An average MLB team scores about 4.5 runs a game. But very few games end with a team scoring exactly four or five, and the shape of the distribution matters as much as its average when you want to know how likely a shutout, a one-run game or a slugfest is.
What real scoring looks like
From 2023 to 2026 a team was shut out 6.5% of the time, scored one run 10.7%, two runs 13.2%, three runs 14.0% (the single most common outcome), four runs 12.5%, and ten or more about 7.5%. The distribution has a long right tail: big innings happen, and when they do they add several runs at once.
Why a Poisson curve undershoots the tails
A Poisson distribution assumes runs arrive independently at a steady rate, which forces the variance to equal the mean. Real baseball scoring is clumpier than that: runs come in bunches within innings, and some games are simply high-scoring environments. The variance of a team's runs is roughly twice its mean. BullpenEdge therefore uses a negative binomial distribution, which adds one parameter for that extra spread; it is re-estimated from the training seasons each time the model is fit (the current value corresponds to about four 'runs of clumpiness').
The odd-number quirk
Look at game totals and something strange appears: 7 total runs happened in 11.2% of games but 8 in only 7.5%; 5 runs in 9.8% but 6 in 7.2%. Odd totals are more common because the home team does not bat in the bottom of the ninth when it is ahead, and a walk-off usually ends the game the moment the winning run scores — both cut off scoring in ways that favour certain final scores. The model's win probabilities and one-run chances come from the full combined distribution, so these structural features are handled approximately; the calibration check is how we make sure the approximation does not bias the results.
The same distribution gives the chance of a one-run game; see MLB win margins explained.