As football fans, we have an intuitive understanding of regression to the mean: Certain players are performing at such a high level that they’re likely to perform worse going forward, while others are performing at such a low level that they’re likely to perform better going forward. For instance, Drew Brees ranks 11th in fantasy quarterback (QB) scoring through Week 2 of 2014, whereas he’s never ranked lower than sixth during his Saints career. Therefore, it’s reasonable to guess that he’ll be moving up the rankings as the season progresses.
The difficult part comes when we try to answer the question, “by how much?” That’s because doing so requires transforming our abstract intuition into a concrete number. Luckily, quantifying regression to the mean isn’t difficult, as it merely requires the sort of reliability analysis I’ve been publishing in this space over the past couple of weeks.
In the standard fantasy football scoring system used by FootballGuys.com (FBG), QB points are calculated from passing yards, passing touchdowns (TDs), interceptions (INTs), rushing yards, and rushing TDs. Albeit on a per-attempt basis, my posts of late have already identified the half-skill/half-luck points for all of the pass-related parts of the equation:
- Yards per attempt (Y/A) stabilizes at 396 attempts
- TD Rate (TD%) stabilizes at 1,059 attempts
- INT Rate (INT%) stabilizes at 1,681 attempts
Using these stabilization points alongside a QB’s current passing stats, we can estimate his True Fantasy Points (TFP) and calculate how many points he’s scored above or below his “true” fantasy scoring ability. And once we know this, we can use TFP to objectively identify those QBs that are most likely to see increases (or decreases) in fantasy production going forward.
Better Assumptions Mean Better Results
But before we do that, there’s one final subjective decision we need to make. Namely, should we assume that (a) all of a QB’s attempts prior to 2014 have an impact on TFP, (b) none of a QB’s previous attempts have an impact, or (c) some of a QB’s previous attempts have an impact; and if (c), then which ones?
Our choice has major implications for our TFP estimation because it determines how much weight we put on the “observed” part of the formula, which you’ll remember is
So let’s again take Drew Brees as an example and focus on calculating his “true” Y/A. If we ignore his pre-2014 attempts, the calculation is
[(6.95 * 82) + (6.93 * 396)] / (82 +396) = 3,314.18 / 478 = 6.93
If we include all of his attempts prior to this season, then it’s
[(7.51 * 6,881) + (6.93 * 396)] / (6,881 +396) = 54,420.59 / 7,277 = 7.48
and if we only include his previous attempts with the Saints, then it’s
[(7.75 * 5,072) + (6.93 * 396)] / (5,072 +396) = 42,052.28 / 5,468 = 7.69
I think we’d be making a mistake if we pretended that Brees’ career before 2014 doesn’t exist, so the real choice here is between including all of his previous attempts or just the passes he’s thrown for the Saints. The fact that I’ve been doing the latter in my reliability analyses tells you where I stand: We should calculate TFP based on a QB’s observed performance with his current team.
TFP Through Week 2
Now that we’ve made our decision, we can use the third equation above to calculate TFP and then compare it to each QB’s actual point total through Week 2. Subtracting the former from the latter creates a +/- stat, whereby positive values suggest decreased scoring per pass attempt going forward and vice versa. Below is the payoff in table form, and I’ve included TFP assuming zero team-specific pass attempts prior to 2014:
|Player||Tm||Obs FBG||Rk||TFP14||Rk||TFP||Rk||+/- 14||Rk||+/-||Rk|
As an example of how to read it, take a look at the row associated with Peyton Manning. The “Obs FBG” column says he’s accumulated 49.6 points in the passing game. The next two columns tell us Manning’s TFP depending on which assumption we make: Manning’s scored 31.7 TFP if we exclude his pre-2014 pass attempts with the Broncos, but 38.1 TFP if we don’t. Finally, the last two columns display a +/- estimate: Manning’s overperformed by 17.9 points if we ignore his past two seasons in Denver and overperformed by 11.5 points if we don’t.
You’ll notice that, under both assumptions, Manning is the most overperforming QB in fantasy football right now, and is therefore likely to exhibit the most mean regression going forward. However, ignoring his 1,242 previous attempts for the Broncos infers nearly 60% more mean regression than if we (more sensibly) include those attempts. Other QBs on Manning’s level (e.g., Aaron Rodgers) also have large disparities between “+/-” and “+/- 14.”
The main use of TFP is identifying buy-low and sell-high candidates for transaction purposes: In general, acquire QBs near the bottom of the list and unload QBs near the top of the list. Of course, it’s important to keep in mind that the +/- scores are just a guide. Would I trade Peyton Manning because he’s overperformed the most through Week 2? Of course not. Several factors suggest he won’t regress to the mean all that much. And even if he does, he’s likely to remain among the highest-scoring QBs. On the other hand, if I had Ryan Fitzpatrick in a two-QB league with deep rosters, I’d trade him ASAP because he doesn’t have a stellar track record and Houston won’t be playing Oakland every week.
In that same league, however, Rodgers, Brees, and Romo are ripe for the taking. They’ve got great fantasy track records, they’ve faced tough schedules so far, they’re in pass-happy offenses, and TFP says they’re among the most likely QBs to enjoy increased scoring going forward.
DT : IR :: TL : DR
Using reliability analysis and current stats, we can calculate a QB’s “true” fantasy points (TFP), and can therefore identify which QBs are the most (or least) likely to exhibit regression to the mean as the season progresses. A vital consideration for this calculation is whether or not to include pass attempts prior to the current season. I believe it makes good sense that we should.
That said, TFP isn’t gospel; it’s just a general guide and non-TFP factors matter. Through Week 2, I’d be trying to trade for Aaron Rodgers, Drew Brees, or Tony Romo.