We're going to talk today about fantasy schedule difficulty, and how good teams can be unfairly punished in the rankings due to luck of the draw. When one team spends a couple of weeks scoring near the top of the league, but losing to the highest scorer, it artificially depresses the ranking - and in that way fantasy schedule difficulty matters as much as schedule difficulty means in regular sports! Read on and we'll lay out a framework - using fantasy football as an example (but universal) - to unskew the team rankings for the relative difficulty of fantasy team schedules.

## Unskewing Team Rankings for Fantasy Schedule Difficulty

Fantasy football, for the neophytes out there, is a game played by fans of the NFL who select players to fill a simulated team and then are awarded points based off of their real life performance. It has left an indelible mark on the viewing patterns and marketing techniques of NFL firms. So many people play today it lead former Quarterback Jake Plummer to claim that "it has ruined the game".

Despite Plummer's reservations, fantasy football is going strong, and for those of you who are familiar with the game and the patterns of the fans, one topic always comes up: Fantasy Schedule Difficulty.

I have devised a statistical method that accurately predicts where a team **"should"** land based on their performance, *if luck were not a factor*. It can then be reasonably compared with the actual performance to see who has the best luck in the variance of their schedule. A couple notes:

- This method only works in head-to-head points based leagues. Rotisserie style leagues can't apply it.
- This method does
*not*determine the luck inherent in the actual scoring of points. For an example of bad luck? Any injury... some would consider this unlucky for the owner, but this would not count in the "luck" I am talking about.

A couple notes on why this method is far greater than the PF/PA (points for/points against) argument for unskewing team rankings.

If the high score in the league besides your team is at 100, and you score 180, it is effectively no different than you scoring 101 points. Thus, *Points For* are often swayed by massively large weeks and the variance is very important to capture. Similarly, if the lowest score in the league is 50, there is no difference between 49 and -20, you would have lost no matter which number you put up.

Points against are *a lot* easier to see the problem with. If you score 40 points in a week, it does not matter what the other person scores... above 41, you lose the matchup. Thus, you could lose to an 80 or 120 or a 160 and they will look vastly different in your final points against totals.

Week by week variance is also very important. Some weeks score more *in total* than other weeks. Week 1 may be a particularly high scoring week, with Week 4 one of the lowest. *Points for and Points against measures do not determine the effect of these swings on point outputs.*

Now, onto the method to account for fantasy schedule difficulty:

For these examples, I am going to assume eight teams. The same exact method can be used for any number of teams in any number of divisions, it still works the same.

In Week 1, the following scores are tallied: A-80, B-85, C-75, D-70, E-60, F-110, G-82, H-40

Without knowing who played who, it is impossible to say what the record is after week one. If you are Team B and you played team F, well tough luck, you just got screwed. If you are team E and you happened to play team H, you are in great luck. What this method does is capture the probability of winning *that particular week*.

Assign a rating from 0-7 (zero to one under the number of teams in your league) by points total. Thus, F-7, B-6, G-5, A-4, C-3, D-2, E-1, H-0 Divide these numbers by 7 and you have the probability each team wins that week. G has a 5/7 chance of winning (they beat A,C,D,E,H and lose to B, F). Ties can be split down the middle (if they are tied for the 4th position, assign 3.5 to each of them to take up the 3 and 4 positions).

Throughout the season there will be lucky and unlucky breaks (and hopefully they even out, but very often they do not - which is part of the appeal of the game!). Add up these point totals for each week and divide by 7 (or one under the number of teams in the league) and you have your expected number of wins. Week 2 could thus be A-85, B-95, C-65, D-80, E-45, F-100, G-105, H-70 with the points being G-7, F-6, B-5, A-4, D-3, H-2, C-1, E-0

The total points would then be A-8, B-11, C-4, D-5, E-1, F-13, G-12, H-2 and by dividing each of these by 7 you get the projected win totals.

A luck factor can then be crudely made by taking the number of wins each team actually has and subtracting expected wins from it (positive for lucky, negative for unlucky). The great thing about the method is that all the luck factors sum up to zero. It creates a zero sum reliable indication of luck. After all, somebody's good luck is another person's bad and vice versa.

Use this method to see which teams are the contenders and which are the pretenders around week 6 and see how well it correlates with late season collapses.

Cheers,

Cameron Daniels