Research notes

Why we project Josh Allen for 8 rushing touchdowns, not 14.

July 16, 2026 · 6 min read

Josh Allen ran for 12 touchdowns in 2024 and 14 in 2025. Open our board and you’ll find him projected for about 8. That number looks timid, and it is the single line most likely to make a Bills fan close the tab. This note shows the exact math that produces it, the evidence that touchdown rates deserve the least trust of any stat in football, and the three-year receipts showing that the group of players we shrink comes in almost exactly where the shrink says.

Every rate is a negotiation between evidence and average

Our model splits every player into two questions: how much work will he get (volume), and what will each touch produce (efficiency). Volume comes from his own role history, and we take it close to face value; Allen’s carries are projected off Allen’s carries. Efficiency is different. For each rate, touchdowns per carry here, a player’s history and the position average negotiate, and the weight his own history gets is set by how much evidence it contains. The formula is old-school empirical Bayes: his touchdowns plus k times the average rate, divided by his carries plus k. That k is fitted by backtest, per rate, and for touchdown rates it lands at 200. In plain terms: your touchdown rate needs 200 carries of evidence before we trust it as much as the position average.

Even a quarterback who runs as much as Allen only banks about 110 recency-weighted carries across three seasons. So he keeps 35% of his own spectacular 12.5% touchdown rate, the position average supplies the rest, and the negotiated result is 7.5% of his projected carries: about 8 touchdowns.

Note the third row, because it proves this is not a pessimism dial. Lamar Jackson’s recent touchdown rate is unusually LOW for his role, one score every 33 carries, and the same formula pulls him UP toward the average. Shrinkage is symmetric. It moves outliers toward the middle from both directions, and workhorses like Derrick Henry, with 300-plus carries of evidence, mostly keep their own number.

Why touchdown rates earn the least trust

The k values are not opinions; they are fitted to whatever made four seasons of backtests most accurate, and the fit consistently assigns touchdown rates the heaviest shrink. Our stickiness study found a receiver’s touchdown rate explains under 2% of his next season’s, closer to a coin flip than a skill, and our regression file showed that expected touchdowns predict next season better than the touchdowns a player actually scored. Touchdowns are a handful of binary events sitting on top of hundreds of touches. A stat that noisy is exactly where a projection should lean hardest on the average, and exactly where the eye test overpays.

The receipts: timid on one name, right on the group

Here is the fair test of whether 8 is a coward’s number. You cannot judge a projection by comparing it to whoever ended up leading the league, because the league leader is partly whoever ran hottest; someone always beats every projection. The honest comparison is matched: take the players the model itself ranked highest, then check what those same players went on to do.

Across 2023 to 2025, the touchdown totals we projected for our own top picks came in within a few percent of what those players actually scored. Individual seasons scatter wildly around that, and Allen himself has beaten his shrunk line two years running. But for every Allen who repeats, the cohort contains a 2025 Jalen Hurts, whose rushing touchdowns fell from 14 to 8 in a single season as his goal-line carries dried up. The model cannot tell you in advance which star keeps the outlier rate, and neither, the data says, can anyone else. What it can do is price the group correctly, and it does.

We tested the obvious improvement, and it was a wash

The strongest objection goes: Allen’s touchdowns are not luck, they are a goal-line ROLE, so regress him toward what his red-zone usage deserves, not toward the average quarterback. We agree enough that we built it. In that version, each player’s touchdown rate shrinks toward his own situation-based expected-touchdown rate (which teams hand the ball to him inside the five, weighted by how often those chances score) instead of the flat position mean. Run over the full 2022 to 2025 backtest, it moved overall rank accuracy from .7586 to .7588 and points error from 38.72 to 38.66, with the only visible gain a slightly smaller quarterback undercall. That is a rounding error, not an edge, so the simple prior ships. The idea stays in our ablation records and gets re-tested as more seasons of red-zone data accumulate.

The honest cost, stated plainly: if any player in football can hold a 12% rushing touchdown rate through sheer goal-line gravity, it is Josh Allen, and if he does it again our line misses low by six scores. We take that miss with open eyes, because a board that chases every outlier rate buys last year’s touchdowns at full price, and the three tables above say full price is the wrong price.

Fine print: rates use 2023 to 2025 weighted 20/30/50 toward recency; position averages come from the same window. k values are fitted per rate by backtest (touchdown rates per touch: k=200 for rushing and receiving, k=400 for passing). The matched top-N test composes each season 2023 to 2025 with the current model and compares its top-12 QBs / top-24 RBs and WRs / top-12 TEs per stat against those same players’ realized totals. League-level 2026 aggregates sit within 2% of the 2024-25 averages across every major category. Numbers reproduce from research_td_shrinkage.py and ablate_xtd_prior.py in the model repo.