Winning DFS is About The Format Part 3

In the first two parts about how the format changes the strategy of winning daily fantasy sports I discussed the difference between tournaments and cash games and how tournaments you are looking to differentiate yourself with contrarian plays and in cash games you are looking for the wisdom of the crowd to help you win DFS cash games and maybe a few superior projections assuming such a thing exists.

Now I want to show how the format of tournaments and the example given regarding the dice roll can produce a positive result by doing something that on the source might seem very countertuitive... Playing against yourself and putting money on a losing bet to "cover all options". If you knew the field was unevenly distributed according to certain probabilities, there would be the potential to gain without trying to even handicap. Since in a given game you don't KNOW how many select 1,2,3,4,5,6 and which selections will be uncommon, we are going to show that betting $1 on all possible entries can be positive.

Rather than spend $1 with $1,000 entrants trying to guess the most profitable option of either a 1 or a 6, with KNOWN information about how others distribute their bets, you can simply distribute your bets according to probability. If an event is going to have a 1/6 chance of producing, you put 1/6th of the week's risk towards that outcome. You repeat for 100% of your capital. So the yield per $6 entry spent can be calculated based upon a distribution.

To review, the distribution of dice roll guesses is as follows:
50 people guess 1
150 people guess 2
300 people guess 3
300 people guess 4
150 people guess 5
50 people guess 6

You could randomize the actual number so that 300 people select 1 and 50 people select 3 as long as you have equally uneven betting, the strategy of betting on every single outcome is going to work. You profit to the degree by which opponent's error in their distribution. The mathimatically correct distribution is going to be 1/6th of a population guessing each number.

Given these assumptions, when a 3 or 4 are rolled, you only win $3.333. Since you only win this 1/6th of the time the "expected value" of making this bet is 3.333/6 which is $.55556. but remember, you paid $1 to place this bet so you've actually lost an average of $0.4444 for every dollar spent.
When a 2 or 5 are rolled, you gain 6.67. divide that by 6 and you gain 1.11 per dollar spent or $0.111.
When a 1 or 6 are rolled, you gain a whopping $20. Divide this by 6 and you gain $3.333 per dollar spent or a net gain of $2.333 per roll.

Add this all up and you end up with a net gain of $4 per every $1 risked! Think about that! By playing a game where you have a 1/6th chance of any outcome, and you bet 1/6th of your total bet size for the week on each and every possible option, you can win $4 for every $1 you risk simply by opponent's trying to guess an option that's consistently "close" rather than being a contrarian.

This strategy clearly doesn't work when there are only 3 options or only one single better. A rock paper scissors strategy isn't profitable unless it's a mass multiplayer version in which the profits of all the winners are added and losers are deducted and ties are split. If you are able to randomize your responses so you have each option 1/3rd of the time and the opponents end up disproportionally going with Rock, the tiems in which you go paper you are going to win more due to you facing more rocks than scissors. But the more people and the more uneven the distribution in representing equally likely outcomes proportionally, the greater the advantage, regardless of if you can actually identify it.

For those that are still unconvinced I want to give a specific daily fantasy sports example that contains a few core DFS principals that we will discuss later. One of the principals is "stacking", and another is "fading". For example, let's say you always pick a QB's less popular option and pair that player with the QB. There are a few reasons you might do this, but nevertheless, let's just say player A does this ONCE per week for 32 weeks. Player B does this 32 times in week 1. Who has a better probability of getting the highest scoring QB for the cost of 32 entries? Clearly the person who has 32 entries with 32 different QBs has a 100% chance of getting the best QB. It's very important to understand that with massive player pools the payout is so massive but competition is so heavy that you have to get the roster almost exactly right, so getting close might still return significant value but because of this, maximizing your odds of getting the exact right answer over the same cost is valuable.

While this player does NOT have any chance of getting the best combination more than once, he also is certain to have the 2nd, 3rd, and 4th highest scoring QBs, and if any one of those QBs connect with multiple TDs to an underowned, cheap WR, that player has a shot with the remaining roster of doing very well. Because it's rare for a WR to have a top performance without his QB having a top performance and because "getting CLOSE" to the best roster isn't enough, you want to STACK QB and WR combos mostly all of the time in tournaments.

A player who picks all, or a vast majority of entries adds value. I am not sugesting you should enter an insanely large number of lineups every single week, although a lot of the winning players do, but I am saying to at least do enough to cover a lot and cast a wide enough net each week. You're better off playing at smaller buy in games like $1 and $2 where the competition is lower quality and the payout per dollar risked is probably better 10 times than $10 or $20 once. in a given week.

The value comes from all of the similar lineups by your opponents that unfairly and disproportionally stack their lineups to the seemingly "best options" if the goal were simply to have the highest accuracy rate possible in having a relatively average to above average lineup 50% of the time. But remember, the payout is super massive if you win, so you instead should be okay losing several times in a row before you hit and you can be very very profitable.The goal is not to try to win every entry, but just increase your chances and value when you ARE hitting on your picks, and have your chances be stronger of hitting on those picks than the field allocates to those picks. (I.E. if you identify a player with a 5% chance of 'success' and less than 5% of the people have him on their roster he adds value despite a low probability of him succeeding).

When you have a lineup that is similar to everyone else, just as in the dice roll example, you don't win as much, but more accurately you are competing with a much higher amount of people. For example, if there are 100,000 entrants and you go with the two most popular options that occur maybe 40% of all rosters each, when this player does as expected you still have 9,000 remaining opponents that are EVEN in score when you hit the top combo and even then there are 91,000 others where 1/3rd has one, 1/3rd has the other and many of the remaining 1/3rd either aren't too far behind or have enough salary cap room that they are able to catch up by getting many highly talented players that are more likely than your remaining players to do well and can easily "close the gap".

But if you get say 32 QBs and mostly pick any WR, you have maybe a 20% chance on a given week of having the very best QB and best WR combo and are competing with the remaining positions, typically a lot more salary cap, AND everyone that picked the obvious choice at WR is  pretty much out of the running. If your QB is NOT throwing to the obvious choice at WR and instead the other guy, that means that not only on good weeks you will be in the running, but also that the popular choice will be basically OUT of the running. Anytime someone pays a premium price for a WR who fails they aren't going to be very likely to win.

Aside from a 20% chance of having the best QB with his best WR combo (assuming your WR has a 20% of being the top receiving scorer of the offense), you have about a 67% chance of having at least one of your top 5 QBs connect with your WR you paired with him as his top scorer. The odds are quite good that you will find substantial value in covering your bases and stacking.  If there aren't so many entrants and such a huge price for first proportional to the bankroll, you wouldn't want to make contrarian picks like this and you wouldn't have as many entries that are so unique and you probably wouldn't pair a QB/WR combo.

The only QBs you might make an exception on are the QBs with lots of target and a tendency to spread the ball around and for no option in that offense to score multiple times and be the focal point, particularly if the QB also gets a lot of his points from running as well. I probably wouldn't stack Kaepernick or Russel Wilson or Teddy Bridgewater for various reasons, but mostly a strong running game, strong defense and QB running ability makes it much more challenging for any one player dto do very well. It isn't like if a player is double covered and shut down the offense will only target a second or third option. The QB can run, the team can hand the ball off a lot and there are multiple options that all are equally viable who will receive a mixture of passes.

Winning DFS Is About The Format Part 2

In the last post, we discussed how winning in daily fantasy sports is about understanding the format. I probably could have elaborated more but I started to go in a different direction of trying to give examples, demonstrations, and "toy games" or "models" of what it was I was trying to say applies to tournaments. So I want to continue the discussion.

If the dice roll is a metaphor of DFS, a heads up or 50/50 can be the "closest" 50% of the field gets paid and "guessing 3,4, or 3.5 is the only viable strategy". An analogy for being "closest" might be not looking for any of the longshot plays and instead just trying to split the difference between all entrants and hope that enough of them have enough individually bad picks.

Here's a better illustration of how "being average" can actually win more than 50% of the time. Imagine there's a simple game where you only have 3 choices at each position. B is the average. IF you believe no one can consistently handicap the market, or at least that for every winner there's a loser and most decisions balance out such that the market is efficient meaning that players are most strongly distributed across the mean, median and mode and evenly on both sides.

source:http://www.regentsprep.org/regents/math/algtrig/ats2/normal67.gif

Then always using the wisdom of the crowd is still a winning strategy even though "most (mode) people are often about average(mean)".

Imagine stacking several of these distributions at each position. Some half the people are above average, half are below average at a given position. But the percentage of people that consistently beat the average is very low.

While some players may have an edge picking RBs, and others may have an edge picking WRs, and some may get lucky, and some may get unlucky, over a very long time frame, it's entirely possible a very very small percentage of people, and perhaps no individual will consistently beat the average. Based upon this theory, if we consider "b" to be the average response we can add up the totals.

	a	b	c
QB	14	15	12
RB	15	20	10
WR	16	17	18
WR	19	20	21
WR	13	15	18
TE	20	15	19
K	7	8	10
D	10	14	10

on average choosing ALL b wins even though individually sometimes c is better and sometimes a is better. The point of this is that going with the crowd actually can win in a cash game. Why? Your profit comes from the people who THINK they can pick better than average but are not. those that THINK they can pick better than average generally outnumber those that actually can, and so very few lineups will be exactly average in every single spot.

I'm not entirely convinced that "being average" all the way across the board is necessarily enough to always not only beat 50% of the field more than 50% of the time, but also beat the "rake" or the "fees" that are collected by the operating site such as fan duel or draft kings. So you may have to find an edge, or not play in a given week.... OR otherwise you must use a combination of tournament strategies and cash game strategies. I'm more confident tournament strategies do actually have a positive expectation after fees.

However, since tournament strategies are often looking to play a few longshots, you will rarely have the most common players on your roster. If those players happen to go off and have one of those 3TD performances you will be very very likely to see your bankroll go down that week. There is a complex bankroll management tactic that actually shows one of the ways to more boost your bankroll over time is to apply an edge and reduce varience. Risking a small amount is one way to reduce varience. Another way is inversely correlated outcomes. In the case of fantasy sports the inversely correlated options are betting on the more common players. However, if you bet on the more common players in a tournament format, we already covered you are going to be more likely to be negative EV. So instead what you do is you use a tournaent philosophy for tournaments, and use this cash game philosophy of going with the crowd to "normalize" your results. I would aim for a ratio of 2 to 1 where you have 2 times as many cash games as tournaments, ortwo times as much money at stake in cash games as you do in tournaments. So if you are risking 9% of your bankroll in a week, you'd risk 6% in cash games and 3% in tournaments.

I'm not sure of the exact number in a given week that you should have at risk for a number of reasons yet, but I will work on getting a better answer for that later.

Going with the most common options at a minimum will get you to win 50/50's 50% of the time. Higher if enough people have individually bad picks.

Winning Daily Fantasy Sports Is About The Format

Let's play a hypothetical game of rock paper scissors (officially named "roshambo"). In rock paper scissors, what we call the theoretically optimal strategy doesn't actually have an edge. But you can completely neutralize the edge opponents have over you by randomizing your response. Contrast this to someone who always goes "paper" and never changes strategies. This is easily exploited over time by people who figure this out and always go scissors, or at least go scissors far more often than 1/3rd of the time to give the illusion to the player that they have a chance at their strategy working.  The problem with strategies that try to exploit opponent's strategies is that there is the possibility of deception.

What if a player "Bob" initially assumed that an opponent won't usually doesn't go paper twice in a row but after 3 paper's in a row assumes their opponent is using an "always paper strategy" and counters with an "always scissors" strategy? furthermore, what if BOB always starts out rock, assumes that anyone who goes paper will go back to scissors, and then if there are two papers in a row, certainly the opponent will go to scissors the 3rd time. If an opponent KNEW that Bob always operated this way they could counter-exploit, by going 3 papers and then rock. The point of this is showing how any strategy that attempts to exploit weaknesses are vulnerable to their assumptions being wrong.

However, there are other games in which the perfect strategy CAN be profitable if opponent makes a mistake. Take for example a dice role in which the closest guess wins. There are only 3 answers that have the potential to show a profit in the long run vs a single opponent. A 3, a 4, or a fraction between 3 and 4 such as 3.5. With a guess of 3.5 you are never exactly right, but you are never more than 2.5 off of the correct answer. You are within 1.5 or less 50% of the time. Even if thousands of players played this game, as long as it paid the top 50%, you should probably guess a 3,4, or 3.5. Your profit comes from people who guess a 1, a 2, a 5, a 6 or a fractional number above 4 or less than 3.

However, what happens if we change the payout from the top 50% to the top 20%? Or what if only those who get the number exactly, or nearly exactly right split the prize pool? Now guessing 3.5 becomes foolish, and actually guessing a 3 or a 4 while frequently close, and equally as likely to be correct as any other single number actually becomes a poor choice if you expect the vast majority to play to be "close" and guess a 3 or a 4.

Let's prove this by an example.
50 people guess 1
150 people guess 2
300 people guess 3
300 people guess 4
150 people guess 5
50 people guess 6

Those that guess the prize pool exactly right split the profits with the remaining field.
So if you pay $6, let's look at the possible outcomes

1,6: you win $1000/50 people 1/6th of the time each (1/3rd total).
2,5: you win $1000/150 people 1/6th of the time each (1/3rd total).
3,4: you win $1000/300 people 1/6th of the time each (1/3rd total).
This type of distribution is actually fairly common, and fairly rational. Afterall, those who guess 3 and 4 are going to be closest to accurate most of the time. But unlike in a cash game where you only need to be better than half the field, you need to be EXACTLY right on at least a handful of positions, or very close to exactly right on all of them.




Please don't depend on me explaining it to you entirely and stop now and reflect on all of this and try to extrapolate this information to fantasy football daily games.
--------------------------------------------------------
(you did stop and think about it, right?)
/end of reflection

We can obviously see that it pays to be a contrarian PROVIDED the odds of the outcome occuring is greater than the percentage of people who guess that outcome.

That same knowledge applies to daily fantasy games in that in these large contests you have to get your roster close to exactly right, and as such, the probability of the player scoring the most points at his position must exceed the percentage of players who selected that player. Note: We can complicate things if we want to be slightly more accurate since a player who does not score the most points at the position but is the cheapest and still scores among the top may actually have more value IF those salary cap dollars can be put to work to produce a better roster. However, whether you define the "best" as the most points, or the most points per dollar of salary cap or some blend of both isn't as important as understanding the concept. It often pays to be a contrarian.

How To Win At Daily Fantasy Sports

This blog was started with the intention of discussing winning strategies for daily fantasy sports (or DFS for short). It will primarily focus on fantasy football for now. I believe that winning fantasy football is much less about actually knowing the sport than most think, and since everyone else is playing trying to use their knowledge of the sport, you may have a sizable edge knowing a few basic principals.