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).
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:
- All players are using the same draft list.
- All players select the best player available unless they've already filled that player's position in their lineup.
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:
- We draft first, then second, and so our lineups are different.
- We draft second, then first, and so our lineups are different.
- We draft first both times, and so our lineups are the same.
- We draft second both times, and so our lineups are the same.
|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.
- 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).
- 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).
- 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).
- 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).
- 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).
- 71% on the first game.
- 21% on the second game (i.e. [100% - 71%] * 71%).
- 6% on the third game (i.e., [100% - 92%] * 71%).
- 1% on the fourth game (i.e., [100% - 98%] * 71%).
- 1% on the fifth game (i.e., [100% - 99%] * 71%).
week 2 draft lists
|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|
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