Let's say we have two baseball teams in a division, we're about halfway through the season, and we want to see how likely each team is to win the division at the end of the season. This is good to know not only for fans, but for front offices as they decide whether it's worth it to be a buyer at the trade deadline (i.e. try to make trades to make their team better for this year at the cost of future years), or whether they're so unlikely to make the playoffs that it would be better to be a seller and trade players that are good now for prospects that will hopefully be good in the future.
↪ Click Simulate Division below to calculate the probabilities.
Great! So, being 2 games back, the Blue Jays have around a 38% chance of winning the division.
But, now let's add a few more teams to the division.
↪ Click Simulate Division below to calculate the probabilities.
Even though the Blue Jays are still the same number of games back, and the new teams are further behind, this still reduces them to around a 21% chance to win the division!
This comes up a lot with wild card races, where the top 3 teams that aren't division leaders also qualify for the playoffs. Sometimes fans will think "hey, my team is only two games back of a wild card spot, that's hardly anything!", like the Pirates in this example:
↪ Click Simulate Division below to calculate the probabilities.
And an over 50% chance is indeed pretty good! But let's look at the full standings (this is roughly based on the NL wild card standings as of July 1, 2024):
↪ Click Simulate Division below to calculate the probabilities.
The actual chance is less than half of that!
Here you can play around with your own scenarios! See the Details section below for more information about the assumptions being made.
First of all, if you actually want to see playoffs odds for baseball, you should just look at FanGraphs or Baseball Reference.
The calculations here assume there are exactly 80 games left in the season for all teams (which is why no half-game increments are allowed), every team has a 50% chance of winning each game, and it simulates this 5000 times. It also doesn't assume any of the teams are playing each other, although I don't think that would make a difference in the percentages.
These calculation also handle ties in the least sophisticated way possible by giving "partial credit", so if two teams finish with the highest total wins they each get credit for half of a scenario for winning the division. If more than one team advances it's handled in a similar way.
Here's the GitHub repo for this project, and here's a writeup of how I wrote this and problems I ran into along the way.