At the start of every MLB season, some team will rattle off a bunch of wins. In 2016, the Orioles went 7-0 to start and in 2015, the Royals went 7-0. I thought 7 wins in a row was pretty rare so I went through mlb.com’s standings history and found the longest winning streak to start the season for each year. The data goes back to 1901 which is impressive, but I just went back to 1974. Before 2015, a team had won at least 7 in a row to start in 9/41 seasons, or 22.0%. The odds of that happening two years in a row were 4.8%. So, it was pretty rare that a team went 7-0 two years in a row.
I calculated the odds of a team winning a certain number of games in a row if there’s a 50% chance they win each game. There are 4 parts to the equation. The odds of one team winning n games in a row would be
The odds of one team not winning n games in a row is
The odds that no team out of the 32 wins n games in a row is
Finally, the odds that any team of the 32 does win n games in a row is
The theoretical values are never more than 10% off from the actual. The correlation was 99.0%.
I made a second theoretical attempt by modifying the winning percentage from a constant 50% to a linear model. In other words, a team would have a certain chance to win the first game and that chance would go up as they kept winning. The best fit I could get was a initial winning chance of 43% and an increase of 3% per game. This had a correlation of 99.7%. It was off by 6% at most.
If you start out at 50%, the closest match to the actual data requires keeping the increase in winning percentage at 0%. This is the same thing as the first projection.
The most common wins in a row for a year is 4 at about 25%. There have never been less than 3 wins or more than 10 wins to start a season.
