The bonus statement that I am looking at is "Upsets are more frequent in Davis Cup competition."
@JaredPine Can you do Myth vs Math ? more upsets in DC or lower ranked perform better in DC .... I don't believe that notion .The Myth
— Kelvin Gray (@0try) September 12, 2014
Kelvin Gray (who you should all follow by the way) sent this tweet, asking the see if the numbers backed up the claim that it is easier to pull off an upset in a Davis Cup match than other best-of-5 matches. Kelvin believed that the numbers won't sustain the claim that upsets are easier to achieve in Davis Cup play.
So where does this claim even come from? Well, Davis Cup clearly has a very unique environment to the rest of the tour. Fans are much more involved during matches. It isn't a tournament style in a tie, so each players' first match of the weekend is just as important as the second (assuming it's not a dead rubber). Ties are also frequently held on a different surface than what players were on the week before. Also the courts are typically of a lower quality than the standard maintained on the world tour. When players play, they are representing more than themselves, putting a much different kind of pressure on them. The final thing that is different is the players in the match. Many top players don't participate in Davis Cup, leaving some potential match ups that would rarely occur on the world tour.
All these differences are reasons that there would be more upsets. Since rankings are based almost entirely on world tour play, someone who prefers a Davis Cup setting could beat a higher ranked player that is uncomfortable with the changes. Thus, many fans and experts believe that upsets are easier to achieve during Davis Cup than during the world tour.
Not a lot of heavy-duty math was required to test this myth. All we need is a compilation of results with respect to rankings from both Davis Cup and the world tour. Compiling those numbers was actually much harder than I expected since there is no way to tell the ranking of players from just looking at a draw, so excuse my extremely small sample sizes. I typically prefer to use unnecessarily large sample sizes rather than risk going to small.
The two samples I took were all Davis Cup matches in 2014 through the semifinals and all second round matches at the 2014 US Open. At first glance, the gap in upsets is not that big between Davis Cup and the US Open. In 41 live rubbers at Davis Cup so far this year, the higher ranked player has gone 29-12 (70.7%). In 31 second round US Open matches (there was one walkover), the higher ranked player went 23-8 (74.2%).
To look at it a little more closely, let's look at in how many sets a match/rubber was won or lost. In Davis Cup, the higher ranked player had 21 three-set wins, 6 four-set wins, 2 five-set wins, 5 five-set losses, 2 four-set losses, and 5 three-set losses. At the US Open, the higher ranked player had 14 three-set wins, 7 four-set wins, 2 five-set wins, 3 five-set losses, 0 four-set losses, and 5 three-set losses. The table below breaks down the percentage of times each occurred at each event.
So it is more difficult to win in straight sets at the US Open for a higher ranked player, but it is harder for that player to finish a match in five sets at Davis Cup. However, no wide conclusion can be made about these numbers because ultimately a win is a win.
Based on those numbers it seems that big upsets are only slightly more likely, while small upsets are pretty close to equally common.
It seems that for the most part, Kelvin was right about upsets being not much more common in Davis Cup than at the US Open. To really prove this idea would require a much larger sample size from a variety of tournaments and rounds, but these numbers show that it's just as hard to beat a better player at Davis Cup as anywhere else.
The reason that people tend to think there are more upsets in Davis Cup is because of the format of the event. An upset in Davis Cup is just as likely in the first rubber of the first tie as it is in the fifth rubber of the final. However, at tournaments, an upset can only occur in the first week, making upsets at grand slams much more forgettable (other than Wacky Wednesday).
This is the problem that I wanted to point out with the Myth vs. Math series. Simply making large assumptions without checking the numbers will frequently result in false assumptions, because we rely heavily on memorable matches to form these wrong opinions. To the numbers, every match is remembered and measured. Tennis is so far behind other sports in its dependence and organization of stats, allowing experts to state opinions that often go unchecked and are assumed true. Opinions should be accompanied by a stat that supports it - otherwise it is just fluff.
*If you have any story ideas for me for Myth vs. Math or any topic, send me a tweet. I might write something up if it's a topic that interests me and is something I can research or at least know a little about. This story idea was completely created by Kelvin's tweet.