NFL Advanced Metrics
Primary Factors Determining a Player’s Fantasy Football Score
About the Writer: Blinders is an employee of FSL and a proven NFL Grinder. Last NFL Season Blinders went 71-10 on FanDuel alone.
I thought I would delve a little into the math behind a players fantasy football score. I am not talking about taking their rushing yards and dividing by ten. I am talking about what mathematically determines a player’s statistics for a given game that in turn leads to their fantasy score. It turns out that there are three factors that are responsible for a fantasy football score. These include the baseline fantasy strength of the individual player, an aggregate of the factors from the upcoming match-up that would tend to make the player score higher or lower than their baseline, and a game variance factor that accounts for the fact that we can only run a single game trial in the real world. The equation looks like what is shown below.
| Fantasy Score | = | Baseline Strength | X | Match-up Factors | X | Game Variance |
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I will go into some more depth into exactly what each term is, how they can be estimated, and how understanding these factors leads us to the approach that we take with player pricing at FSL.
Baseline Strength
This is the underlying strength of the fantasy player. This is the average fantasy score that a player would score against a completely neutral opponent over an infinite number of trials. This is what makes Chris Johnson a better selection than Larry Johnson this year if they had a similar cost. He simply is going to score more fantasy points than Larry will over the long term against the same match-ups.
Match-up Factors
These are all the things that will tend to make your player score more or less than their baseline strength in the exact upcoming match-up. Factors like the ability of the defense that you will be facing, if the game is at home or away, if your player is injured or healthy, if your player has been hot or cold lately, if your player has been getting more or less snaps, and other game specific factors. You aggregate all of these factors into a single factor that is applied to your player’s baseline strength to determine their expected (projected) score before the evils of variance come into play.
Game Variance
If you could run the game 1000 times, like they do in simulations, you would find that the average fantasy score obtained would be exactly the player’s baseline strength multiplied by the game’s match-up factors. Unfortunately in the real world the game is only played once, and all sorts of unaccounted for things can happen. You player could get tackled on the 6 inch line and not get the TD. A Safety might be out of position allowing your player to get a long TD they otherwise would not have made. Tons of things like this can and do happen each week that prevent your player from landing exactly on their projected score. There is nothing that you can do about this. Variance is part of the game. Over the long-term variance washes away, as an equal number of good and bad things will happen to your player. Over the short term, variance can easily outweigh a player’s baseline strength and match-up factors, and make the worst player look like a stud, and the best player look like a dud, when neither is true. Game variance is player specific with the more consistent players having a lower game variance, and inconsistent players having higher game variance.
Where the Skill Applied in Weekly Fantasy Football
Fantasy Sports is designed to be a game of skill with the better players being able to beat the worse players over the long-term. At FSL we feel it is our job to set individual player salaries at their baseline strength, and it is the RotoGrinder’s job to determine the various match-up factors. Outside of that, it is the Fantasy Football God’s job to determine the game variance. So each term has its own domain. The baseline strength can be estimated by anyone to decent accuracy depending on the sample size, and should be proportional to a player’s salary cost. The match-up factor is where the fantasy football skill is applied, and is what differentiates the good from the bad at weekly fantasy football. The variance factor is what allows poor fantasy football players to beat the best fantasy football players often enough that they will keep playing, and is what can cause the best players to have losing streaks that can last for months.
Calculating a Players Baseline Strength
Since we know that variance washes away as the sample size gets large, we can remove that term, but to get to the baseline strength we also need to remove the match-up factor term. If in the NFL, each team played each other team twice each year (home and away), at the end of the season the match-up factors would have also completely washed away. This does not happen, in the NFL so it is not that easy. In other sports with 80+ game seasons things get easier. At FSL we use the following formula for baseline strength.
| Baseline Strength | = | Average of | (Fantasy Score 1, Fantasy Score 2,…Fantasy Score Y) |
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We only use this season’s fantasy scores, so that factors that effect season to season performance are removed. In the limit of x getting very large, this is a perfectly good approximation. With x at about 25 the error is probably less than 5%. So once we get 50 games or so into a season our player baseline strength calculations are very accurate, and you will see player cap values settling down. Before that they have issues due to small sample size, and this is true during the entire fantasy football season. So for football you are looking at an obvious first order approximation determining our player costs (we multiply raw baseline strength by 10 to get a players cap value). As a result some skill can be applied in this area for fantasy football to try to find baseline strength errors in our approximation, and pricing mismatches as a result. The same is true early in the season of other fantasy sports. For example we schedule the next week’s leagues prior to Monday night’s game. Our player cap values can’t include Monday’s data as a result, and an error in our baseline values can be found there. Also, if you know what the match-up factors are to a decent level of accuracy, you can use them to get a better estimate of baseline strength that we are making.
Calculating Match-Up Factors
At FSL we do not try to account for any match-up factors, as that is where the skill is applied, and we do not want to remove any skill from the game. There are numerous match-up factors and most of them are not obvious to the fantasy football novice. We want the people who put the time in to really understand what is likely to happen, to have a big enough advantage over those that do not to be able to make money long-term from fantasy sports. That is the whole point of daily fantasy sports, right? To calculate the match-up factors you need to have a player projection model with numerous match-up factors applied. You can then project scores for the top 200 or so fantasy players, and compare that to their actual results. You then start tweaking your match-up factors to where the sum of the errors gets close to zero (so you are not over or under projecting in general), and so that the standard deviation of the projection errors is minimized. I will not go into any more detail, but the point is that player projection models can be validated by testing against 100s of players each week, and once validated they can be used to generate pretty accurate match-up factors.
Calculating Game Variance
You can calculate this for each player based on their individual projection errors, but there is not much you can do about variance overall. You just have to live with it. A good fantasy player should select lower variance players where possible. It is variance that allows worse fantasy football players to beat the better fantasy football players in the short term. The more variance that can be removed, the better the chances are for a good player to beat a bad player. You also have nine player selections to spread the variance around. Many times the variance will wash away over these 9 trials, but some times it will really stack up against you. Over the long-term variance always washes away, and the quality of your match-up factor calculations will determine if you are a winning player or not.
Fantasy Team Variety
At FSL we have designed our fantasy football leagues to provide the highest possible variety of individual fantasy teams. To keep everyone from selecting similar fantasy teams, two requirements need to be met. First, you need to have accurate player costs that are proportional to a player’s baseline strength. If there are any obvious errors in player pricing, many people will take advantage leading to similar teams. Secondly, you need to have tight fantasy team caps. The tighter the cap, the more variety of fantasy teams that can be competitive in a given league. At FSL, we have tight caps in general, but also offer a spread of cap values for our fantasy leagues. This allows people to build an All-Star type team if they want, knowing that they are trading away some variety, or they can build a high variety sleeper team under the cap that will be very different from their competitors.