Game Theory in Daily Fantasy Sports
With all of the heat around Daily Fantasy Sports, this article is especially relevant. Recently, New York state banned DFS because they were not deemed to be skill-based games and were deemed to be gambling on chance. However, supporters of DFS boast certain statistics and skills that demonstrate the prevalence of skill in DFS.
One strategy often discussed in the debate is the strategy of picking players with low usage rates (the percentage of DFS user using the player on a given day) to gain an advantage over their competition. In a DFS tournament set up, it is not always the dominant strategy to pick the players with the highest projected points. If everyone were to pick the same players, then there would be no winner. Thus, it is sometimes advantageous to pick players that are not projected to do as well, but who have the potential to have a break out game and outperform the other players at that position. For example, Marcus Mariota was only owned in about one third of leagues in Week 1 when he broke out for 4 TDs. Mariota was one of the best Week 1 QBs in the NFL but had a low usage rate.
For those who picked Mariota, they gained a large advantage over competitors going with QBs with higher projected point totals like Aaron Rodgers or Phil Rivers. This proves the statement that the goal of DFS isn’t to maximize expected point totals, but expected probability of winning. The article further explains a situation in which this rings true:
“If RB1 has a 25 percent chance to score big points and RB2 has a 15 percent chance to do it, RB1 would seem to be the better choice. But again, what if RB1’s usage is so much higher that it drives down the value of being right? If you have a two percent chance to win a tournament if you hit on RB1 and a five percent chance to win if you nail your selection of RB2, the latter is the better choice, even though he’s less likely to be productive.
… the running backs’ value is equivalent to C(P), where ‘C’ is the chances of hitting their ceiling and ‘P’ is the probability of winning if they perform at that level. RB1’s value would then be 0.25(0.2), or 0.05, whereas RB2’s value would be 0.15(0.5), or 0.075. In this scenario, RB2 would offer around 50 percent more usable value than RB1—i.e. a 50 percent greater chance of being in the winning lineup (on a per-lineup basis)—despite being worse value in terms of strict dollars-per-point.“
This plays into the game theory of DFS. It is a single-run many player game in which each player has many strategies with different expected values. One may assume the highest expected value is always the best play, however, according to the situations explained above, and the accompanying math, we can see that there is not pure dominant strategy and that you would instead have to employ a mixed strategy of choosing some players with the best expected values (to minimize total risk) and some players with high potential but lower expected value (to gain an edge over the competition if you pick correctly).
Source:
http://www.fantasylabs.com/articles/using-game-theory-in-daily-fantasy-tournaments/