing a team that gives up more passing yards on average for a given week? Is there a correlation? One would expect there to be a significant, positive correlation across all teams based on common sense. It’s a logical rationale: if a team’s defense averages more “passing yards allowed” then it would make sense that opposing quarterbacks would throw for a roughly equivalent amount of yards or greater (disregarding all of the other variables like home field advantage, injuries, and the like). This is the logic used by Brad Evans when he made his prediction. It makes sense, but is it mathematically verifiable?

Using this as my research guide, I began combing the past week’s NFL box scores and stats summaries. The spreadsheet below contains stats based on defenses.

Take Matt Schaub as an example. Schaub, the quarterback for the Houston Texans (HOU), played the Tennessee Titans (TEN). Looking at the Tennessee defense, the average passing yards allowed per game given up by the Titans is 278 prior to the game against the Texans. Schaub threw for approximately 158 yards (assuming he was the primary quarterback) against the Titans, a value that is well under Tennessee’s cumulative average to date.

Is Matt Schaub’s passing yards significantly (statistically and mathematically) different from the opposing team’s passing yards allowed? Can we draw any conclusions about all quarterbacks in the NFL based on the variables of (1) defensive passing yard average and (2) actual passing yards allowed? I crunched the numbers in SPSS and came up with the following correlations for passing in week 12 in the NFL.

The table shows a statistically insignificant relationship between defensive passing yards allowed and passing yard average at any common level of significance. Even if it was significant, the correlation is both negative and so small that we can’t draw any conclusions about a quarterback’s passing yard performance based on the opposing team’s defense! Quarterbacks are just as likely to throw for fewer yards as more yards when facing a team that allows a certain average.

Brad Evans, using the NFL stat of defensive passing yards allowed to suggest predicted passing yards allowed by a quarterback just did not work for week 12. Sorry.

I wonder how middle or high school students might use this data to interpret and model a solution that is mathematically-based?

A couple of notes:

1. A player’s point total in fantasy football is calculated by using more than just total yards accumulated. Touchdowns and fumbles also factor into the final tally, although this varies in different leagues.
2. The correlation culls data from week 12 only. Incorporating additional weeks and looking at an entire season would provide more information about the connection between passing/rushing yards and defensive averages.
3. There is probably some interesting longitudinal connections that could be made by examining correlations throughout the NFL season. For example, Week 1 statistics would be significantly positive. I imagine that this would fluctuate and drop as the season progresses.
4. I did not consider home field advantage, injuries, and other relevant/influential variables that likely impact a team’s weekly yardage totals.