The Playoffs are a Coin Toss

The improbable success of the St. Louis Cardinals this October has many people talking about the inherent randomness of the playoffs. We examined the outcomes of every playoff series since the start of the modern world series in 1903. We tabulated the number of times that the "better" team won a playoff series, with "better" being defined as the team with the superior winning percentage in the regular season. The proportion of series won by the better team are given below:

All Series since 1903: Proportion = 0.529
Only 5 Game Series: Proportion = 0.512
Only 7 Game Series: Proportion = 0.533

We see that all the proportions are pretty close to 0.5, which suggests that a playoff series isn't much different from a coin toss. In fact, none of these proportions are significantly different from a null hypothesis of p = 0.5. Not surprisingly, we also see that 5-game series are even closer to being a coin toss than 7-game series.

We can also look at the trend over time by calculating the proportion of the better team winning as a 20-year moving average around each year. The plot of this moving average proportion is given in the plot below:

We see that the proportion of times that the better team wins seems to be generally decreasing over time, though there are have been some other interesting dips in the past. Finally, we can look at some of the greatest playoff upsets, in terms of the winning team having a much lower regular season winning percentage compared to the losing team. A table of the top 5 greatest upsets is given below:

Year	Round	Winner	%-age	Loser	%-age
1906	WS	Chicago White Sox	0.616	Chicago Cubs	0.763
2001	ALCS	New York Yankees	0.594	Seattle Mariners	0.716
1973	NLCS	New York Mets	0.509	Cincinnati Reds	0.611
1954	WS	New York Giants	0.630	Cleveland Indians	0.721
2006	NLCS	St. Louis Cardinals	0.516	New York Mets	0.599

A special thanks to Matt Koizim for assembling the data and running the initial analysis.