How Common Are Playoff Sweeps?

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


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Alex is a writer for FanGraphs and The Hardball Times, and is a product manager for The Washington Post. Follow him on Twitter @alexremington.


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TKDC
Guest
TKDC
3 years 10 months ago

I think you are mixing up best-of-five and best-of-nine.

TKDC
Guest
TKDC
3 years 10 months ago

To clarify, if a team has to win 3 games, it is a best-of-five, if they have to win 4, it is a best-of-seven, and so on.

John Choiniere
Member
3 years 10 months ago

“None of the four official best-of-five World Series were sweeps”

I think you mean the best-of-nine ones?

TKDC
Guest
TKDC
3 years 10 months ago

And in fact there is a 25% chance that one of two evenly matched teams would sweep a five game series. One team has to win the first game. Whichever wins has a 25% chance of winning the next two.

Craig
Guest
Craig
3 years 10 months ago

That should be 12.5% chance of sweeping a 5-games series, no?
0.5 * 0.5 * 0.5

Justin
Guest
Justin
3 years 10 months ago

That’s for one specific team. Team A or Team B can sweep, so you’d add the chances of Team A sweeping to the chances of Team B sweeping to get the overall chances of a sweep in the series.

Justin
Guest
Justin
3 years 10 months ago

Between this and the “games over .500” incident, Alex has shown a curious lack of understanding of commonly used baseball terms.

dewbeckc
Member
dewbeckc
3 years 10 months ago

Not just baseball terms, but terms used in all major professional sports, or any child’s game like rock, paper, scissors; it’s mind boggling

Kumar
Guest
Kumar
3 years 10 months ago

Best of 5 and Best of 7. Jeez.

David G
Guest
David G
3 years 10 months ago

I want a breakdown of all the ties in the best of 4 series…

Mookie
Guest
Mookie
3 years 10 months ago

Would two wins and a draw in a best of four series constitute a sweep?

daniel
Guest
daniel
3 years 10 months ago

One advantage of the 1887 best of 19 series was that there were less discussions about how lucky the winning team was.

Spa City
Member
Member
Spa City
3 years 10 months ago

Fewer discussions

Marver
Guest
Marver
3 years 10 months ago

“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.”
No, we’d expect a sweep 25% of the time. All that has to happen is that the team that wins the first game wins two in a row; the odds of that are .5 * .5 = .25.

“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.”
No, we’d expect a three-game sweep .7^3 + .3^3 of the time, which is 37% of the time. And we’d expect a four-game sweep ~25% of the time. The reason for the difference is that the poor team can still sweep the good team, albeit at it much less likely clip.

Additionally, more sweep in the LDS series is a pretty easy phenomenon to explain — the worst playoff teams are still around, and they’re slotted against a better team. When the LCS comes around, you’ve pruned the worst teams (probably) and therefore have a more even matchup.

B N
Guest
B N
3 years 10 months ago

A 70% win probability is still REALLY high, however. Think about teams in general that reach the playoffs: most of them win about 70% or less of their games against ALL competition and they’re now facing a truncated distribution that won at least 50% of their games (realistically, more like 60%). So they’re facing tougher competition… and getting better results than they did during the regular season? Either there is far less variability in a short series (possible) or the postseason has some additional weirdness that tends toward one-sided series.

Newcomer
Member
Newcomer
3 years 10 months ago

Home field advantage also mucks with the probabilities, aiding one team’s chances for some of the games and switching sides for the other games. That should make a sweep slightly less likely than it otherwise would be.

ZenMadman
Guest
3 years 10 months ago

1951

The World says
Guest
The World says
3 years 10 months ago

This was a very well thought out article.

tyke
Guest
tyke
3 years 10 months ago

is it just me or is this article highly unreadable due to the strikethroughs?

B N
Guest
B N
3 years 10 months ago

And the amendments… and the writing. Pretty much for all reasons. Really, the meat of this examination is based on comparing two things:
1. An estimated probability of teams of X1 and X2 strength having a sweep in their series, for best of 5 and best of 7 series.
2. The actual observed probability of sweeps in these series.

This article could be condensed into a single table with those figures, plus a bit of exposition. Instead, it has a ton of content, onto which there are a ton of corrections. I try to generally be positive, but I kind of wonder if this warrants a revise and resubmit.

Which, if there is a follow up, I’d say that the interesting thing would be this: assuming some static strength of each team (X1 and X2) respectively, that results in a probability p of team 1 winning each game, so p = F(X1, X2). What level of disparity between teams would result in the frequency f of sweeps that were actually observed? If we have p be the probability of team 1 winning a game and N being the number of games to win the series, we have:

f = p^N + (1-p)^N

So for a best of 7 series, f=17% of series were sweeps. For a best of of 5, f=38%. These are our observed values. Solving for these roots, we get p=0.622 for the best of 7 and p = 0.708 for the best of 5. Obviously, it doesn’t matter which team is team 1, so 1-p would provide the same frequency.

Or, to summarize:

Wins To Sweep | Actual Freq | p given Actual | F given p=0.5
—————————————————
3 | 38% | 0.708 | 25%
4 | 17% | 0.622 | 12.5%

Obviously, the probability to win each game is not static (nor are team strengths static across games either, due to matchups, home field advantage, etc). However, this gives a decent view of the fact that we’re seeing more sweeps than expected, by a pretty significant margin (as you wouldn’t expect one team in the division series to win 70% of its games against another division winner. As such, it might be more interesting to plot all combinations of series for the p=0.5 case and for the actual cases, just to see how the overall frequencies differ.

B N
Guest
B N
3 years 10 months ago

Also, can I just say “My kingdom for a verbatim mode.” It’s impossible to format a table in these comment boxes.

B N
Guest
B N
3 years 10 months ago

Sent along an HTML version. And definitely, the actual data is the more interesting thing. Anyone with half a brain can tell that a coin-flip style approach to looking at this is about as elegant as playing golf with a sledgehammer. With that said, it’s at least curious to see what kind of disparity we’d need under those assumptions.

Nivra
Guest
Nivra
3 years 10 months ago

The actual observed data got buried in a paragraph full of strike throughs. I thought you never posted it anywhere. After I saw them mentioned in the comments, I had to go back up and re-read.
Blech. And you never even compared them with the generic 50% probability, never saying the observed is higher or lower than expected, and never postulated why that would be.

O's Fan
Guest
O's Fan
3 years 10 months ago

This seems like too much analysis for a very simple question.

In a best-of-7 series, there are 4 possible outcomes: 4-0, 4-1, 4-2, 4-3. If the outcome is random, we’d expect a sweep to happen 25% of the time. 27/158 = 17.1%, which is quite a bit less, which confirms a reasonable expectation that a series between two good teams should be more even than not.

In a best-of-5 series, there 3 possible outcomes: 3-0, 3-1, 3-2. Random outcomes means a sweep 33% of the time. 41/108 is 38.0%, so slightly more than random, which suggests that perhaps the practice of matching the best division winner with a (presumably) worse wild card team leads to more imbalanced series.

Sample sizes aren’t enormous for any of these. Best-of-7 results pass a 5% significance level, but not by a ton, and best-of-5 results don’t come close to passing.

seth
Guest
seth
3 years 10 months ago

If it was a bigger market team than the giants ( mainly the yanks or red sox) or some other storied franchise, this would be considered one of the greatest and improbable playoff runs EVER. WHat this group acclomplished deserves to be talked about and they deserve a lot of credit. You wont see it happen too many more times if ever. Hats off to the the 2012 GIANTS on a monumental RUN THROUGH THE PLAYOFFS.

seth
Guest
seth
3 years 10 months ago

IF this was the yankees all the networks would be slobbering all over the team anointing heroes left and right. But because it was the giants, it is just another lucky WS run that was improbable and ended up happening. This team’s accomplishments from the dodgers to melky to lincecum to losing brian wilson to winning the division to the playoff run are so surreal that you still don’t believe what has just happened if you follow the team regularly. And at the same time it is being pushed aside to make way for football because of a FOX broadcast that did not have good ratings. This WORLD CHAMPIONSHIP RUN deserves to be talked about forever with playoff legends being written in the process.

Mark
Guest
Mark
3 years 10 months ago

Or this monumental run by the White Sox in 2005. A team just sweeps through Boston, loses one game in the LCS and sweeps the World Series. http://mlb.mlb.com/mlb/schedule/ps.jsp?y=05
4 complete game wins in a row.
ALDS – 27.0 IP, 3.00 ERA, 1.22 WHIP, 14 Ks, 8 BB, 24 Hits. 3-0
ALCS – 45.0 IP, 2.20 ERA, .689 WHIP, 22 Ks, 4 BB, 27 Hits. 4-1
WS – 41.0 IP, 2.63 ERA, 1.12 WHIP, 36 Ks, 17 BB, 29 Hits. 4-0

“Small market” teams get no love. Yankees lost in the divisional series so it wasn’t important anymore.

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