A first-5-inning run line model that originates its own number from the ground up. Every plate appearance against the starter is priced from the K and hits models, then twenty-five thousand simulations of innings 1 through 5 build a run distribution and a fair ±0.5 run line, which we compare to the market.
Three ways our first-five number differs from the market's, built one plate appearance at a time.
Books set a line off the starter's ERA and the lineup as a whole. We price every batter-versus-pitcher matchup instead, factoring in times through the order, pitch mix, and platoon splits. That is a level of detail books don't build lines around.
Through five innings, plenty of games are tied. The +0.5 run line wins on a tie; the other side loses it. We price that in, and in testing the value keeps landing on the +0.5 underdog.
The same K model and hits model that already beat the prop market feed a single Monte Carlo engine. Their per-PA probabilities are the inputs; the F5 model turns that proven signal into a run line. Any sub-model retrain flows straight through.
From a single plate appearance to a fair ±0.5 first-5 line, across five traceable stages.
For each batter facing the starter, five models combine into one outcome vector: the K model gives P(strikeout), the hits model gives P(hit), and empirical-Bayes rates supply walks, hit-by-pitch, the hit-type split, and the ball-in-play out type.
The result is a full distribution over every way a plate appearance can end, strikeout, walk, single through home run, or out, normalized to sum to one before anything is simulated.
A hitter does better the second and third time he sees a starter. Every probability is keyed by times-through-order, and the simulator tracks the batting order and each batter's TTO across inning boundaries, not just within an inning.
That is what makes a five-inning model different from five copies of a one-inning model: the leadoff hitter in the fifth is on his third look, and the math reflects it.
Per-PA probabilities are not independent within a game. A starter's stuff that night, and the park-and-weather offensive environment, push every plate appearance in the same direction.
So each simulation draws one strikeout shock and one hit shock and applies it to every plate appearance in that game. That keeps the range of team runs realistic instead of letting it collapse toward the average.
Each simulation plays five half-innings per team through a base-out state machine: outcomes are drawn from each batter's vector, runners advance on a calibrated advancement model, and runs are tallied for innings one through five.
Across twenty-five thousand games this produces a full run distribution for each side, and from the margin distribution, the probability that the home team covers any run line.
The margin distribution gives the probability each side covers the ±0.5 first-5 run line. That fair price is de-vigged against the reference book, the edge is measured, and the bet is then shopped to the best available number across books.
The run line is the official, staked play. Moneyline, totals, and team totals are priced from the same simulation and tracked, but only the run line carries the bankroll, since moneyline and run line are two views of the same outcome.
We ran the model over every game from 2023 to 2025, using only what was known before each game. The actual first-five result was only used to grade it, never as an input.
Every run-line play comes with the full simulation. Projected first-five runs for each side, the cover probability, the fair line, the edge after de-vig, and the best price across books. You can see how we got there before you bet.
Get First 5Daily first-5 run-line plays with the full pitch-level simulation behind each one, delivered to Discord.
First-5 ±0.5 run-line plays at the +5% edge threshold are the staked picks, with the best price across books shopped for each one. Moneyline and totals are tracked alongside but not bet.
The simulation is rebuilt once lineups and confirmed starters are posted, so the run line reflects the actual nine hitters and the right pitcher, not a season-long approximation.
Each play ships with projected first-five runs per side, the cover probability, the fair line, the edge versus the book, and the price we would shop it at.
Plays land in the subscriber Discord with opening lines locked, so every pick is graded against where the market closed, the cleanest measure of a real edge.
First-5 run-line plays through the season. Available on its own or as part of the All Access bundle, alongside every other Whizard model.