I started this analysis because sometimes, I hear commentators speak about 'momentum' in a series. This made me curious about whether certain patterns of wins/losses in a series are more common than others.

I investigated win/loss patterns in best of five series (Bo5). I chose Bo5 because they are reasonably common (compared to Bo7s) and because they have enough games to show interesting patterns. I manually entered all playoff Bo5 results from 31 premier and major SC2 LANs in 2017-18, copying them from Liquipedia. I removed two matches that had draws from the dataset, leaving me with 341 Bo5 matches.

Question 1:

Does the distribution of maps dropped in a Bo5 differ from what is expected by chance?

There are three options for number of maps dropped:
no maps dropped
one map dropped
two maps dropped

These are not, however, equally common. See this quick drawing of possible win pathways in half a series to see how the percentage chances break down. In the end, there's a 25% chance that a completely randomly decided series is 3-0, and a 37.5% chance each that it's 3-1 or 3-2.

I used a chi-squared goodness of fit test to investigate how well my observed counts of each type of series matched with the random chance expectation:

Losses Observed Expected Chi-Squared Value
114 85.25
1 119 127.875
2 108 127.875
Totals 341 341 13.401

This chi-squared value is a bit large, and indicates that there's a less than half a percent chance that our distribution of 3-0s, 3-1s, and 3-2s came from a completely random one. I declare the distribution is not random. 3-0s are much more common than expected, and 3-1s and especially 3-2s are somewhat less common than expected.

These results make lots of sense if some players are better than others, which is, of course, the case.

Question 2:
Are some patterns of losses in 3-1 and 3-2 series more common than expected by chance?
Within these two tests, all options have the same probability.

Read:  How i decided that i need a break.
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3-1 series:

Pattern Observed Expected Chi-Squared Value
L-W-W-W 34 39.667
W-L-W-W 44 39.667
W-W-L-W 41 39.667
Totals 119 119 1.328

This is a small chi-squared value, and it indicates that this distribution is fairly likely to have come from one decided by random chance. With this set of data, one lost map is similarly likely to occur anywhere in a series.

3-2 series:

Pattern Observed Expected Chi-Squared Value
L-L-W-W-W 16 18
L-W-L-W-W 20 18
L-W-W-L-W 17 18
W-L-L-W-W 12 18
W-L-W-L-W 19 18
W-W-L-L-W 24 18
Totals 108 108 4.556

This is also a relatively small chi-squared value, indicating this distribution is fairly likely to have come from one decided by random chance. Any of these options is as likely to happen as any other.

Of all of my results, the last one surprised me the most, specifically the fact that even with plain eyeballing, the famed reverse sweep isn't any less common than expected. I was not expecting that.

TL;DR: There are more one-sided Bo5s than expected at random, which is probably a result of player skill disparities. However, there is no support in my data for certain patterns of wins and losses within a series being more common than others. Not even reverse sweeps are less common that expected.

Afterthought: The real truth is, though, I need to think a bit about what momentum would look like in a series. Perhaps I should try making a little model of it to see if it would actually have an impact on series patterns.