A few days ago, the San Francisco Giants swept the Detroit Tigers out of the World Series. It was the 21st World Series sweep in history, out of the 108 played since 1903. (The was no World Series in 1904 or 1994.) When the Tigers swept the Yankees, it was the 19th total LCS sweep, out of 86 total since 1969.

Obviously, not all playoff series are created equal. Some are best-of-five, like the Division Series, and the LCS between 1969 and 1984. Some are best-of-seven, like the LCS since 1985, and all but four World Series — the Series was best-of-nine in 1903 and between 1919 and 1921. (The Black Sox famously lost the World Series five games to three.) The Wild Card Game obviously isn’t a “series,” nor are the occasional 163rd games played at the end of the season.

Since the inauguration of the modern playoff format with the creation of the World Series in 1903, all playoff series have been either best-of-five, -seven, or -nine, though that was not always the case. The Detroit Wolverines beat the St. Louis Browns 10 games to five in the 1887 World Series; that was not an official championship series, but can you imagine a best-of-19 series? It’s more like a skins golf match than the playoffs.

There have been 270 playoff series played since 1903: 108 World Series, 86 League Championship Series, and 76 Division Series, counting the Division Series games played in 1981 following the strike. Naturally, the best-of-fives are the series that are most prone to see a sweep.

By my count, the World Series and ALCS sweeps were the 26th and 27th sweeps of a best-of-seven series, out of the 158 total best-of-seven series ever played. There were no Division Series sweeps in 2011 or 2012, but in 2010, the Phillies swept the Reds and the Yankees swept the Twins, the 40th and 41st sweeps of a best-of-five series out of 108 best-of-five series ever played. Out of all of the best-of-sevens, 17% have been sweeps, while 38% of best-of-fives have been sweeps. Requiring just one more win cuts the chance of a sweep in half.

The LCS expanded from best-of-five to its current best-of-seven format in 1985, and you can see graphically just how sharply the incidence of sweeps dropped:

By contrast, the World Series and LCS have had the same format for almost all of their lives, and you can see that sweep incidence is roughly even over the years:

None of the four official best-of-nine World Series were sweeps, and it’s easy to understand why. Mathematically, sweeps should become exponentially more rare as the number of games you have to win increases. If two teams are perfectly evenly matched, then you would expect that there would only be a 12.5% chance that one would sweep the other in three games, just a 6.25% chance that one would sweep the other in four games, and a 3.1% chance that there would be a sweep in five straight.

Even if they’re unevenly matched, you would expect sweeps to be relatively rare. If one team were 70% likely to beat the other in a single game — if, that is, the probability of one team beating the other is 70% — you would only expect a three-game sweep 34% of the time, and a four-game sweep 24% of the time. That’s a large drop, but not as drastic as the 38% to 17% drop that we observed in the data. What accounts for this?

**UPDATE:** Or it could be that my math is wrong, as several commenters have pointed out. The chance is essentially doubled. If the teams are equally matched, there’s a 12.5% chance that one of the teams will sweep the other in three games, but that chance applies to both, so there’s a 25% chance that a sweep will occur.

Maybe it’s an artifact of small sample size. After all, we only have 270 playoff series to work with. Or perhaps there’s a true all-hands-on-deck effect: maybe managers’ in-series strategy actually changes their teams’ likelihood of winning a game, so that the team that was 70% likely to lose the first game (regardless of matchups) is only 60% likely to lose the fourth game when down 3-0, because they were likely to conserve their effort in the first game but have no incentive to conserve energy in the fourth game.

Whatever the reason, the data are clear: it is strikingly easier to get swept in the Division Series than in the League Championship Series or World Series. Losing the first game of the LCS hurts, but it isn’t an existential threat. But losing the first game of the Division puts you on the ropes.

Unless, of course, you’re the 2012 Giants, who were down 2-0 in the Division Series and then swept the World Series. It worked for them. But it is likely that we will go a long time until we see that again.

**POSTSCRIPT**: The commenter B N, who commented below, sent along the following table:

Wins To Sweep | Frequency given p=0.5 | Actual Frequency | p given Actual |

3 | 25% | 38% | 0.708 |

4 | 12.5 | 17% | 0.622 |