Elo-based approach to point-scoring fantasy

One of the challenges of Elo rating and ranking of hockey players with regard to fantasy sports is that the given rating only characterizes the given stat it describes. Many fantasy games - head-to-head and rotisserie require a player, or a team to excel at a variety of such stats, and the superposition of many ratings is neither easy nor necessarily answering the question of which player is preferable over another.

However, in points-based fantasy, where separate single-stat scores combine through a formula into a performance is naturally and relatively easily evaluated through Elo through the following steps:

1. For a season three years ago (you can go further but you don't really need to) calculate the performance of each player in every game.
2. Calculate the average, the best and the worst performances, averaged over each six consecutive games (so that we get about 13-14 rating time points)
3. Set the half-span of the performance range according to this formula:

$s = max (max-avg, avg-min)$

Now, for each game, we accumulate the performances by six games, once a player has played six games, we apply his average performance over these six:

• We can scale all the performance $P$ into a [0,1] score $S$:

$S = 0.5 + (P-avg)/(2*s)$

• And then translate the performance into the change of the rating:

$ΔR = N_{games} * 32 * (R - 1 / (1 + 10^((2500-R_0) /200))) $

$R = R_o + ΔR$

The initial rating $R_0$ is set to 2500, too. As the rating of the player grows, it becomes much harder to maintain, as it falls, it's easier to climb back up. The averages become rolling and are being updated after each game day.

And then from each rating at the end of the calculation, we can derive the expected performance in a single game in two steps:

Expected result:

$R_x = 1 / (1 + 10^((2500-R_0) /200))$

Expected performance:

$P_x = avg + 2*s(R_x-0.5)$

The total performance would be the expected performance multiplied by 82 games.

Please note, that we do not need to take into account the opponents the players are going to face over a long span of games, it's safe enough assume the opponents are just average.

Here are the top ten lists per position when ranking the points system used by Daily Yahoo Fantasy:
Goalies: 5 × wins + 0.6 × saves - 3 × ga + 5 × SHO
Skaters: 6 × G + 4 × A + 2 × +/- + 0.9 × Sh + 1 × B + 2 × PPP

Goaltenders

Name	Elo	Exp.
BEN BISHOP	2,630	1217.9
DARCY KUEMPER	2,619	1153.0
ANDREI VASILEVSKIY	2,617	1141.2
SERGEI BOBROVSKY	2,610	1100.2
MATT MURRAY	2,610	1099.1
ROBIN LEHNER	2,609	1092.3
PHILIPP GRUBAUER	2,607	1077.7
CONNOR HELLEBUYCK	2,605	1066.1
ANTTI RAANTA	2,600	1036.6
PETR MRAZEK	2,600	1035.8

Defense

Name	Elo	Exp.
MARK GIORDANO	2,559	781.2
ERIK KARLSSON	2,558	773.4
VICTOR HEDMAN	2,557	768.6
BRENT BURNS	2,556	762.6
KRIS LETANG	2,553	742.2
ALEXANDER EDLER	2,551	728.3
JOHN CARLSON	2,549	714.7
ERIK GUSTAFSSON	2,547	704.8
TYSON BARRIE	2,547	702.2
SHEA WEBER	2,542	671.3

Right Wing

Name	Elo	Exp.
NIKITA KUCHEROV	2,593	995.3
ALEXANDER RADULOV	2,581	923.4
PATRICK KANE	2,577	892.6
VLADIMIR TARASENKO	2,573	868.0
DAVID PASTRNAK	2,571	858.4
ANTHONY MANTHA	2,553	741.2
MATS ZUCCARELLO	2,545	689.6
MARK STONE	2,540	658.1
MIKKO RANTANEN	2,535	627.2
REILLY SMITH	2,535	624.5

Left Wing

Name	Elo	Exp.
BRAD MARCHAND	2,581	919.6
JONATHAN HUBERDEAU	2,571	855.5
TAYLOR HALL	2,568	836.9
ALEX OVECHKIN	2,563	809.0
GABRIEL LANDESKOG	2,558	775.6
VIKTOR ARVIDSSON	2,543	679.6
MAX DOMI	2,542	668.7
TEUVO TERAVAINEN	2,539	651.8
JOHNNY GAUDREAU	2,537	641.0
ARTEMI PANARIN	2,536	632.6

Center

Name	Elo	Exp.
STEVEN STAMKOS	2,579	905.9
ALEKSANDER BARKOV	2,577	896.6
TYLER SEGUIN	2,576	890.7
NATHAN MACKINNON	2,573	870.9
PATRICE BERGERON	2,572	864.1
CONNOR MCDAVID	2,567	830.5
LEON DRAISAITL	2,566	828.2
JOHN TAVARES	2,561	792.7
SIDNEY CROSBY	2,557	769.7
DYLAN LARKIN	2,553	742.6

The positions are projected as provided by the NHL player files. Since your fantasy game may have players in differing positions, modify the lists accordingly.

We provide a service of ranking all players according to any formula. For a small fee paid via paypal (\$1) you'll receive a full CSV list of players with their ratings and 82-game expected score. For any extra formula add \$0.5 . For example, for \$3 you can get five formulas processed. Contact us on Twitter or by email for more details.

Please note that this list is less applicable for the Daily Fantasy itself because of the budget limitations.