Every number on this page is a model
Nothing here was observed. It is a simulation resting on projections that are themselves guesses. Its assumptions are listed in full at the bottom, and the one most likely to be wrong is named — because a simulation whose assumptions are hidden is rhetoric, not evidence.Release settings supplied explicitly
This run used 14 regular-season weeks, a 6-team playoff field, and the payout values listed below. These settings were supplied at release invocation rather than inherited from the prior configuration. The prize schedule totals $900, while 10 teams × $75 contributions produce a $750 pool; the funding source for this confirmed mismatch is unresolved and is not normalized away by the model.The question _PLAN.md left open
Where does the ceiling-over-floor tilt stop biting? "Do not sacrifice mean in rounds 1–4, prefer upside from round 7" is a defensible reading of a convex payoff, but the crossover round is asserted rather than measured.
This league's payout is convex — first pays more than second and third combined, and ninth pays what fourth pays, which is nothing — so variance should be worth buying. But it is a two-stage tournament, and pure variance never reaches the second stage. So there ought to be a round where you stop buying floor and start buying ceiling.
What was simulated
A 10-team snake from the locked 1.01, 40 drafts × 400 seasons at every cell of the grid below. Opponents draft off ADP and off projections with noise. Every player carries a weekly distribution built from his own projected stat line — touchdowns as a six-point Poisson count, the rest smoother — plus his three-year availability, plus a role-change mixture: a modelled chance that a backup inherits a job or a young player wins one, which is where real upside actually comes from. 14 random head-to-head weeks, top 6 qualify, and the explicitly supplied payout configuration.
The touchdown inputs are the certified FFToday July 30 base-plus-pagination stat-line snapshot. ADP is Fantasy Football Calculator's 10-team PPR, 4,121-mock snapshot captured August 2, a public proxy rather than ESPN ADP. Kicker scoring remains a distance-mix model; D/ST retains the existing certified model and treats raw FFToday D/ST as audit-only.
Our drafter takes the highest-value player available — value over replacement on the correct expectation, mixture included — until round R. From round R he tilts, taking the highest value + T × residual variance, where residual variance is the variance a player carries beyond what his projection level already implies. That residual is the crux: a season standard deviation is mostly a function of projected volume, so ranking by raw standard deviation is just ranking by points again. Two earlier versions of this file did exactly that and reported a volume effect as an upside effect.
The grid
Expected dollars per season. T is how hard the tilt is; R is the round it starts. never is the control: always take the highest-value player.
| Tilt T | R=1 | R=3 | R=5 | R=7 | R=10 | R=13 | never |
|---|---|---|---|---|---|---|---|
| T=0 | $+171 | $+170 | $+175 | $+174 | $+174 | $+174 | $+173 |
| T=1 | $+167 | $+165 | $+172 | $+173 | $+174 | $+175 | $+173 |
| T=2 | $+166 | $+163 | $+170 | $+172 | $+175 | $+175 | $+173 |
| T=5 | $+159 | $+160 | $+164 | $+168 | $+175 | $+175 | $+173 |
| T=10 | $+113 | $+115 | $+141 | $+155 | $+170 | $+175 | $+173 |
And how many of the sixteen picks the tilt actually changes, which is the check that the experiment is testing anything at all:
| Tilt T | R=1 | R=3 | R=5 | R=7 | R=10 | R=13 | never |
|---|---|---|---|---|---|---|---|
| T=0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 | 0.0 |
| T=1 | 2.7 | 2.7 | 2.4 | 1.5 | 0.5 | 0.5 | 0.0 |
| T=2 | 3.5 | 3.5 | 3.1 | 1.7 | 0.6 | 0.6 | 0.0 |
| T=5 | 7.1 | 7.1 | 5.7 | 3.2 | 1.4 | 1.1 | 0.0 |
| T=10 | 9.4 | 9.4 | 8.4 | 6.8 | 3.1 | 1.9 | 0.0 |
The answer
Never tilting wins. The control is worth $+173 a season. No cell of the grid beats it by more than noise, and the cost of tilting grows monotonically in both directions — the earlier you start and the harder you push, the more it costs, down to $+113 in the corner.
So the answer to the question is not a round. It is that the question assumed something the simulation does not support. Round 7 is not wrong because the true crossover is round 5 or round 9. It is wrong because, once you value players correctly, there is no round at which deliberately preferring variance pays.
Two secondary readings worth having:
- From round 10 onward the tilt is nearly free — because it barely does anything. The divergence table shows why: by then the value gaps between available players are larger than the variance differences, so "take the higher-ceiling player" almost never changes who you take. Late-round upside advice is mostly self-cancelling.
- The damage is concentrated in the first four rounds, which is the one place the original advice was right: do not sacrifice mean early. It was right for the wrong reason, though — not because ceiling should wait, but because ceiling is not worth buying at any point.
Why this does not disprove the convexity argument
Convex payoffs and roster variance is still correct that this payout rewards variance. What this simulation shows is narrower and more useful: the variance you can buy at the draft is not the variance the payout pays for.
The variance available to a drafter is variance around a projection you believe. The player with high residual variance is usually a touchdown-dependent committee back — genuinely spikier, and genuinely worse. Paying for his spikes costs more mean than the convexity refunds.
The variance that actually wins leagues is different in kind: it is the projection being wrong, a player who is simply better than anyone thought. That is not higher variance around a correct mean, it is a mean nobody has yet. No simulation built on projections can represent it, because the projections are its ground truth. That is the honest limit of this note, and it is the reason not to read it as "never take a flyer."
Assumptions, in full
| Assumption | Value |
|---|---|
| Drafts per cell | 40 |
| Seasons per draft | 400 |
| Opponents | half draft ADP with noise, half draft projected value with noise |
| Weekly distribution | Normal; mean and variance exact in closed form per roster |
| Touchdowns | Poisson, 6 points (4 for a passing touchdown) |
| Non-touchdown variation | coefficient of variation QB 0.32, RB 0.48, WR 0.52, TE 0.5, K 0.45, DST 0.65 |
| Roster correlation | 0.06 between starters, for shared game environment |
| Availability | three-year rate per player from player_context.csv |
| Role-change mixture | 6–34% by archetype, draft capital, age and role contest |
| Byes | real 2026 byes; a player on bye scores nothing |
| Payout (supplied at release) | 1st $+425 · 2nd $+175 · 3rd $+75 · else $-75 |
| Gross prizes / contribution pool | $900 / 10 × $75 = $750 |
Read the differences, not the levels
Our simulated drafter values players on the same model the season is drawn from, which is an information edge no real room concedes. That inflates the absolute expected value badly — a real 1.01 does not win a third of its seasons. Opponents are held identical across every cell, so the **comparisons between cells are meaningful and the levels are not.**Open questions
- Weekly scores are Normal, and normal has no right skew. Skew is precisely what a convex payout pays for, so this is the assumption most likely to be wrong in the direction that would favour tilting. A skewed weekly model is the single most valuable thing left to try here.
- Nobody touches the waiver wire, so this cannot see whether the weekly priority reset changes optimal draft strategy — the build's other unmeasured question.
- Upside is residual variance around a projection. The upside people actually chase is the projection being wrong, which no projection-driven simulation can test.