The Ledger Model: Pythagorean Log5 On Four Moneylines
Four moneylines are on the board this afternoon and every one of them is a favorite. Three of the four are priced above minus 129 and two are above minus 155. The question a model exists to answer is not which team is better, because the prices already say that. It is whether the number being charged is larger or smaller than the gap between the two clubs actually justifies.
The Ledger Model answers that with three numbers per team and nothing else: runs scored, runs allowed and games played. No starting pitcher, no lineup, no weather, no park. It is deliberately blind to everything that happens today, because the point is to produce a baseline that cannot be talked into anything, and then to say out loud where that baseline is going to be wrong.
The Three Steps
Step one, the ledger. Convert each club's season runs scored and runs allowed into a win expectation with the Pythagorean exponent 1.83. Milwaukee has scored 674 and allowed 496 in 135 games, which is a .637 expectation. The Athletics have scored 588 and allowed 774, which is .377. That is the whole team rating.
Step two, log5. Combine the two ratings into a head to head probability with the log5 formula, which is the standard way of asking what happens when a .637 club plays a .458 club. It has been in baseball since Bill James published it and it needs no calibration.
Step three, the building. Multiply the odds ratio by the season's actual home field edge. Across all 2,025 completed 2026 regular season games the home club has won 1,068, which is 52.74 percent. That is the entire home adjustment. No park factors, no travel, no rest.
Does It Work
The model was run over every 2026 game in which both clubs had already completed 40 games, using only results from before each game. That is 1,418 games. It picked the straight up winner 774 times.
| Method | Straight up record | Hit rate |
|---|---|---|
| The Ledger Model | 774 of 1,418 | 54.58% |
| Better season run differential | 763 of 1,418 | 53.81% |
| Better run differential over the last 15 | 758 of 1,418 | 53.46% |
| Home team, always | 1,068 of 2,025 | 52.74% |
Fifty four point six percent is not a large number and it is not supposed to be. Baseball is the least predictable of the major sports and a three run favorite does not exist. What matters is that a model built from three inputs per club beats the raw run differential it is built from by three quarters of a point, and beats home field by nearly two. That is the ceiling on how much a ratings model can know before it starts looking at who is pitching.
Tonight's Four Moneylines, Priced
Every fair price below comes out of the three steps above using season totals through August 28. The taken price is what the card actually paid.
| Game | Model win probability | Model fair price | Taken price | Break even needed | Edge |
|---|---|---|---|---|---|
| Brewers vs Rangers | 69.8% | -231 | -160 | 61.54% | Plus 8.3 points |
| Orioles at Athletics | 58.6% | -142 | -129 | 56.33% | Plus 2.3 points |
| Guardians vs Royals | 57.9% | -137 | -157 | 61.09% | Minus 3.2 points |
| Mets vs Astros | 51.5% | -106 | -138 | 57.98% | Minus 6.5 points |
Two of the four clear their price and two do not. A model that agreed with every ticket on a card would be a model that had been fitted to the card, so the disagreements are the useful part of this table.
American Family Field, where a .637 Pythagorean club hosts a .458 one. The Ledger Model makes Milwaukee minus 231 and the market charged minus 160. Photo: DiscoA340, Wikimedia Commons, CC BY-SA 4.0.
Milwaukee Is The Only Real Gap
The Brewers have outscored their opponents by 178 runs in 135 games. No other club on this card is within 90 runs of that. Texas is at minus 52. Log5 turns a .637 against a .458 into 67.4 percent before the building is considered and 69.8 percent after, and that is a fair price of minus 231 against a taken price of minus 160.
An 8.3 point gap is the largest the model has produced on any single game this week, and it is worth saying why the market is not stupid for pricing it lower. Cal Quantrill starts for Texas carrying a 2.90 ERA and a 1.14 WHIP across ten starts, against Shane Drohan's 3.84 and 1.29. A pitcher matchup that favors the underdog is exactly the information the Ledger Model refuses to look at, and the market is looking straight at it. The honest reading is that most of the 8.3 points is a real edge and some of it is the model's blindness.
Where The Model Is Simply Wrong
The Mets line is the clearest example of a ratings model failing on purpose. New York has scored 553 and allowed 607, which produces a .457 expectation, barely different from Houston's .470. The model calls the game a coin flip and prices the Mets at minus 106 against a taken price of minus 138.
Houston is opening this game with Bennett Sousa, a reliever with zero starts, an 18.2 inning sample, a 6.27 ERA and a .312 opponent average. New York starts Nolan McLean, who holds opponents to .208 with a 3.21 ERA across 148.2 innings. That is the single largest starting pitcher gap on the board and the Ledger Model cannot see one inch of it. When a model is blind to the biggest input in a game, the correct thing to do is not to trust the model, it is to say which input it is blind to and let the reader weigh it.
The Guardians Line Is A Genuine Disagreement
Cleveland has scored 543 and allowed 550 in 135 games. That is a .494 Pythagorean club, which is to say a .500 team, and it happens to be a .500 team that is 8-2 in its last ten. Kansas City has scored 581 and allowed 659, a .443 club that is 9-1 in its last ten.
The model puts Cleveland at 57.9 percent at home and prices the game at minus 137. The card paid minus 157, which needs 61.09 percent. That is a 3.2 point gap in the wrong direction and, unlike the Mets line, there is no enormous hidden pitcher edge to explain it away. Foster Griffin carries a 3.19 ERA and Daniel Lynch IV a 2.93 across a four start sample. Both starters are good. The model's verdict is that Cleveland's season ledger does not support laying a number that steep, and the counterargument is that the ledger includes four months of a Cleveland team that no longer exists at the same run prevention rate.
Why This Model Does Not Price Totals
Two of tonight's six tickets are game totals and the Ledger Model has nothing to say about either one. Runs scored and runs allowed across a season describe how a club wins games, not how many runs a specific afternoon produces. A total needs park run environment, both starters, both bullpens and the umpire, and a season ledger contains none of it in usable form. A model that produced a number anyway would be making one up.
What The Model Is Not
- No starters. Every rating treats a club as its season average, which is wrong on any day the ace or the bullpen game is scheduled. That is the single largest omission and it is deliberate, because pitcher adjustments are where a simple model turns into a fitted one.
- No injuries or roster changes. A club that traded for two bats in July carries three months of its old lineup inside its ledger.
- No strength of schedule. A run differential built against the softest schedule in the league scores identically to one built against the hardest.
- No market feedback. The fair prices above have no vig removed from the market side, so a comparison against a posted number slightly flatters the model on every line.
- One season of validation. A 54.58 percent hit rate on 1,418 games carries a standard error near 1.3 points, so the true rate could sit anywhere from about 52 to 57.
The Card The Model Would Build
On its own numbers, the Ledger Model backs Milwaukee at minus 160 with conviction, takes Baltimore at minus 129 as a thin play, passes on Cleveland at minus 157 and passes hard on the Mets at minus 138. That is two of four, which is roughly what an honest ratings model should produce against a market that prices baseball well. The two it passes on are not predictions that those teams lose. They are statements that the price has already taken the profit out.
Data note: Runs scored, runs allowed and results come from the MLB Stats API for the 2026 regular season through August 28, 2026. The backtest used only games in which both clubs had completed 40 or more games, and every rating was computed from games finishing strictly before the game being predicted. Pythagorean exponent 1.83. Home field taken as the season's realized 52.74 percent and applied as an odds ratio multiplier. Fair prices are rounded to the nearest whole American number.