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How We Used Monte Carlo Simulation to Solve the Best Ball League Puzzle
globalgrind.com
globalgrind.com

When we were kids, Star Wars cards got HUGE in our school. Everyone wanted the best cards so they could show off to all the other kids how good their decks were. Thing was, nobody knew the right rules to play. The rulebook was way too long for our fourth grade heads, so we made up a hybrid method that made games last about 5 minutes. One decent card like Cloud City Boba Fett was an auto-win. It was stupid, but that’s what we did.

MFL10s are like Star Wars cards: they’re new, cool, and nobody has any idea how to play them.

Good news though! MFL10s are not hard. Just nail the draft and you win money. That’s it. No trades, no waivers, no start/sit nonsense. Nail the draft and you win money, simple as that. But nailing the draft means you need to get every last bit of value out of the 22 picks allotted, and that’s the challenge. Success will inevitably come to the person smart enough to maximize value at every one of those 22 picks. That’s exactly what we’ve done.

RB TE RB RB RB WR WR WR QB WR TE WR QB QB WR WR K DEF K DEF DEF K

That, according to the last 3 years of ADP data from myfantasyleague.com, is the optimum draft lineup to use in a MFL10. After running 500,000 Monte Carlo simulations, that lineup comes out on top with a projected points per week of 173.4 for the team with the sixth overall pick. The number does vary slightly depending on which spot you draft from, but only by about a half a point.

Disclaimer: This does not mean you definitively stick with that order in all circumstances. We’re just saying that in an average draft with average expected points and standard deviations, that’s the draft order that will produce the most points per week.

So how did we get here?

First, a very quick overview on Monte Carlo Simulation. This technique is a way to simulate actual events as many times as you have the computing power for by leveraging the power of random number generation and expected point distributions. Basically, you have a set of possible outcomes for every player in every game they play. Monte Carlo simulation takes a random number, say 0.78253746, and equates that to the 78.2537th percent best score that player could get that week. That is done for every player on your roster using different randomly generated numbers, and then the team score is optimized via best ball rules. We then ran this simulation 500,000 times to eliminate the huge levels of variation you see in any given week, allowing us to see the true optimal decision without getting bogged down in the details of real results which are hugely variable week to week. Essentially: Process > Results

We took the past 3 years of ADP data from myfantasyleagues.com and cross referenced it with the scoring data from the past 3 years to come up with a metric called Expected Points Per Pick1 (EPPP) for every position. For example, the sixth overall pick as a quarterback has an EPPP of 25.3 with a STDev of 8.5. What we’re saying here is that if you ran 500,000 football seasons and fantasy drafts, the average points scored per week for a quarterback drafted sixth overall would be 25.3. For example, Tom Brady’s ADP in 2012 was 6th overall, and he scored an average of 26.7 points per week. Way to go Tom, you outperformed your expectation by 1.4 points, you’re terrific!

Let’s break it down position by position to see how things look:

Running Backs

rb

Running Backs drop off quickly, from a solid 16-17 points in the first round to an unusable 5 points by the 200th pick. If you don’t get your RBs early, don’t bother. Many of us think we can find the diamond in the rough in the late rounds who will gain a starting role, but the opportunity is (usually) priced into ADP, and you would need to find truly egregious ADP mispricing to make this gamble worthwhile.

Wide Receivers

wr

Value, Value Everywhere! Wide Receivers don’t drop off nearly as quickly as Running Backs do. This is intuitive since there are (at least) twice as many starters at WR, but what’s also interesting is how steady Standard Deviation is. Wide Receiver production does drop as you go further into the draft, but no matter where you get it, the expected standard deviation only fluctuates between 8 and 6 pts. Intuitively, this makes sense as we see second and third wide receivers have huge days unexpectedly in the NFL every week. This high variance is incredibly valuable in a best ball format, and is what led our optimal team to draft so many mid-round WRs. Rather than drafting a few elite WRs, just draft as many mid-round WRs as you can and a handful of them should score just as highly as the elite guys every week.

Quarterbacks

qb

Quarterbacks are a little different. Whereas Running Back and Wide Receiver standard deviation moved with ADP, for quarterbacks it’s the opposite. What this means is that stud quarterbacks not only put up better numbers than everyone else, but they also do it more consistently. Stud quarterbacks will score their 20-25 weekly points very consistently, but with trouble going a ton higher than that because they’re already crushing the other team all the time and they only have 60 minutes. Even at pick 175, you can expect 15 points per week out of a quarterback however, and the increase in standard deviation means that these low-end starters have more room for improvement against bad defenses or with a few big plays. No other position has such a combination of staying power and late-round upside, so our simulation says to wait on QBs.

Tight Ends

te

Tight End is interesting because there’s not as many data points, especially towards the top. You don’t need pretty graphs to tell you what production you should expect out of a first round TE though, just look at Jimmy Graham’s expected production and use that instead. Same thing for Gronk in the second round, which our analysis pointed out is the most valuable pick in the entire draft. Remember that optimum draft lineup from before? It had TE as the second round pick, which only works if Gronk (or better yet Jimmy) is there. In fact, the second best projected lineup was the exact same thing but a TE in the first instead of the second. Lesson here: If Jimmy is there at the end of the first, take him, but better yet, if you can grab Gronk in the second, that’s the best pick you can make.

At other (non RB) positions you can make up for not drafting them early with the high variance you get at those positions late, but TE is another story. Since TEs generally see far fewer targets than their WR counterparts, their variance is inherently lower. Because of this, it’s much more difficult to make up the gap between late round tight ends and Gronk/Graham just by drafting a lot of them, since they don’t have the same potential upside as late round WRs. If there is any one thing you take from this article, let it be this: DO NOT PASS ON AN ELITE TE IN ROUND 2.

Defenses

def

Defenses are a crap shoot with relatively high variance. In a best ball format, you want to maximize your chances of a defensive touchdown, so wait until the last rounds of your draft and then grab three to capitalize on the variance here.

Kickers

k

At first glance there may appear to be a trend here, but we’re of the opinion that K production is relatively random and you can wait until the last few rounds on them. Again, the simulation tells us to take 3 of them to maximize our variance and get a high scoring week.

Comparison to Other Strategies

We walked through why our optimal lineup construction worked out like it did, but here are the results from a few other common strategies for Comparison:

Strategy Picks in Order Avg. FPPW
Optimal (Early TE, RBx4) RB TE RB RB RB WR WR WR QB WR TE WR QB QB WR WR K DEF K DEF DEF K

173.4

Balanced RB WR RB WR RB WR RB TE QB WR TE WR QB QB WR WR K DEF K DEF DEF K

172.1

Early WR WR WR WR RB RB RB RB TE QB WR TE WR QB QB WR WR K DEF K DEF DEF K

171.2

All over the place WR RB QB TE RB WR RB WR RB WR QB TE WR WR RB QB TE DEF  DEF K K DEF

168.7

QB First, only 2 DEF, K QB WR RB TE RB RB WR QB WR WR TE WR RB QB TE WR WR RB DEF DEF K K

167.2

Kickers FTW K K K DEF DEF TE TE RB RB RB WR WR WR WR WR QB QB QB QB WR DEF

149.5

The differences in point totals may not seem large, but over 500,000 simulations these are gigantic differences. An advantage of a few points per week can be a 40+ point advantage over the competition over a full year, just because you picked your positions in the proper round and quantity. Add in the advantage in player evaluation we’ll provide in part 2, and you should breeze to your MFL10 title!

Potential Blind Spot

Every time you do complex analysis like this, you need to be aware of the blind spots you may be missing. One potential issue is that we used a normal distribution for every player simulation, when in reality, the point distribution may take an entirely different shape. Late round RBs for example will either break out and start getting a full workload or languish on the bench. Their point production will likely be at one of the two extremes as opposed to the normal distribution assumed (which may be more accurate for a time-share back for instance). Separate analysis needs to be done to determine how much value that uncertainty has and what your hit rate needs to be on RBs to be worth selecting them late.

Lessons Learned

We all have super short attention spans now, so if you just blew through all those pretty graphs and you want a nice summary, here it is:

  1. Grab Jimmy Graham or Gronk in the first two rounds if you can. They are so much better than other TEs that it will be worth it.
  2. At least 4 of your first 5 picks should be RBs. RBs any later than the 5th round aren’t worth the risk in the MFL10 format when you could be loading up on WRs instead.
  3. QBs hold their value for a long time, so wait. Just be careful that late round QBs are very inconsistent, so we recommend grabbing at least 3 of them.
  4. Load up on WRs. We recommend 7.
  5. Take 3 kickers and 3 Defenses to maximize your upside with the positions that behave most randomly week to week.
  6. Be prepared to deviate if value falls. Yes, there is an optimum drafting strategy if the draft goes according to ADP, but don’t stick to the order we’ve given you if it means passing up on a significantly higher projected player. This analysis should help you make selections when there are multiple similar options, but If Peyton Manning is still there in the 7th, you can forget all about this and take him.

If you all find this informative, let us know! We’ll do a part two showing which players are most valuable at each position in the best ball format if there’s enough interest. Hint: take the fast guys.

Good luck! Unless you’re playing one of us, and then we hope your team is riddled by injuries.

  1. Used a moving average EPPP of including the slot immediately before and after each ADP to smooth data  (back)

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