Tell a Consistent Story

Tell a Consistent Story

By Maurile Tremblay

Telling a consistent story means that your lineup's success should not depend on mutually contradictory occurrences. For example, don't pick a high-priced quarterback and also pick the high-priced NFL defense he is going against. For each of those selections to reach value, they'll both have to have great games; but a great game by a quarterback and the defense he faces is contradictory. The quarterback's success comes at the defense's expense and vice versa.

In cash games, the story your roster relies on should be consistent because it should generally be the same story that is told by the Vegas spreads and over/unders.

In tournaments, the story your roster relies on may vary from the story told by the Vegas spreads and over/unders, but it should vary in a consistent way.

Consider a toy game we might play with a six-sided die. You can select any real number you want, and your score is determined by how far off you are from the result of rolling the die. If you pick five and the die lands on two, for example, you were three off, so your score is minus-three.

In a head-to-head contest, choosing 3.5 would be a perfectly good strategy, but picking six would be terrible. If you pick 3.5, you'll be off by 1.5, on average, and you'll never be off by more than 2.5. If you pick six, you'll be off by 2.5, on average, and you'll sometimes be off by five. Someone who picks 3.5 will beat someone who picks six two-thirds of the time.

Now consider a mid-sized winner-take-all tournament instead of a head-to-head contest. Picking six becomes a decent strategy while picking 3.5 is horrible. To win, you're pretty much going to have to nail the exact result. That means six will win about one-sixth of the time while 3.5 will win never. You may have deduced that the best strategy in this game is to pick the integer between one and six (inclusive) that your competitors are least likely to pick. If you can find a number that is picked by fewer than one-sixth of the field, you will have a positive expectation (ignoring any rake).

Let's translate what that means for DFS games.

The story told by the Vegas spreads and over/unders can be thought of as the most likely scenario. In a cash game, you want to play it safe and construct a roster that is consistent with the most likely scenario.

In a tournament, however, especially those with top-heavy payout structures, you will not want to play it safe. Although the Vegas lines might represent the most likely scenario, the actual results from the NFL games will likely depart from the Vegas lines in a number of ways. The contestants that finish high in DFS tournaments will be the ones whose lineups depart from the Vegas lines in the same way that the actual NFL results do.

To oversimplify things in what is hopefully an instructive way, consider three scenarios:

Scenario A: Results from NFL games closely mirror the Vegas lines (and mainstream projections consistent with those lines).

Scenario B: Results from NFL games mostly mirror the Vegas lines, except the Packers score far more points against the Bears than expected.

Scenario C: Results from NFL games mostly mirror the Vegas lines, except the Packers score far fewer points against the Bears than expected.

Let's give Scenario A a probability of 40%, and let's give Scenarios B and C probabilities of 30% each.

If your opponents' lineups are distributed evenly, such that one-third of them are consistent with each scenario, it is apparent that the bulk of your lineups should buy into Scenario A. Your chance of finishing high in the standings is proportional to the product of (a) the reciprocal of the fraction of the field going with the same scenario you are, and (b) the probability that your scenario is the right one. (The reciprocal of a fraction just reverses the numerator and denominator, so the reciprocal of 1/3 is 3/1, the reciprocal of 2/5 is 5/2, etc.) In this case, Scenario A (3 * 40% = 1.2) gives you a better expected result than Scenario B (3 * 30% = 0.9) or Scenario C (3 * 30% = 0.9).

But in DFS contests, even in tournaments, your opponents' lineups will not be evenly distributed across all scenarios: they will tend to cluster around scenarios most consistent with mainstream projections that are based on the Vegas lines. So let's say that instead of 33/33/33, your opponents' lineups are distributed as follows: 50% are consistent with Scenario A, 30% are consistent with Scenario B, and 20% are consistent with Scenario C.

In this case, your best bet is to submit a lineup consistent with Scenario C. Scenario C (5 * 30% = 1.5) is preferable to Scenario A (2 * 40% = 0.8) or Scenario B (3.33 * 30% = 1.0).

Going with Scenario C here is similar, in the toy-game example above with the die, to picking the number six when fewer than one-sixth of the field is doing so. The general rule is that if you think there is an X% chance that a particular departure from the Vegas line will come to fruition, and you think that Y% of the lineups submitted by your opponents will be consistent with that departure, it makes sense to submit a lineup based on that departure as long as X > Y. (Poker players might find an analogy here to the concept of pot odds.)

The key, though, is that any departure or departures from the Vegas lines that one of your rosters is based on must be self-consistent. If you are adopting Scenario C above, that doesn't mean only that you should be less likely to include Aaron Rodgers in your lineup. It also means that you should be less likely to include Jordy Nelson in your lineup, and more likely to include the Bears defense in your lineup. Don't simply add to or subtract from one player's projected points. Players in the same game are interrelated, and if you're adding to one player's projected points, you must add to or subtract from other players' projected points in a way that is consistent with the story you're creating.

(The concept of stacking can be derived from this way of thinking.)

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