A daily fantasy sports lineup’s expected prize is the probability-weighted value of its payouts against the opposing field. Its projected point total is the expected value of a score, which does not specify the probability of reaching each paid rank.
Expected points and covariance
For a fixed lineup, expected points equal the sum of the selected players’ expected points. Dependence between player outcomes enters the lineup’s variance through covariance, the measure of how two random totals vary together.
For two point totals X and Y:
Variance of X + Y = variance of X + variance of Y + 2 × covariance of X and Y.
Take two players whose point totals each have variance 100 and whose covariance is 30. Their combined variance is 100 + 100 + 60 = 260 squared fantasy points. Adding the individual variances alone would omit their dependence.
Stacking selects players with a shared game context. Its value requires the actual dependence between their outcomes and the contest’s rewards. Neither a shared team label nor a larger calculated variance establishes a larger expected prize.
Two lineups with the same projection
Take two feasible lineups, each with two variable player scores. All remaining slots contribute the same fixed total, set to zero in this construction. Each variable player scores either 40 or 60 points with equal probability, giving each player an expectation of 50 points.
In lineup I, the two player scores are independent. The lineup scores 80 with probability 1/4, 100 with probability 1/2, and 120 with probability 1/4. Its expected score is 100 and its variance is 200.
In lineup C, the two player scores move together perfectly: both score 40 or both score 60, each joint outcome having probability 1/2. The lineup scores 80 or 120 with equal probability. Its expected score is also 100, but its variance is 400.
These are alternative entries. The construction fixes their feasibility and individual player expectations so that dependence supplies the difference in their score distributions.
The prize schedule changes the comparison
Take a two-entry contest paying $20 to the higher score and nothing to the lower score. Each entry costs $8 and a sponsor supplies the remaining $4. Fix the opposing entry’s score at 105; neither candidate can tie it.
Lineup I wins only when it scores 120, with probability 1/4. Its expected gross prize is $5 and its expected net return is −$3. Lineup C wins with probability 1/2, giving an expected gross prize of $10 and an expected net return of $2.
Now change only the opposing score to 95. Lineup I wins with either 100 or 120, a combined probability of 3/4. Its expected gross prize becomes $15 and its expected net return becomes $7. Lineup C still wins only with 120, leaving its expected gross prize at $10 and net return at $2.
The more variable lineup wins the first comparison and loses the second. Equal projections and a known variance ordering do not determine the preferred entry, even under the same winner-take-all prize schedule.
Opponents, ties and actual contests
An actual opposing field has its own distribution of lineups and scores. Expected reward therefore requires the joint distribution of the candidate score and the scores it must beat. A complete evaluation also includes the prize schedule, entry cost and tie procedure.
For the cash-contest ties covered by DraftKings’ September 9, 2026 guidance, tied entrants share the combined awards for the positions they occupy. Specialty and ticket-contest rules require their own treatment. A guaranteed prize total that remains payable in an unfilled contest fixes the total awards; it does not fix an individual entry’s share.
Mean and covariance describe parts of a score distribution. Pricing an entry requires the payout-relevant probabilities, including ties. Before additional costs, the break-even entry price is the resulting expected gross prize.