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Many people think of ownership and think that as long as their lineup isnâ€™t duplicated, theyâ€™re good to go. Unfortunately, it isnâ€™t quite that simple. While not having your lineup duplicated (duped) is integral to success in DFS, we also should be weighing a few other factors to determine if the lineup has a positive Expected Value (+EV). Weâ€™ll use MLB as the example for this concept, however, it should be applied to all sports.

It all starts with determining what we deem to be a â€śsuccessfulâ€ť outcome for our lineup. Letâ€™s use a stack in baseball. We typically say a stack â€śsucceededâ€ť when it was the top stack on the slate. The reason for this is because it is unlikely to win a GPP without having the top stack in the lineup. Now that we have defined what a successful stack means, our next step is to assign a probability that the successful outcome occurs. There is a multitude of ways one can approximate success probability. Projection rank relative to other teams is a simple and easily implementable way to approximate success probability.Â

The common thought in DFS is that a highly owned stack (chalk stack) should be avoided (faded). This type of thought process is missing a key component in how profitable lineups are built. A team that is the highest owned on the slate doesn’t tell us enough on how we should use them in lineups. We have to use that data in conjunction with the stackâ€™s success probability to garner an accurate depiction of the stackâ€™s value. We shouldnâ€™t mind having the highest owned stack (say LAD) at 25% ownership if we estimate their success probability is 30%. However, we might limit our exposure if the success probability was 15%. In the first example, LAD is under-owned, in the second they are over-owned. Itâ€™s important to note here that LADâ€™s ownership % did not change, yet in one case we would be happy to use them in most lineups, and in the other, we would be more selective.

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We want to be controlling how the pieces of our lineup fit together. Say you have TOR and BOS that are both highly owned and over-owned by the market. If we lower their cap (say to 5%) and let Fantasy Cruncher run, we may still get lineups where we have TOR and BOS together. We generally see this when thereâ€™s a chalk value stack and a chalk projection stack. Without constraints, the optimizer will just jam whatever the best median projected lineups it can into our portfolio. So even though our overall portfolio has very little BOS and TOR, we could have lineups that have both BOS and TOR together, making for an over-owned (relative to their success probability) lineup.

So if TOR is over-owned by 5% and BOS is over-owned by 5% then when we stack them together, the hittersâ€™ portion of our lineup is going to be over-owned by 10%. Itâ€™s not really getting duped thatâ€™s the concern, itâ€™s more so a concern that when weâ€™re right and those stacks are the top stacks, weâ€™re competing with more people than we should be relative to the probability that both stacks hit. Capping exposures is a great start however it does not necessarily mean that the lineups that are produced will be profitable.

Once we have the success probability of our stack, the ownership of our stack, and the number of entrants in the tournament, we can solve for two extremely important data points: Efficient number of lineups and Actual number of lineups.**Â **

Hereâ€™s an illustration of the concept:

10 000 entrants in the tournament

NYM is the top stack 20% of the time and is 23% owned

TEX is the top stack 11% of the time and is 5% owned

The Efficient Number of Lineups in a tournament tells us how many of that specific type of lineup **should be **represented by the field so that the lineup has a neutral expectation (EV of 0). This is calculated by multiplying the number of entrants by the success probability.

The efficient number of NYM stacks in the tournament is 2000 (10 000 x 20% success probability)

The efficient number of TEX stacks in the tournament is 1100 (10 000 x 11% success probability)

The Actual Number of Lineups in a tournament tells us how many of that specific type of lineup is **actually **represented by the field. This is calculated by multiplying the number of entrants by the ownership.Â

The actual number of NYM stacks in the tournament is 2300 (10 000 x 23% ownership)

The actual number of TEX stacks in the tournament is 500 (10 000 x 5% ownership)

Once we have the efficient number of lineups and the actual number of lineups we can calculate the differential between the two:

NYM = 2300 (actual number) – 2000 (efficient number) = +300Â

TEX = 500 (actual number) – 1100 (efficient number) =Â -600

This tells us that there are 300 more NYM lineups than there should be and 600 fewer TEX lineups than there should be.

A lot of people tend to focus on attempting to pick the stacks that are more likely to be the best stack on the slate. Itâ€™s very important to understand that it doesn’t matter that NYM will be the best stack twice as often as TEX. The goal isn’t to increase the frequency that we’re correct about the top stack on the slate. The goal is to select the stacks that when we’re correct, we’re competing with fewer lineups than we should be.

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So with NYM, we’re competing with 300 lineups more than we should be relative to their success probability. This means that the Win Equity gets diluted across those extra 300 lineups. Based on our data, before the first pitch of the slate is thrown, 20% of the time each NYM stack should have a 1 in 2000 chance of winning the tournament. We find this number by using the efficient number of lineups calculated above (in this case 2000). So at the start of the tournament, we placed a bet with the assumption that 20% of the time we will have a 1 in 2000 chance of winning the tournament. The stack is inefficiently over-owned, meaning when the 20% probability hits and NYM are the Top Stack, the actual odds of our lineup winning the tournament are 1 in 2300. With the NYM stack, weâ€™re forced to split our Win Equity (odds of winning the tournament) with more lineups than is efficient. This is often referred to as Equity Dilution.

Conversely, letâ€™s explore TEX. Before the first pitch of the slate, our data indicated that the odds of a TEX stack being in the winning lineup was 11%. The efficient number of TEX lineups was 1100. This means that if we played a TEX lineup, 11% of the time we should have a 1 in 1100 chance of winning the tournament. Now, there are only 500 actual TEX stacks in the tournament, so while the odds of a TEX stack winning the tournament is still 11%, when that 11% hits, we actually have a 1 in 500 chance of winning the tournament. The field not rostering enough TEX lineups increased our odds of winning by more than double! There should be 600 more lineups to compete against, but those lineups don’t exist. So the Win Equity of those 600 lineups gets concentrated to the existing 500 lineups. This is often referred to as Equity Concentration.Â

Now we repeat this process for every aspect of our lineup to make sure that overall the lineup is profitable. It’s not about choosing the right players, or the right stacks, or the right pitchers. It’s about choosing the right combinations of players/stacks/pitchers to form a cohesive lineup that is underrepresented by the field. You can play over-owned pieces in some lineups and not others. Itâ€™s not about fading the chalk stack/player/pitcher, itâ€™s about fading chalk lineups constructions

As you can see, ownership is integral to evaluating the profitability of your lineups. It always matters, and always should be weighed relative to the success probability of your lineup. Too many people misapply ownership by arbitrarily picking players that are lower owned. They think theyâ€™re doing a good thing by reducing the overall ownership of their lineup to be more â€ścontrarianâ€ť. They often fail to realize that playing an 8% owned stack that has a 4% success probability is usually worse than playing a 15% owned stack with a 20% success probability. The inverse is also true. Quite often people assume that because theyâ€™re unlikely to get duped they can play whomever they want without any thought to the relationship between success probability and ownership.

The goal in GPPs has always been to build lineups that have an underrepresented construction relative to the success probability of that construction. The common thought in the industry is to use ownership to gauge one’s lineup vs the field. While this does have merit, it’s often more powerful to use and compare ownership of a lineup relative to the success probability of itself.Â Â

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