Alpha DFS Model

Probability Distributions and Optimal Lineups

A Change in Perspective

When the average DFS player thinks about what they need to succeed at DFS they are automatically attracted to projections. Indeed, we see this reality in the most popular products and subscriptions people pay for: fantasy point projections. These projections have countless flaws, especially in methodology. How are these projections calculated? Are they simply adjusted averages? Are they produced algorithmically, perhaps using some sort of regression? Did the individual producing the projection manage their data and back testing correctly? Maybe it’s just intuition?

But let’s put methodology aside for now, questioning the statistical legitimacy of projections isn’t a revelation. The real flaw in projections is the projection itself: the focus on a single number to encapsulate the potential performance of a player. You should never be thinking about the single outcome, you should be thinking about the probability distribution of all possible outcomes.

A Distribution of Outcomes

A projection will typically come from the mean of some outcomes. For example, a crude projection may take the historical mean and standard deviation of a player’s performance, recognize a weak opponent, and adjust the average upward by some standard deviation. A more advanced algorithm may create some projection using some sort of regression or machine learning technique. Regardless, focusing on a single value misses the third and fourth moments of the distribution of these possible outcomes:

If you were trying to win a DFS GPP, are you interested in a player with a distribution that’s positively skewed or negatively skewed?

Clearly, you would be interested in a player with a positive skew, as the probability of an extremely positive outcome is more likely than an extremely negative outcome.

Are you more interested in a player that has a high kurtosis (Leptokurtic) or low kurtosis (Platykurtic)?

Clearly, a Leptokurtic distribution is more desirable in a GPP, as the probability of a tail event (an extreme fantasy point score) is higher than that of a Platykurtic distribution.

Simply put: by focusing on a single projection you’re missing the forest for the trees. In any betting market, any serious bettor does not care about predicting the outcome of an event as there is far too much randomness in such outcomes. Instead, a bettor is more interested in the probability of all possible outcomes occurring.

Back to Projections…

So how the hell do you come up with a probability distribution of fantasy point projections? To model your own fantasy point projections you need an enormous amount of information. You may look at a player’s past performance and calculate their average and standard deviation, and create some assumptions based on this data. But every one of those samples is tainted in some way: How good was the opponent? Was it a back-to-back? Who was the referee? Is that statistically significant for that player? The questions that need to be answered are endless. And of course, the question that’s always looming over your head: How much of this is just… random?

Making Markets

I come from the world of Stock and Index Options and have an interest in Market Making. Market-Makers create liquidity (buy and sell options) and do so by projecting the future distribution of the stock or index, and buy and sell options with a price reflecting a distribution of outcomes favorable to their side of the trade — this priced in distribution is commonly extracted from price and referred to as Implied Volatility. Countless methods have been used to predict future Realized Volatility, or the actual volatility that took place in the underlying stock or index. And what we find to be empirically true time and time again is that Implied Volatility is the best predictor of future Realized Volatility.

Essentially, Market-Makers and the market at large are damn good at what they do. And it makes sense, after all, as their profitability is directly tied to the accuracy of their projected probability distribution. They are incentivized to be accurate.

But Why Market-Makers?

Why am I telling you about options and Market-Makers? What if I told you there exists an older cousin of the Market-Maker called the Odds-Maker? Business is booming in the world of prop bets and someone with a lot of incentive is setting those odds. As it turns out, a lot of those stats FanDuel and Draftkings are converting into fantasy points are being projected by these very same people.

Efficient Markets

Differing opinions aside, the consensus in liquid markets is that the market is efficient at least most of the time, or all known information is priced in. Extrapolating this to prop bets: the information of all aggregated bettors, as well as the Odds-Maker’s access to supply and demand information of the bettors, should result in a fairly accurate probably distribution of outcomes related to the prop bet. By no means am I suggesting the sports prop betting market is nearly as efficient as the options market — the latter dwarfs the former in size. What I am suggesting, however, is that the prop betting market is likely more accurate and more efficient than anything the average DFS player and projection provider can come up with. Essentially, why bother trying to model or project a player’s performance, when the most liquid, efficient and incentivized sports-betting markets already do so for you?

Putting it Together

Everything you’ve read so far should be painting a picture of potential in your head. If we look at prop bets for each statistical category for every player, we can convert those odds into probabilities. We now have a range of statistical outcomes and a probability associated with each one of those outcomes. We can loop through each player any number of times, select a statistical result based on it’s associated probability, and convert those statistics into FanDuel and Draftkings fantasy points. The end result is a game or slate simulated x number of times with every player’s simulated performance derived from the probabilities of what should be the most efficient and effective sports betting market.

The Question You Should Be Asking

When most DFS players are constructing a lineup, the question they’re asking themselves is usually:

Which players are going to score the most points?

In reality, the question you should be asking yourself is:

Which players are going to be on the winning lineup most of the time?

As any seasoned DFS player knows, what makes DFS unique is the limitations applied to team creation: salary and position. At the end of the day, a player’s performance isn’t what matters most, what matters most is whether or not that player fits into the constraints of a winning DFS lineup — or, more accurately, how often that player fits into the winning lineup.

Optimal Lineups

So, instead of just simulating the fantasy point score of every player several times, why don’t we create the best lineup of each unique simulated slate/game? For every simulation loop, we can run the simulated scores through a lineup generator using linear programming to select the highest scoring lineup within the team constraints of the DFS provider.

We now have a list of every highest scoring team (optimal lineup) for every unique simulation. From there, we can answer the most important question:

Which players are going to be on the winning lineup most of the time?

According to Odds-Makers and the prop betting market, we now have the percentage of time any given player shows up in the most optimal lineups, bypassing the need for projections, ceilings and floors. We no longer care about whether a player is on a back-to-back, whether a certain defender shuts him down, how he performs against a certain defensive scheme. In theory, all of this information should be captured in the final odds presented by Odds-Makers. We no longer care about projections, nor the skew and kurtosis of those probability distributions — all of this information is captured in the final Optimal Lineup percentages.

This can be taken a step further for Single Game Contests, where players selected as MVPs or STARs score bonus points: What player showed up as MVP or STAR on the most winning lineups? A keen DFS player might even take this another step further by comparing the Optimal Lineup percentage with Ownership percentage statistics. If you believe a player is going to have an Ownership percentage significantly lower than their Optimal Lineup percentage, that suggests a strong potential for arbitrage.

What This Model Isn’t

I make no claims about the accuracy or profitability of the model. Firstly, I do not have nearly the sample size needed to even begin to suggest such claims. Secondly, there is no realistic way to back-test this method, as acquiring historical individual player game prop odds is effectively impossible.

What This Model Is

The Alpha DFS model relies on the following assumption to be true:

Odds-Makers and the prop betting market at large are mostly efficient and more accurate than most alternative sources of predictions and probabilities.

Perhaps more accurately, they are more accurate than the DFS side of DraftKings and FanDuel, and they are more accurate than the majority of DFS participants in any given contest. If this is true, what we should see are arbitrage opportunities taking advantage of the pricing of players on one end, and the ownership of those players on the other, relative to their Optimal Lineup percentage.

And that is what this model is about. Alpha DFS is trying to provide a new and unique way to view the world of DFS, throwing away projections and focusing on the ultimate goal: Who will be on the winning lineup most of the time?

The model makes several assumptions I believe to be accurate and true, and progresses toward what I believe to be a logical conclusion. My goal with this post is to present this logic as a form of transparency to describe how the model works. Unlike other resources that pull projections seemingly out of thin air, you have the ability to decide whether the model is representing an accurate view of reality.