While this thinking is pretty evident in the QB/WR combo, we wanted to look deeper to see if there were any other hidden interactions (both good and bad). For example, a team will throw the ball a lot more when they are down, so maybe it would be bad to own a defense and a quarterback on the same team.
To test this, we generalized the same simulations we ran last time. Draft Kings' lineups require 1 QB, 2 RB, 3 WRs, 1 TE, 1 FLEX (RB/WR/TE), 1 D/ST. Other DFS sites also include kickers, so for this analysis we looked at every combination of QBs, WRs, RBs, TEs, D/STs, and Ks.
Our dataset consisted of weekly fantasy data from the last five years including teams, opponents, positions, scores, lines and final results. For this analysis, we limited the player pool to the end of season Top 15 for QBs, TEs, DSTs and Ks. This is because you only start one player at these positions and we wanted to limit the pool to players who would be started often. For WRs and RBs, since you need to start more of these positions, we instead limit our sample to the Top 45.
However, we would like to note that there is a valid strategy that includes starting obscure players who will be picked a lot less frequently to differentiate your entry from others. While this is valid, these players are likely one week fill-ins who will have very low scores in other weeks by virtue of being a backup, and due to there being a higher number of these players any potential effect we might find would be obscured. Thus our cutoff although somewhat arbitrary is justified.
The actual mechanics of the simulation are as follows. We iterate through each week of each season, and calculate the scoring of every single pair of positions. So when analyzing the interaction between a QB and a TE we have 15x15 possible pairings, or 225 groupings each week (assuming there were no byes or injuries).
If we are instead analyzing RB and WRs, we then have 45x45 combinations, or 2,025 combos. We don't try combinations of players from the same team and position, because either it makes no sense, as in you would never start two QBs or TEs, or we don't have enough data with WRs and RBs. For all the pairs, we calculate their combined score that week and mark them with an indicator if they are on the same team. Doing this for each week of every season, we generate a very unbalanced dataset that has ~4.2% of pairs coming from the same team.
Next we need a way to compare our results to derive meaning. For example, when a defense/special teams and a kicker are on the same team, the Standard Deviation (SD or Std Dev) is 8.97, but when they aren't we have a Std Dev of 8.39. Because our dataset is so unbalanced and complicated to produce, it isn't easy to calculate whether these differences are statistically significant.
Instead, we take a more frequentist based approach and simulate a bunch of randomly generated seasons. For each week, we randomly assign teams (with replacement) to our two position groups. Then we run the same procedure as before to once again generate pairs of players on the "same team" and "different team", but in this case these teams were randomly assigned and have no relation on reality.
If we run 1,000 simulations with randomized teams, we can compare where our actual result fits in. This answers how unlikely it is that our actual result just came from chance. Since we care about both winning - and not losing - we want to look at this from a two-sided perspective.
When looking at the percentiles of Std Devs, a small value indicates that random chance would've predicted a higher standard deviation, (and so we want to avoid these cases) and a high value indicates that we have exceeded what randomness would dictate (and so we want to choose these cases).
Now ideally, we could just use a computer with a lot of computing power, but alas we don't have one. Since each simulation of the five-season chunk takes about 5.5 seconds to run, and we ideally want 1,000 or more simulations per position pair, with 15 pairs this would take just under 24 hours to run.
Instead, we first ran smaller test samples with 50 simulations to cut down on the runtime. Since false negatives (where our small simulation would say there is no effect but if we had run a full simulation we would see an effect) are more costly, we set our cutoff at the top and bottom 20 percent to run our full simulations. This left us with eight pairs (cutting down our runtime by about 12 hours): QB/WR, QB/TE, WR/RB, WR/D, WR/K, RB/D, RB/K, and D/K.
Since we already covered QB/WR in our last post, in this one we will focus only on these new combinations. However, we want to note that while some of these new combos are significant, none are even remotely close to the QB/WR effect. Basically, if you aren't rostering a QB/WR pair in DFS you exponentially decreasing your probability of winning.
Here are the percentiles of our new combos:
The only combo to avoid is Wide Receivers and Defenses of the same team. While initially it looked like you also needed to avoid WR/RB pairs, it isn't as bad as initially thought (although it still is clearly not good).
Similarly, the only ones we would call significant are QB/TE pairs and DST/K pairs. However, WR/K, RB/K and even RB/DST seem to be closely related.
Our astute readers may have noticed that there is a correlation between the percentile of the mean and the percentile of the standard deviation. This is because our data has a much larger and more drawn out right tail, (eg: when a player goes for 30-plus points), compared to its left tail which essentially stops at zero (there are extremely few data points with negative fantasy scoring).
Looking at the comparison between quarterbacks and tight ends essentially reveals that we are looking at a QB/WR-lite relationship. However unlike with the WR, most of the added variance is due to the higher mean. This is not to say that a higher mean is bad especially since the whole point of fantasy is to score the most points. Instead, we want to maximize our mean and variance, but to put a number on this tradeoff would be subject of another post.
Our next most significant value of Standard Deviation is the interaction between a DST and a K. It is also the hardest to explain why. Our hypothesis is that when a defense is playing well, this holds the opposing team to fewer points. Thus, a field goal is worth relatively more, so coaches will opt to go for longer field goals or go for a field goal on fourth down instead of trying for a touchdown.
Our next two - RB/K (left) and WR/K (right) - are very similar. The thought process here, is that kickers benefit when either a running back or a receiver is having a good game because the offense is more productive giving the kicker more opportunities. Since this interaction is very indirect, the higher variance is due almost exclusively to the fact that there is a higher mean. This is mitigated because kickers aren't very reliant on any one position, as yards can be gained by a WR, a RB or a TE, and sometimes even a QB or DST.
This is a very, very weak trend. Some of this relationship is likely due to a team running the ball more to kill the clock if they are winning. However, this is likely obfuscated by the fact that when a running back is having a good game, the opposition will probably pass more attempting to catch up, hurting the DST.
Now for the negatives:
Unfortunately, this was only significant at an alpha of .15 (which is never used). However, given the mediocreness of the relationship, there is a somewhat large difference in standard deviation between the expected and the actual. This is likely due to WRs and RBs taking touches away from each other. However, if a RB or WR is doing well, the defense will likely adjust opening up the field for the other player, clouding the overall effect.
Finally, the most significantly negative result. The concept is that when a defense if playing poorly, a team is forced to throw downfield more. At the same time, if a wide receiver is playing well, this likely means the other team is going to try to throw more too, and in a shootout nobody's DST does well.
After all of that, I'm going to break my promise and bring you back to the QB/WR effect I told you I wasn't going to talk about. Well, I lied. Numbers are sometimes hard to put into context, but images aren't.
Now, you must be thinking… "How do I know this is valid, you used five years of data and ran same random simulations?" This brings us to the overriding question: How repeatable are these trends in the future?
The answer is that these trends are way more probable to continue than any player's continued success. This is a trend based on a whole bunch of players over years of data. So, while it may not continue for individual pairs, the trend should continue overall. For example, let's take a look at the current Top 7 scoring fantasy TEs. They are Gronkowski, Eifert, Barnidge, Olsen, Kelce, Watson, and Walker.
Gronkowski is just Gronk, and if you need to be told he is good at football, you probably shouldn't bet money on DFS. But anyway, Brady's best four performances were also Gronk's best four.
Eifert didn't play in Dalton's highest-scoring game, but in Dalton's next two highest-scoring games were Eifert's best and third-best performance.
Barnidge has been a model of consistency, but his best game also coincided with Josh McCown's best game. His three worst games all occurred unsurprisingly when Manziel played more than McCown.
Although not in this order, all of Newton's Top 5 scoring games have been Olsen's Top 5 scoring games as well.
Kelce's Top 3 performance's coincided with Alex Smith's second, first and fourth best performances respectively.
Besides Brees' seven-touchdown, 500-yard game which was also Watson's highest-scoring game, this relationship doesn't work as well.
Lastly, Delanie Walker has had half of his scoring come in his Top 2 games. "Coincidentally" these are the two games Mariota threw for four TDs.
Instead of continuing, it seems pretty clear that this trend has been here and will continue until there are significant rule changes. For the DFS aspect, the point is that these aren't all superstar QBs who are going to be priced highly.
Instead, they are players who have had a few good weeks at the same time their TEs did too (and vice versa). This now tells us what to do when we feel a QB or WR is going to have a good game. The next topic of interest will be to predict when these big games will happen and then choosing a QB/WR or QB/TE pair from that team. Oh, and make sure to avoid the defense for both that team and their opponent.
Carlos Pena-Lobel is a member of the Harvard Sports Analysis Collective, a student-run organization at Harvard College dedicated to the quantitative analysis of sports strategy and management.