The Rundown: FantasyScore Week 2

A weekly guide to FantasyScore's Draft-and-Go contests.

Last week, I advised you to only play the following Draft-N-Go's (DNGs) offered by FantasyScore:

  • 2 players, 1 payout
  • 5 players, 2 payouts
  • 8 players, 3 payouts

I also gave you a value-based drafting (VBD) list to use for each of those DNG games. Hopefully, that produced DNG success for you in Week 1! Today, I'm going to reveal another piece of the DNG bankroll equation. Namely, I'm going to show you how drafting in each of these games affects the Kelly Criterion for buying into them.

For those unaware, the Kelly Criterion says you should wager X percentage of your bankroll based on the consideration of four factors:

  • Your current bankroll.
  • The net odds on your wager (e.g., finishing first in a 2-player $1 DNG wins you $1.80 for a net odds of 1.9-to-1.)
  • Your inherent probability of winning (e.g., you have a 5 percent edge on your opponent, so you have a 55% chance of winning).
  • Your inherent probability of losing (e.g., you have a 5 percent edge on your opponent, so you have a 45% chance of losing).
The formula that combines these factors is
Bankroll Percentage = [(Odds * Win Probability) - (Lose Probability)] / Odds
So, as an example, let's say you have $100 bankroll and a 55% chance of winning 1.8 times your buy-in in a head-to-head DFS game. In that case, you should devote $30 to this game because [(1.8 * .55) - .45] / 1.8 = .3, and $100 times .3 is $30.

Typically, the above can be your default guide for bankroll management. In certain circumstances, however, there's a fifth factor: how much your DNG lineups overlap. As fellow FootballGuys colleague Steve Buzzard detailed last year, the amount of money that the Kelly Criterion tells you to wager in one game is directly proportional to the percentage of players you have in your lineup for that game that are the same in another game of the same type. This is an advanced daily fantasy sports (DFS) concept, so I'll unpack it a bit.

Let's say you want to enter two head-to-head (H2H) games this week with one lineup that you deem the best, and one that you deem second-best. Your second-best lineup is the same as your best except for three players. In that case, because only one-third of your second-best lineup is different from your best lineup, the math says you should wager one-third as much on your second-best lineup as you do on your best lineup (e.g., $1 vs. $3, $3 vs. $10, $10 vs. $30, $100 vs. $300, etc.).

This kind of math can also can be applied to FantasyScore's DNGs, even despite the fact that you don't know your lineup going into it. That's because, although we may not know our lineup, we know two important hints as to what our lineup is likely to be: (1) our draft list, and (2) the fact that the draft order is randomly generated. Armed with these pieces of information, we can engage in a little thought experiment about the likelihood of any given DNG lineup being unique. For this thought experiment to work, however, we need to make two assumptions:

  1. All players are using the same draft list.
  2. All players select the best player available unless they've already filled that player's position in their lineup.
Sure, these assumptions aren't going to hold in real life, but, again, we're trying to figure out a theoretical uniqueness estimate that can at least give us some kind of guidance for our bankroll decision-making.

OK, so given the above assumptions, I'll first illustrate how this works with the easiest example: a 2-person DNG. Let's say we have a bankroll of $100, and have a 55% chance of winning 1.8 times our buy-in. In that case, as before, Kelly Criterion says we should devote 30% of our bankroll to said game. But let's say we play the 2-person DNG two times, meaning we've now exposed ourselves to the possibility that both of our lineups will be the same. The vital question becomes, "What's the probability of that?" Mathematically, the answer is 50% because there are only four possible random draft pick outcomes, and the times when our randomly generated pick is the same is equal to the times when it's different:

  1. We draft first, then second, and so our lineups are different.
  2. We draft second, then first, and so our lineups are different.
  3. We draft first both times, and so our lineups are the same.
  4. We draft second both times, and so our lineups are the same.
Based on this theoretical exercise, we should split our earlier 30% 2-person DNG exposure into two 15% exposures. With a $100 bankroll, that means $15 on one 2-person DNG and $15 on the other. And again, just to make sure you're following the logic in this thought experiment, our assumptions of (1) everyone using the same draft list, and (2) everyone selecting the best player available given position availability, means that our theoretical lineup when drafting first is never going to be the same as our theoretical lineup when drafting second. To wit,these are the only possible 2-person DNG lineup outcomes this week given our assumptions:
Position No. 1 pick No. 2 pick
QB Aaron Rodgers Andrew Luck
RB Justin Forsett Matt Forte
RB Adrian Peterson Marshawn Lynch
WR Antonio Brown Julio Jones
WR Odell Beckham Jr. Randall Cobb
WR Calvin Johnson Keenan Allen
TE Rob Gronkowski Jimmy Graham
FLEX Julian Edelman Alshon Jeffery
DEF Baltimore Ravens Miami Dolphins

As you can see, they're different. If you draft first against a "perfect" theoretical opponent, you're never going to have the same lineup drafting second against that same "perfect" theoretical opponent.

When we move to the 5-person game, things get incredibly complicated mathematically if we decide, as before, to play the same number of games as the number of participants (i.e., five 5-person DNGs). Unlike the previous example, where two 2-player games means four possible lineup outcomes (i.e., 22), five 5-person games means 3,125 possible lineup outcomes (i.e., 55). In short, obtaining a theoretical estimate of uniqueness probability is a bear. Luckily for our readers, I'm here to help.

Provided our earlier assumptions hold true, it turns out that we can boil those 3,125 lineup outcomes into five sets:
  1. 3.8% of the time you're going to end up in 5 different draft slots with 5 unique lineups (e.g., 1st pick, 2nd, 3rd, 4th, 5th).
  2. 38.4% of the time you're going to end up in 4 different draft slots with 4 unique lineups (e.g., 1st, 1st, 2nd, 3rd, 4th).
  3. 48.0% of the time you're going to end up in 3 different draft slots with 3 unique lineups (e.g., 1st, 1st, 2nd, 2nd, 3rd or 1st, 1st, 1st, 2nd, 3rd).
  4. 19.2% of the time you're going to end up in 2 different draft slots with 2 unique lineups (e.g., 1st, 1st, 1st, 1st, 2nd).
  5. 0.2% of the time you're going to end up in 1 different draft slot with 1 unique lineup (e.g., 1st, 1st, 1st, 1st, 1st).
Adding these all together (i.e., [.038 * 5] + [.384 * 4], and so on), we get an expectation of 3.55 unique lineups out of the five we're going to play, or 71% of all lineups. Therefore, if you're going to play five 5-person DNGs, then your entry fees should be allocated as follows:
  1. 71% on the first game.
  2. 21% on the second game (i.e. [100% - 71%] * 71%).
  3. 6% on the third game (i.e., [100% - 92%] * 71%).
  4. 1% on the fourth game (i.e., [100% - 98%] * 71%).
  5. 1% on the fifth game (i.e., [100% - 99%] * 71%).
Or, extrapolated to a total allocation of $30, that's $21 - $6 - $2 - $1 -$1 (or so, given intentional rounding).
It's important to note that this is only the optimal bankroll strategy for playing five 5-person DNGs. If you play only two 5-person DNGs, then your lineup will be the same 20% of the time (e.g., 1st pick, then 1st pick) and different 80% of the time (e.g., 1st pick, then 5th pick). Compare that 80% uniqueness to the 71% uniqueness above, and you see that there's a good, common sense heuristic underlying all of this fancy math: The more of the same type of DNG that you play, the quicker your DNG buy-ins should decrease. For example, if Kelly Criterion says we should wager $30 on 5-player DNGs, then playing two of them means a $24-$6 split, whereas playing five of them means the aforementioned $21-$6-$2-$1-$1 split. The latter decreases faster than the former, $21 to $6 (and so on) versus $24 to $6.

week 2 draft lists 

With all that math out of the way, below are the draft lists you should use for Week 2 DNGs based on FootballGuys' average FantasyScore projection and VBD: 
2-Player DNGs  5-Player DNGs  8-Player DNGs  
Antonio Brown WR PIT Antonio Brown WR PIT Antonio Brown WR PIT
Julio Jones WR ATL Julio Jones WR ATL Julio Jones WR ATL
Matt Forte RB CHI Matt Forte RB CHI Matt Forte RB CHI
Rob Gronkowski TE NWE Odell Beckham Jr WR NYG Odell Beckham Jr WR NYG
Odell Beckham Jr WR NYG Rob Gronkowski TE NWE Rob Gronkowski TE NWE
Andrew Luck QB IND Andrew Luck QB IND Marshawn Lynch RB SEA
Marshawn Lynch RB SEA Marshawn Lynch RB SEA Calvin Johnson WR DET
Calvin Johnson WR DET Calvin Johnson WR DET Julian Edelman WR NWE
Julian Edelman WR NWE Julian Edelman WR NWE Randall Cobb WR GNB
Randall Cobb WR GNB Randall Cobb WR GNB Keenan Allen WR SDG
Keenan Allen WR SDG Keenan Allen WR SDG Andrew Luck QB IND
Justin Forsett RB BAL Alshon Jeffery WR CHI Alshon Jeffery WR CHI
Baltimore Ravens DEF BAL Jordan Matthews WR PHI Justin Forsett RB BAL
Aaron Rodgers QB GNB Justin Forsett RB BAL Jordan Matthews WR PHI
Alshon Jeffery WR CHI DeAndre Hopkins WR HOU DeAndre Hopkins WR HOU
Adrian Peterson RB MIN Adrian Peterson RB MIN Adrian Peterson RB MIN
Jimmy Graham TE SEA Eddie Lacy RB GNB Eddie Lacy RB GNB
Miami Dolphins DEF MIA A.J. Green WR CIN A.J. Green WR CIN
      Brandin Cooks WR NOR Brandin Cooks WR NOR
      Jarvis Landry WR MIA Jarvis Landry WR MIA
      Aaron Rodgers QB GNB Ameer Abdullah RB DET
      Ameer Abdullah RB DET DeMarco Murray RB PHI
      DeMarco Murray RB PHI Brandon Marshall WR NYJ
      Brandon Marshall WR NYJ Mark Ingram RB NOR
      Drew Brees QB NOR Jimmy Graham TE SEA
      Mark Ingram RB NOR Larry Fitzgerald WR ARI
      Baltimore Ravens DEF BAL Baltimore Ravens DEF BAL
      Miami Dolphins DEF MIA Aaron Rodgers QB GNB
      Jimmy Graham TE SEA Jason Witten TE DAL
      Jason Witten TE DAL Roddy White WR ATL
      Larry Fitzgerald WR ARI Miami Dolphins DEF MIA
      Roddy White WR ATL Latavius Murray RB OAK
      St. Louis Rams DEF STL Bishop Sankey RB TEN
      Matt Ryan QB ATL Drew Brees QB NOR
      Latavius Murray RB OAK Carlos Hyde RB SFO
      Carolina Panthers DEF CAR Kendall Wright WR TEN
      Bishop Sankey RB TEN Jonathan Stewart RB CAR
      Tyler Eifert TE CIN Tyler Eifert TE CIN
      Kendall Wright WR TEN Joseph Randle RB DAL
      Carlos Hyde RB SFO Davante Adams WR GNB
      Ben Roethlisberger QB PIT St. Louis Rams DEF STL
      Davante Adams WR GNB Heath Miller TE PIT
      Jonathan Stewart RB CAR Carolina Panthers DEF CAR
      Heath Miller TE PIT Jordan Cameron TE MIA
      New Orleans Saints DEF NOR Mike Evans WR TAM
            New Orleans Saints DEF NOR
            Danny Woodhead RB SDG
            Terrance Williams WR DAL
            Jeremy Hill RB CIN
            Matt Ryan QB ATL
            Amari Cooper WR OAK
            Steve Smith WR BAL
            Chris Ivory RB NYJ
            John Brown WR ARI
            Steve Johnson WR SDG
            Arizona Cardinals DEF ARI
            Donte Moncrief WR IND
            Minnesota Vikings DEF MIN
            DeAngelo Williams RB PIT
            Ben Roethlisberger QB PIT
            Pierre Garcon WR WAS
            Greg Olsen TE CAR
            Darren Sproles RB PHI
            Russell Wilson QB SEA
            Carson Palmer QB ARI
            Lamar Miller RB MIA
            Sam Bradford QB PHI
            Andre Johnson WR IND
            Vincent Jackson WR TAM
            LeSean McCoy RB BUF
            Ladarius Green TE SDG
            Tennessee Titans DEF TEN

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