Game Theory and Fantasy Football

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Game Theory and Fantasy Football

First, Spoon, stop reading.  Seriously, dude, I’m doing you a favor.  Go fill the bird feeders, drink a Steel Reserve, anything, just stop.  The rest of you, I hope you enjoy my gin fueled ramblings.  I recently completed an online course on Game Theory through Stanford University (Institutional name drop bitches!) at with the sole purpose of applying it to fantasy football auctions and more specifically, FFKL.  In a drunken ego fueled moment of braggadocio I decided to charitably share a bit of what I learned.  A bit.

The FFKL Auction is a complex first-price auction.  There are many factors to consider throughout, and that of course is why it’s so much fun.  The following formula shows how an optimal bid can be determined in a simple first-price auction.  I’ll spare you the details, yes, translation, I don’t know them.  Game theory can describe how and why this formula holds true, but I am neither bright enough, or ambitious enough to explain it.

U = Expected utility

V = Value of player

D = # of bidders competing

B = Optimum bid

B = V * (D-1)/D

U = V – B


You value Tom Brady @ $50

His true market value is an unknown

12 bidders who are all interested in Brady

B = V * (D-1)/D

V = 50

D = 12

B = 50(11/12)

B = 45.83333

Round up B = 46

U = V – B

U = 50 – 46

U = 4

Let’s define ‘U’, expected utility.  This is what it’s all about.  The owner who maximizes his expected utility wins the auction.  As the Funk can attest, that doesn’t always guarantee a championship, but it represents the best you can do.  Bidding below a player’s value and winning saves you money to bid on more players and accumulate more value, thus building a better team and earning the envy of guys like this.  In the example above.  If the owner wins his U = 4, a bargain.  He can now take that $4 and accumulate more value.  Why not bid $47?  You’d still get a utility of 3, right?  Not bad.  Well, your goal is to maximize the utility on each player you bid for and win.  Remember, you value Brady at $50.  Now if you don’t have confidence in your estimate, that’s different, but remember, we’re outlining a simple first-price auction.

Next, let’s discuss ‘V’, your assigned value for Brady.  It’s not how the rest of the league values him, it’s how you value him.  How is this determined?  Well, that depends on you, your team, your opinion on what he’ll produce this season, and how consistently he’ll produce it.  In the complex world of FFKL, his value may also be impacted by how many other quarterbacks are available, who else needs them, what is the FFKL contract situation of the QB you already have on your roster, what he’ll produce over the next two seasons, the prospects for one of your taxi-squad QB’s making the jump to fantasy starter, are you a contender, are you rebuilding, is Gisele Bundchen pregnant, and on and on.  In a word, it’s difficult.  Difficult, but necessary to determine.

So, again, how?  Spreadsheets based on season projections have been tried, many use historical information, but one way or the other you’ll need a number in mind.  This number should be based on your available cash because it is how you value him.  To place a value of $50 on him when you only have $52 in cap space and 8 roster spots is of no use.

Next, ‘D’, the number of interested bidders, representing demand.  In our simple example, I chose Tom Brady because everyone would want his services, resulting in all 12 FFKL owners, spoken or unspoken, having a bid in mind.  In the complex FFKL world ‘D’ can be anything between 1 and 12 for any given player.  It is an unknown.  Let’s take a player like Randy Moss.  He’s returning this year with a new haircut but the same old character questions surrounding him.  How do you determine ‘D’?  Certainly someone will put him in the “don’t bid under any circumstances” category, maybe more than one.  Issues decrease the number of interested bidders, which could potentially deflate price.  So you could classify Moss as risk/reward. I know, duh, but if you pay $40 for $40 worth of production where’s your utility?  There wouldn’t be any.  Estimating the ‘D’ allows you to make a bid that is in-line with his built in risk factors.

Now we have the optimal bid, ‘B’.  This is the bid that will optimize your utility.  If you bid too little you lose out on a player you value.  If you bid too high you experience buyer’s remorse, or what’s known in economics as the winner’s curse.  In fact, you may feel as though the whole room is quietly, or not so quietly, laughing at you.  You paid too much, chump sucka.

As it is overly difficult to determine ‘V’ or ‘D’ in practice, all this shit only explains FFKL bidding in theory. Game theory involves the study of mathematical models to explain the decisions of intelligent rational operatives. The live FFKL auction is something to be experienced, not calculated and has nothing to do with intelligence or rationality.  It resembles the Chicago Board of Trade, drunken men screaming.  Is there a mixed strategy first-price auction algorithm relying on assigned probabilities for demand that also factors in available supply, sentiment, sedatives, Gisele and the Bobby Parker factor?  Yes.  Math is beautiful, but it’s also hard.



Quarter Twain

About the Author:

Yes, I am a stay at home dad. Yes, Gisele Bundchen has an open invitation provided she doesn't speak Portuguese during or after. I am pretty sure my wife would give me the go ahead. Yes, I am superior to the retardees I compete against on a yearly basis in the best fantasy football league in the world. I could easily qualify for a better league, but it doesn't exist. Yes, I am a tri-athlete, thank you for asking. Finally, yes, I have not yet won my championships, but that is easily explained by small sample size. They are not a valid measurement of success at this stage in FFKL history. I could show you the math, but math is hard, that is to say, you would not understand.


  1. Pro Trader
    Pro Trader  May 13, 2012

    3 things.

    1) I read it.
    2) You forgot the L value…Liquor (with subvalues H and S/r, Homerism and Spousal recovery)
    3) This reminds me of your prized spreadsheet with formulas that got you where you are now; top tier loser

    • Zoo of Death
      Zoo of Death  May 14, 2012


    • Quarter Twain
      Quarter Twain  June 14, 2012

      1. *sigh*
      2. Ok
      3. No, it isn’t anything like that, which is why I asked you to stop reading.

  2. G-Funk
    G-Funk  May 23, 2012

    I have a four year degree in Applied Mathematics, so I think it’s cute that you’ve taken an online course. It’s the same feeling I have when my second grader tells me he has “finished learning multiplication” because he knows what 9 x 9 equals. There’s a reason I’ve won more games than anyone else in this league. Brent Celek says hello.

    • Quarter Twain
      Quarter Twain  June 14, 2012

      I never equated this course with a four year degree. The electronic certificate they send you for completion is so full of disclaimers it’s comical. I’ll save my “degree from Auburn” related insult for the private board. 🙂

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