## How many lineups should I play?

There’s not too much discussion about the merits of multi-entry in DraftKings tournaments-most people agree that you can enter a GPP a bunch of times and still maintain a positive expected value-but there’s a fierce debate over how many lineups you should construct for cash games (head-to-heads, 50/50s, and three-man leagues).

Popular wisdom suggests that daily fantasy players should enter just a single lineup into cash games-their “optimal” lineup with all of their top values, or as many of the top values as they can fit under the salary cap. I disagree with the idea that there is one true “optimal” lineup, as well as the notion that playing just a single lineup in cash games is a smart strategy.

**The Problem with Counting Lineups **

I first want to address an important related idea, which is that what determines risk is the number of lineups you play on DraftKings. Instead, risk depends on the number of players you use, the way you combine those players, and the amount of money you have on each player/combination.

Player A might use two different lineups that have completely different players from each other-18 different players in an NFL contest-while Player B might have two lineups with every player the same except one (10 different players across the two lineups). Who is taking on the greater amount of risk? Clearly Player B.

When you frame the issue in this way, it becomes clear that what matters shouldn’t be the total number of lineups, but the total player exposure. How much exposure do I have to this player and how much money do I have on him? In the case of Player B, the total risk and player exposure would be almost exactly the same as with someone who used just a single lineup, while Player A’s diversification would make his risk/reward much different.

**Diversification**

The key word there is ‘diversification’: the risk you assume has little to do with how many lineups you play and more to do with how much you diversify those lineups, i.e. how many players you use and what type of exposure you have to them. In a world with perfect knowledge, we should indeed use a single cash lineup optimized around our values. There’s indeed only one true set of players that will optimize a lineup’s projected points.

The problem is that we don’t have perfect knowledge of outcomes. We’re fallible, our projections are fallible, and our player values are fallible. One of the biggest mistakes a daily fantasy owner can make is not being aware of their own fallibility.

We see this all the time in the NFL when teams give up a king’s ransom to trade up in the draft to snag “their guy.” Many times, the only way those moves work out for the team trading up is if they get exactly what they think they’re getting. They fail to realize that the draft is a game of probabilities, and no one has perfect knowledge of how future events will unfold. They don’t say to themselves, “This is what we think and we’re pretty confident we’re right, but what happens if we aren’t?”

When we assume that our projections and values are flawless, we create an extremely fragile system for creating lineups. Every week, there are numerous players all ranked near one another in terms of value. To use one player because he’s projected to score 0.1 points more than another requires a level of confidence in your predictions that is simply unattainable.

Once we start to account for our own fallibility-once we acknowledge the fact that, hey, we could just be wrong-it opens up the door for greater diversification.

**Risk Minimization: A Balancing Act**

Creating lineups for cash games isn’t all about minimizing risk. The amount of risk you absorb in a given day is very much a personal preference and a function of your bankroll.

However, a small amount of diversification can dramatically reduce risk without significantly cutting into your upside. That’s especially true in a sport like football in which there are so many injuries. You could hit the nail on the head with a particular pick and just get unlucky with a first-quarter injury; all of a sudden, your cash games are shot because of a fluky tackle, for example.

Of course, we can’t diversify too much. If you were to use every single player and have equal exposure to all of them, you’d just slowly lose money; you still need to pick players who offer value and have the most exposure to the most valuable players. It’s not like the game is totally random and it doesn’t matter who you pick.

Thus, much of your cash game strategy is a balancing act between creating “optimal” lineups and reducing your risk such that you don’t have too much on the line with any single player or group of players. The goal is to give up a little bit of upside that the one-lineup approach might offer in favor of a significantly less amount of risk.

**Reaching the Long Run**

The risk/reward balance is related to the idea of “reaching the long run.” Every daily fantasy player who believes he or she has an edge is trying to reach the long run-a period of time after which profitability is inevitable.

In poker, the long run might be a few thousand hands. I could potentially beat a better player over the course of a few dozen hands, maybe even a few hundred. As we play long and longer, however, I would eventually lose out, and that would be a statistical certainty.

Another example of this is something as simple as the flip of a coin. Even though each flip is more or less random, it’s a mathematical fact that as you flip the coin more and more, you also become more and more likely to see a 50/50 split between heads and tails.

So how is this related to cash-game strategy? Well if reaching the long run is really important, it makes sense to do that as fast as possible while still maintaining a positive expected value.

Let’s say you’ve tracked your results for the past year and you conclude that you can win 60 percent of head-to-head games with your optimal lineup and 58 percent with a secondary lineup-a lineup of second-tier values that you employ as a hedge.

In theory, playing solely the optimal lineup would enhance your profitability because you can maintain a slightly higher win rate. In practice, using both lineups can be the superior option because, since you have greater player exposure and you’re taking on less risk, you can place a greater percentage of your bankroll in cash games each week. Thus, you can make up for a reduced win rate by simply playing more volume. And not only that, but using multiple lineups can let you play that additional volume without actually taking on more risk.

The key to all of this is using lineups that have a positive expected value; you shouldn’t diversify simply for the sake of diversification. If you can continue to roll out profitable player groupings, however, the multi-lineup approach to cash games is an underrated one that can improve your profitability and dramatically decrease your risk of ruin.