Run line simulator
Final margin, home team view
Alternate run lines
| Line | Home covers | Fair price |
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Model inputs: each team's 2026 runs scored and allowed per game. Simplified, see the method below.
Pick the away team in the first menu and the home team in the second, then press the button. The tool plays out 20,000 games between those two teams and reports four numbers: how often the home team wins, how often it wins by two or more (the -1.5 cover), how often the away team stays within one run or wins (the +1.5 cover), and how often the game ends by exactly one run. The line under the results shows the expected runs the model gave each side.
Below the four numbers, the bar chart shows how the simulated games ended from the home side: losses on the left, wins on the right, and the gold bars are the margins that cover -1.5. The small table turns the same games into alternate lines at -2.5, -1.5, +1.5 and +2.5, each with the fair American price that matches its cover rate. Type the prices a book shows for -1.5 and +1.5 into the last row and the tool compares them with the simulation: how many points above or below the break-even rate each side sits, and its average value per $100. The model is simple, so treat a big edge as a reason to look closer, not as a bet.
To look at the run line from the other team’s side, swap the two menus. The model has no home-field term, so moving a team into the home slot changes nothing about its chances, and the -1.5 box then describes that team. It is the quickest way to check a road favorite.
How the model works
We kept the model small on purpose, so you can check every step by hand.
Step 1: expected runs
Each team gets an expected run total for the game. The formula is the team’s runs scored per game, multiplied by the opponent’s runs allowed per game, divided by the league average runs per team per game. Both inputs come from each club’s current-season totals in our MLB luck table, which is updated from the official MLB Stats API.
A worked example with round numbers: a team scoring 5.0 runs a game faces an opponent allowing 4.2, in a league where the average team scores 4.5. Expected runs are 5.0 x 4.2 / 4.5 = 4.67. The other side scores 4.3 a game against a staff allowing 4.6: 4.3 x 4.6 / 4.5 = 4.40. The division by the league average is what keeps a good offense against a good pitching staff from being counted twice.
Step 2: run totals that look like baseball
The simplest way to turn an expected total into actual runs is a Poisson distribution. It is also wrong for baseball. Real run totals are more spread out. Teams get shut out more often than a Poisson predicts, and they also put up nine or ten more often, because runs come in clusters: a walk, a double and a homer in one inning.
So the simulator uses a negative binomial, built as a gamma-Poisson mix. In each simulated game the team’s scoring rate is first drawn from a gamma distribution around its expected total, and then the runs are drawn from a Poisson at that rate. The effect is that some simulated nights the lineup is hot, some nights it is flat, just like real games. With our shape setting, a team expected to score 4.5 runs gets a variance of about 7.9 instead of the Poisson’s 4.5.
Step 3: ties and extra innings
Baseball has no ties, but independent run draws produce them about one time in nine. The model sends each tie to extra innings and hands the win to either team with a 50/50 coin flip, by exactly one run. That is a fair approximation of how extra-inning games end: most are decided by a single run.
Step 4: count 20,000 games
After 20,000 games, each result box is just a share. If the home side won by two or more in 7,000 of them, the -1.5 box reads 35.0%. With that many games the random noise is small, around half a percentage point either way, so pressing the button twice will give slightly different numbers. That is normal.
For a reference point, two exactly league-average teams give roughly 50% home wins, 34% home covers at -1.5, 66% away covers at +1.5, and 32% one-run games. Now you know what “even” looks like.
What the model leaves out
This is a baseline, not a projection, and it misses things that matter a lot on a given night.
Starting pitchers. The inputs are season-long team numbers, so a team’s ace and its fifth starter look the same. Check the probable pitchers board and adjust by hand when the matchup is lopsided.
Bullpens. A pen that threw 12 innings over the last two days is not the pen in the season averages.
Park and weather. A game at a high-scoring park, or with the wind blowing out, has more runs, which raises the cover rate for the favorite. The ballpark run environment table shows how much each park moves scoring.
Home-field advantage. The model treats both teams the same apart from their run numbers. Real home teams win a little more often than that.
The skipped bottom of the ninth. This one matters most for the run line. When the home team leads after the top of the ninth, the game ends. The home side never gets that last half inning to add an insurance run, and when it wins in its final at-bat, the game stops the moment it takes the lead, usually by one. Both effects make -1.5 harder for a home favorite than for a road favorite of the same strength. The simulator plays every game as if both teams bat equally, so it overstates the home -1.5 rate. Mentally shave a few points off that box when you are looking at a home favorite.
One more honest caveat: season run totals in April are small samples. Three weeks in, a single 15-run blowout can inflate a team’s runs per game by half a run, and the simulator will happily believe it. Early in the season, lean on the result less. A team’s record can also drift away from its run profile, and that drift is the whole point of the luck table.
Comparing the output with a run line price
The last step is the one that turns a number into a decision. Take the price posted on the MLB run line, convert it to a break-even rate with the odds calculators, and put it next to the simulator’s cover rate after your adjustments.
Say the home favorite is +130 on -1.5. That price needs 43.5%. The simulator shows 45% for the home cover. It sounds like a small edge, but remember the missing bottom of the ninth and the home-field point, which pull in opposite directions, and then look at the starters. If the home team is sending out its fourth starter, 45% probably becomes 41%, and the bet is gone.
Now the other side. The away team is -160 at +1.5, which needs 61.5%. If the away +1.5 box shows 64%, you have something worth a closer look. If it shows 58%, you do not.
The model will not beat the market by itself. The market already knows the starters, the pen and the weather. Where it helps is in keeping you honest. It stops you from assuming a -200 favorite covers -1.5 most of the time, because most of the time it does not. For the lines themselves, our baseball betting lines guide explains how the moneyline and run line relate, and the NRFI numbers cover how often games start scoreless if the first inning is your angle.
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