Embracing Volatility: Quantifying the Value of Variance in Best Ball (Fantasy Football)
Welcome to the summer of Best Ball here at the Fantasy Footballers. This strategy-based article is a collaboration between Matt DiSorbo and myself, Matthew Betz – Matts for the win! DiSorbo takes a look at the analytics and runs the numbers. Later in the article, I’ll give my takeaways as well as some actionable advice. If you’re looking for more best ball content, be sure to tune into the DFS Podcast throughout the summer and check out our Best Ball Primer, an exclusive part of the Ultimate Draft Kit+ out June 1!
This article aims to answer a simple question – are boom/bust players actually better in best ball? Think about it – how often have you heard a fantasy analyst utter the phrase, “I’m not drafting DeSean Jackson this season in redraft. He’s much better in best ball.” Or something like, “Good luck trying to predict Will Fuller’s good games. I’m not taking him in my league. I’ll draft him in best ball instead.”
We’ve all heard it – but does it actually carry any weight, and if so, how much? How should we use this information to help us make better decisions in best ball? Without further ado, here is the data presented by DiSorbo. My commentary and actionable advice is at the end of this article.
DiSorbo’s Modeling
We’re all familiar with the concept of ‘boom/bust’ players. Last year Tyler Lockett was a great example: the Seahawks WR would have week-winning performances followed by complete duds. His scoring distribution looked like the high-variance density on the right. A player like Diontae Johnson represented the other end of the spectrum: less massive ‘boom’ games (he scored 20+ points just once) but far less ‘busts’ as well. His scoring distribution, along with other consistent players, looks more like the density on the left.
I’ve written about how consistent players are generally more valuable in redraft leagues when you have an above-average fantasy roster, since you have less to gain from boom weeks and more to lose from bust weeks. However, that’s in leagues with standard scoring. In Best Ball, scoring distributions look more like this:
Notice how both distributions are ‘cut-off’ on the left. This is thanks to the crucial Best Ball scoring dynamic: your lineup automatically selects the players who performed the best in a given week and inserts them into your roster. This gives you, to put it simply, a bit of bust protection: if one of your WR plays terribly, there’s a good chance that you won’t have to use his score, since one of your other WRs will pick up the slack and score a higher amount.
These charts represent an extreme case: below a certain point, you have a very low probability of actually having to use a score. This isn’t always how it works – there are times when all of your players manage to lay an egg – but it’s helpful for understanding the mechanism. In this case, it should be clear that boom/bust players are more valuable, since we get to enjoy their booms while insuring against their busts.
Theoretical Approach
The implication here is that the actual ‘points scored’ by a player is not the only important factor in determining player value: the distribution of scores, specifically the standard deviation, also matters. In the next two sections, we will be asking the question:
For two players that score an equal amount, how much value – in terms of win probability – does a higher standard deviation add?
This is a natural question: we know that more standard deviation is better in best ball, but how much better? Is the value of variance significant, and should you be targeting high volatility players? Or is variance just an afterthought, a ‘tie-breaker’ between similar players?
We’re going to address this in two ways. First, in this section, via a Monte Carlo simulation. Broadly, we are going to simulate many different fantasy matchups and measure the impact of a high volatility player to a team. The algorithm is outlined below:
- Calculate the mean and standard deviation of fantasy points scored (Half-PPR) across the major positions (QB, RB, WR, TE) for all players that played 7+ games in 2021. All data is from nflfastR.
- Set a ‘multiplier’ value of 1.1, which just means that we are going to increase the variance of a specific player by 10% (multiply by 1.1).
- Draw values for ‘Lineup 1’ from a Normal distribution using the mean and standard deviations from Step (1). In this case, draw 3 QB scores, 5 RB and WR scores each and 2 TE scores; this broadly represents the make-up of a typical roster with 15 slots. Calculate the score of Lineup 1 by taking the highest QB score, the top 2 RB and WR scores, the top TE score and then the best remaining FLEX score.
- Draw values for ‘Lineup 2’ in the same fashion as in Step (3). The only difference is that, for one of the WRs, increase their standard deviation by the multiplier (multiply by 1.1). This creates a ‘boom/bust’ player.
- See which Lineup – the regular lineup or the high volatility lineup – scored more, and mark it down as a win for that lineup.
- Perform steps 3-5 a total of 100,000 times.
- Re-run steps 2-6 but for different values of the variance multiplier (from 1.1 up to 2, or doubling the standard deviation).
Because the only difference between the two teams is a single boom/bust WR, this allows us to measure the impact on win probability – similar to Wins Above Replacement – of said player being high volatility. Ultimately, we get this result:
This tells us the win probability in a single game, which allows us to extrapolate to more common Best Ball metrics like “Top 6 Rate” (chance you finish in the top 6 of your league after the regular season) and overall “Win Rate” (chance that you finish 1st among the 12 teams in your draft). We’ll be focusing on the former, since the latter is highly skewed by late season performances and makes less sense in a theoretical setting (although it is, of course, still crucial, and will broadly agree with the results we find for the Top 6 rates). To apply a single game win probability to a Top 6 probability, we simply estimate the number of wins needed to finish Top 6, which is about 7+ wins in a 12-team league (estimated via simulation).
Applying the win probability from a single game with a boom/bust player*, we find that a 51% probability of winning each game (corresponding to a 100% increase in standard deviation in the chart above) translates to a 64% probability of landing Top 6 in your league. Put another way, doubling an average WR’s standard deviation (while keeping their scoring constant) increases the Top 6 probability of a roster by about 14%.
This is a crucial result! Just one boom/bust player can have a significant impact on your team’s chances of making it to the postseason. Remember that we are holding points scored constant, and that this is an average result. There are plenty of other factors that might produce differences, including roster construction decisions (stacks), draft capital used (which affects the capital you can use for the rest of the roster) and boom/bust timing. Still, we see examples of this effect playing out. Los Angeles Chargers teammates Keenan Allen and Mike Williams are great examples: the former was consistent, the latter the epitome of volatility. Although Keenan scored about 25 points more on the season, Mike Williams had a top-6 Rate about 1% higher.
Empirical Approach
The theoretical approach is helpful to ground us, but it relies on a lot of assumptions. Player scoring patterns aren’t really Normal – they are bounded around zero and right-skewed – this is just a useful distribution where we can control mean and variance. Further, our simulation doesn’t have any concept of a WR1, a WR2 etc. on a team: we assume all players have the same average scoring to simplify things. Again, these assumptions allow us to get a result, but they may restrict the validity we are after, creating (as we will see) a potential overestimate of the effect.
From here, one idea is to look empirically at actual Best Ball Top 6 and win rates. While we only have the data we observe, it can still be useful to learn patterns about the variables we are after. Specifically, we can look at these metrics for players since 2017 with data from RotoViz.
To get our estimates, we can run a regression that includes both the points a player scored and their standard deviation, with the win rate or Top 6 rate as the ‘outcome’ variable we are trying to predict. Here are the coefficients for the regression on predicting if a fantasy team finishes in the Top 6:
| Position | Points Scored | Standard Deviation |
| QB | 20% | 6% |
| RB | 26% | 9% |
| WR | 19% | 8% |
| TE | 26% | 4% |
What’s useful about this multivariate regression is that we are controlling for the other variable. For example, the top-right entry in the table tells us that “on average, for two QBs who score the same amount of points, a 100% increase (doubling) of the QB’s standard deviation will increase the probability of the fantasy team landing in the top 6 by 6%”.
Note that we now have numbers that we can compare to our theoretical approach. In the last section, we saw that a doubling of standard deviation for a WR increases the Top 6 rate by 14% on average. Here, we get 8% for the position. While these are different numbers, I think it’s reassuring that they are in the same ballpark! In this case, it’s probably wise to place more weight on the actual, observed win rates in the empirical section, which means, for RBs and WRs, I would estimate a 10% improvement in Top-6 probability for a 100% increase in standard deviation.
What’s more is that this approach allows us to compare the relative importance of points scored with volatility. For example, we expect a fantasy team’s Top 6 probability to increase by 19% if an average WR sees a 100% increase in points scored. This is an average result – true superstar WRs like Cooper Kupp in 2021 will yield an even higher Top 6 rate – but it’s intuitive. We expect a huge jump in our fantasy team’s success if a player scores a massive amount of points. What’s interesting is that the coefficients for points scored are in general about 2-3 times as large as the coefficients for standard deviation. This is another interesting result. Points scored are of course the most important, but the standard deviation isn’t that far behind: about 33%-50% as important!
A graph sums this up well. Each dot is a player, and the color of the dot represents the Top 6 rate of that player in Best Ball (green = high, red = low). The player’s points scored are plotted on the y-axis, and their standard deviation on the x-axis. You can see that the dots get more green as you move up (more points scored) and as you move to the right (higher volatility). The dots certainly ‘turn green’ faster when moving from down to up, but there is still a noticeable ‘greening’ left to right. The message is clear: pick the players that you think will score the most, but player volatility should be your next most important criteria. At a much higher level than in standard leagues, where volatility is often harmful, roster construction in Best Ball must hinge on maximizing the mean (how much a player scores on average) and variance.
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____*Using the Binomial distribution to model the total wins.
Betz’s Best Ball Strategies and Takeaways
Confused? Overwhelmed by how smart DiSorbo is? Me too. Let’s put some commentary to all this incredible data and give some takeaways and examples of how we can use it to win in best-ball formats.
1. Chase The High-End Outcomes, Especially at WR
Best ball is all about chasing the top-end outcomes – not only for our roster but for each player individually. In most 12-team leagues, only the top 3 spots get paid out. In other words, if you come in 4th place, you might as well come in 12th. We don’t care about safety in this format – we’re trying to chase upside and that means embracing volatility and variance with our draft selections. As DiSorbo’s data pointed out, we’re more likely to get those top-end outcomes if we look for players who have access to a ceiling. If you’re playing in any of the large field tournaments like Best Ball Mania on Underdog, we should care even more about volatility and the “If you ain’t first, you’re last” mentality (shoutout to Ricky Bobby). Remember as DiSorbo’s data shows above standard deviation is 33-50% as important as raw points scored.
Based on late May ADP on Underdog, Mike Williams is going as the WR15 while Diontae Johnson is going as the WR17. We know Johnson’s target share on a week-to-week basis is probably more stable than Williams’, but Williams has an elite QB who has a 45 TD season in his range of outcomes and a QB who is willing to push the ball down the field, giving Williams access to a bigger aDOT. Sure, Williams will have more down weeks here and there, but his spike weeks will far out-perform Johnson. In best ball, give me Williams over Johnson.
2. Take Running Backs Who Have Paths to Elite Production, Pass on Those Who Don’t
I’m not talking about taking Jonathan Taylor or Dalvin Cook. Obviously, the RBs going in rounds 1-2 are elite and their ADP reflects that. They have paths to an elite fantasy season. What I’m talking about here is that in best ball, I don’t want the 3rd down back who only has paths to being a 3rd down back. I want the RB who in the right situation, can have access to a three-down role. Let’s say for example, that you take WRs early in your best ball draft, leaving you with some questionable choices at RB in the middle to later rounds. Should we be going for backs who we know are at least going to touch the football (i.e. a 3rd down back), or should we be going after backs who have the ability to produce top-12 numbers in a three-down role? Of course, give me the backs who have access to elite production. Remember, we don’t care about finishing 4th. We want 1st, and the RB examples I’ll lay out below speak to DiSorbo’s data – they’re far more volatile, but when they hit, they hit in a massive way.
According to late May ADP on Underdog, James Cook is going off the board as RB34 while Alexander Mattison is coming off the board almost two full rounds later as the RB40. Sure, James Cook will have a role in the Bills’ offense no matter what – even if Devin Singletary is healthy, but let’s say Singletary goes down for the year, does Cook automatically become a 20+ touch guy? Given his track record in college, his size, and the way the Bills operate their offense, I’d argue no. If you forced me to pick which RB will have more top-36 weeks this season assuming both guys stay healthy, it’s probably Cook given the projected 3rd down role for Buffalo. But if Dalvin Cook should happen to miss meaningful time this year, we’ve seen Alexander Mattison have one of the best roles in all of football for an RB. He has paths to an elite role if things break right. Remember, we’re drafting as if we’re right – not playing it safe in best ball. Give me Mattison’s elite upside and variance over Cook’s safety, especially at cost.
3. We can live with the down weeks in best ball, so long as we have enough spike weeks and enough WRs on our roster.
Let’s be real. No one likes watching a primetime Seahawks game only to see Tyler Lockett post a 3/29/0 line the week after going for over 200 yards. In redraft leagues, that is beyond frustrating. In best ball, we’re all about it. Okay, we’d love it if our players just did what Cooper Kupp did a season ago and posted a ceiling week every week, but that outlier production isn’t normal. Wide receivers are volatile. DiSorbo’s data shows this, and I wrote an article last summer about how to attack the WR position in DFS. A lot of those same concepts apply here.
Over the last two years on Underdog, the data shows that the ‘optimal’ roster construction requires at least 6 WRs on our team, and ideally, sometimes drafting up to 10 is okay. Well, why is that?
First, we need to account for the fact that Underdog’s format forces us to start three WRs every week. Second, we want to try to absorb the lows where a WR posts a dud. By trying to throw quantity at the position (i.e. 9 WRs instead of 5), we’re increasing our chances that we hit one of (or hopefully multiple) spike weeks. That variance and volatility in best ball will kill your win rate if you only draft 5 or fewer wideouts, as our lineup can’t absorb the lows associated with the most volatile position in football. If we have 9 or 10 WRs however, there’s a good chance at least one of your guys is hitting a big week and posting that outlier score. As we’ve stated a few times now, volatility is good for win rates, but only if we have the quantity to make up for the lows. Along the same lines, however, there remains this notion that you can just take a lot of WRs late and you’ll be okay. In fact, that couldn’t be further from the truth. Rather than give a specific player example I did above, I’m going to use some data from last year’s Best Ball Mania drafts to illustrate a couple of main points.
- 5 Wide Receiver builds resulted in an advance rate of just 12%, and 5 WR builds where only one WR was selected in the first 4 rounds resulted in an advance rate of just 10%, among the worst of all outcomes. On the other hand, the top 3 advance rates came with rosters featuring 6, 7 and 8 WR builds and the advance rate is even higher in those builds if you take WRs early.
- Drafting WRs early matters. We talked above about the notion that volatility at WR especially is good for best-ball rosters. While this is true, the data shows that we can’t just rely on quantity over quality at the WR position. In other words, rosters that drafted at least two WRs in the first five rounds advanced at a far higher rate than those that drafted most of their WRs late in the draft. To put some numbers on this, the top 10 advance rates in terms of roster builds all featured at least two WRs drafted in the first five rounds. On the other hand, rosters that didn’t take a single WR until Round 6 or later had the worst advance rates possible, speaking to the fact that we should be looking for both quality and quantity at the position in best ball. Intuitively, this makes sense when you think about the types of WRs going in Round 10 or 11 vs. those going in Rounds 2 or 3. We can only absorb the down weeks if we have enough WRs, but if they’re all late-round guys, it won’t matter.
Conclusion
Hopefully you found this data and this article helpful. If you’re serious about taking your best ball to the next level (and want to have some fun with it, too!), be sure to check out the Best Ball Primer and our Best Ball Rankings in the UDK+. Until then, happy drafting!