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Fantasy Football and the Minimax Algorithm
Aug. 29, 2014

If you play in a standard Yahoo fantasy football league, you should pick Stephen Gostkowski above Andrew Luck in your draft. Iím serious! Your friends may laugh, but they should be taking notes! In this post, I will show how a game theory tool for analyzing decision making explains why drafting Gostkowski over Luck is the ďoptimalĒ draft strategy.

The mathematical basis for this decision is a game theory algorithm called the Minimax Algorithm. The minimax algorithm describes the optimal choices you should make in games against optimal opponents. The algorithm says you should make choices that maximize your worst case scenario. When your opponent selects a player, they are helping their team and are also harming yours by removing a good player from those remaining available. This means that by drafting the best possible teams for themselves, your opponents are simultaneously leaving you the worst possible choices to fill your roster. So, drafting to maximize your worst case scenario makes sense.

With the minimax algorithm in mind, letís revisit the kicker vs quarterback draft decision. Letís assume you are in a standard Yahoo points league (10 teams, 1 roster spot each for K or QB). If you pick Luck now, the worst case scenario would be that you get stuck with the 10th best kicker (Dan Carpenter last year), as anybody worse would be on a bench or the waiver wire. If you pick Gostkowski, the worst case scenario would be getting stuck with Colin Kaepernick (the 10th best QB last year). Using last seasonís stats, Luck + Carpenter = 450.58 points, and Gostkowski + Kaepernick = 451.28 points. As you can see, the latter option is better - it is the maximum worst case scenario - which is why the minimax algorightm says to choose Gostkowski before Luck.

Gostkowski is the more valuable pick because he is more valuable relative to other kickers than Luck is relative to other QBs. Said differently, thereís no need to use a high pick on Luck when a decent alternative like Kaepernick will be available much later. On the other hand, there arenít many great kickers, so you should pick a good one while they are still available.

You can easily apply the minimax algorithm to every pick: always select the player who is best relative to the worst possible starter at his position. By drafting this way, you will be maximizing your worst-case scenario, and you will be guaranteeing yourself a decent team, even against stiff competition. Itís easy to implement this algorithm, and it gives powerful results!

There is one caveat: using the minimax algorithm in your draft limits your upside. If your opponents do not draft optimally, then it is possible to do better than the minimax algorithm. For example, if you think nobody drafts kickers before the 5th round, thereís no sense on using a third round pick on Gostkowski. But, since you are reading this article, you must be serious enough about fantasy football to play in competitive leagues where your competition drafts with near optimal strategy. When youíre at the draft table this week, you should use the minimax algorithm to help your decisions. Evaluate players relative to others at their own position, and seriously consider picking Gostkowski over Luck!

Use this advice to draft a team at AdvancedSportistics.com!
Who will score the most EPA this week?
Drew Brees
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Andrew Luck
Peyton Manning
Yesterday's Top Winners

Will be posted after NFL Week 1.
Advanced Stat of the Day

Clayton Kershaw finished the 2014 season with 7.2 Wins Above Replacement.