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Fantasy Football and Game Theory: Understanding Your Opponents’ Beliefs

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Fantasy football can sometimes be paradoxical in that the tasks which seem the most simplistic, such as drafting players, are often quite complex.  “Common sense” notions, such as selecting the players who will score the most points, can often lead to sub-par fantasy squads.

The reason for this is an idea about which I have spoken before–game theory.  See, fantasy football isn’t just about knowing football (in fact, we would argue that knowing football really isn’t even essential to being successful at fantasy football at all).

Of course having knowledge of the NFL helps, but even more crucial to your success as an owner is understanding the thoughts of your opposition.  Making decisions based on the projected choices of others is what game theory is all about.

For example, the other day I was talking to my dad (who is in a dynasty league of mine) about the upcoming season.  I asked who he would draft if he had the No. 2 overall selection, and he said Matt Forte (of course no one can believe anything anyone in our league says about players, as the league has reached the point where 95 percent of the information floated out there is “crap,” but that isn’t the point).

When I asked him why he would select Forte with the second selection, he answered quite matter-of-factly, “Because he is going to score the second-most points.”

Let’s suppose that is true.  If the season plays out and Forte ends up with the second-most points, does that justify his selection with the No. 2 overall pick?

The answer:  not at all.  In selecting players based solely on projected points, owners ironically miss the opportunity to secure the maximum overall projected points for their squad. The goal of fantasy football actually isn’t to maximize the point value of each individual selection, but to do so for your entire team.

I talked about this a bit in my article on the importance of creating tiers in your fantasy draft board. There I wrote:

Be sure to project players’ points (according to your scoring system) and then rank the players within each position into tiers. In a way, you can imagine all the players within the same tier as equal, i.e. don’t worry about names–simply acquire as many players in as high of tiers as possible, and you will have maximized the value of your fantasy team.

This strategy will allow you to, in a way, “buy low and sell high”–the same methodology which maximizes value in the stock market, business transactions, and, yes, even fantasy football.

This value-maximization strategy involves a term called VORP–“value over replacement player.”  Advanced NFL Stats has an excellent article on how to utilize VORP during your fantasy draft.

As your pick approaches, estimate the number of each position that will be taken between that pick and your subsequent pick. For example, in my recent 8-team league draft, between my 4th pick in the 1st rd and my 13th overall pick in the 2nd round, I estimated there would be 1 QB, 2 WR, and 5 RBs taken. (Before my 1st pick there was 1 QB, 1 WR, and 1 RB taken.) I calculated the difference between the best available RB and the RB 6 spots down the board, because he’s the next RB available to me if I don’t take a RB this round. I also calculated the difference in value between the best QB available, and the next best QB. Finally, I calculated the difference between the best WR available and the WR 2 spots down the board. These differences are the costs of not picking each position in that round. I picked the position with the highest cost.

In a nutshell, VORP means selecting not the player with the most projected points, but the player with the largest disparity of projected points compared to the next player at the same position who you could secure in a later round.

The graph to the left (provided by Advanced NFL Stats) is a visual representation of this.  The most important part to fantasy owners is not the height of the curves, but rather their slope.  A steep slope means a larger disparity between players, and therefore a larger VORP.

Thus, Forte is the incorrect selection at No. 2 overall not because of anything related to Forte’s skill set or potential 2010 production, but because of other owners’ beliefs concerning these things.  If Forte can be had in the back of the second round (which is likely), my dad could acquire him and, say, Adrian Peterson (as opposed to Forte and LeSean McCoy, for example).  Hmmm. . .which combo would you prefer?

Know football and you will be a decent fantasy owner.  Know football and what others think they know about football, and you have the potential to be great.

But what if another owner really likes Forte?

This is something for which you will have to account and the primary reason game theory is so useful in fantasy football.  If my dad whole-heartedly believes another owner will select Forte before his second round pick, for example, then drafting him in the first round is the right move (assuming he cannot trade).

So is it always smart to maximize VORP?

Unfortunately not.  Fantasy football is about risk/reward.  As such, it is sometimes beneficial to pass on a more “consistent” player for one with larger upside, or vice versa.

For example, let’s assume you are in round five of your draft and have thus far assembled a team of Steven Jackson, Brandon Marshall, Calvin Johnson, and LeSean McCoy–all fairly high-risk players.

The top players left on your board are Jay Cutler and Philip Rivers.  You have Cutler with 20 more projected points than Rivers, and the VORP says Cutler is the pick.  The intelligent decision, however, might be to pass on Cutler due to his inconsistent and unpredictable play.

If you determined Cutler has a 75 percent chance of scoring 300 points, for example, while Rivers has an 80 percent chance to do the same, Rivers should be the pick even though his projected points (if both players perform to their maximum ability) is lower than Cutler’s.

The graph below is similar to the one on the previous page, but it accounts for both the scarcity and consistency of each position.  Notice that the initial slope of the tight end position is greater than that of the wide receivers.  As Advanced NFL Stats writes:

At no point does the TE curve exceed the WR curve in absolute terms. But the TE curve is steeper, which indicates that the differences between the top available TE and the next-best-expected TE is greater than that for WRs throughout the draft.

If everyone knew this, they’d jump on the top few TEs before even picking their first WR (in most years). But they don’t, so you can take advantage by waiting to pick a TE until the last round before you think the first TE will be chosen.

If you have been able to follow along, you may have realized that we have come full circle.  In the example I provided above, my dad was wrong to choose Forte because game theory dictates he pass on him–knowing that other owners are low on Forte can and should influence that decision.

My dad would be maximizing his VORP when he passes on Forte, but I have shown that is not always the most efficient strategy.  Sometimes it is valuable to disregard VORP and select a safer, more consistent player.

Consistency is already factored into the graph above and it should also be in your fantasy rankings.  In the TE/WR scenario above, the inherent inconsistency among wide receivers makes them less valuable than tight ends despite more projected points.

Why do we not simply select a tight end in the early rounds, then?  That brings us back to game theory–even if a top tight end (or Forte) is really valuable, it is more valuable to wait and grab him at the last possible moment, securing high-value players at other positions in the meantime.  The thoughts of the other owners concerning tight ends should influence your own.

Thus, we must sometimes forget about VORP to garner consistency, but understanding the concepts of consistency and scarcity requires an intimate knowledge of VORP.

As the Daoist philosopher Lao-Tzu might say, “To acquire value, you must first relinquish it.  Forget it, and it will be yours.”

And therein lies the fantasy football paradox.

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7 Responses to Fantasy Football and Game Theory: Understanding Your Opponents’ Beliefs

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  6. Bayu says:

    Depends on your definition of “well”. It picks the best aalaivble player regardless of position. So let s say you have 1 RB and 2 QBs and the best aalaivble player was a QB, it would pick them even though you need an RB more then a 3rd QB. Sometimes it works out to your benefit, sometimes it gives you 3 TE s, 3 QB s, or 2 TDSP or 2 K.If its a league owner that takes it anybit seriously and knows anything about fantasy, I d say they d want to do their draft to give their team best chance to win. If you don t know much and don t really care, then autopick will probably work just fine for them. Was this answer helpful?

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