Myth vs. Math: Upsets in Davis Cup

This is a bonus installment in my five-part series called Myth vs. Math. In this series, I took a look at five widely-accepted statements that tennis writers, analysts, fans, and commentators frequently make. I'm checking to see if these statements hold up against the numbers. The five statements in this series were "big servers have a notable advantage in tiebreakers," "Novak Djokovic has the best defensive return in the game right now," "Rafael Nadal tends to get tougher draws than Djokovic since making his return from injury," "The top players play the big points better than their opponents," and "The first set is the most important set in a best-of-5 match."

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 .
— Kelvin Gray (@0try) September 12, 2014

The Myth
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.

The Math
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.

	Frequency (percentage)
	3W	4W	5W	5L	4L	3L
Davis Cup	51.2	14.6	4.9	12.2	4.9	12.2
US Open	45.2	22.6	6.5	9.7	0	16

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.

The next way I wanted to break it down was by ranking disparity. In Davis Cup, when the players are within 50 ranking spots, the higher ranked player went 10-7, including 4-5 when the ranking was within 20. When the ranking was between 51 and 100 spots apart, the higher ranked player went 10-4. Then when the higher ranked player was over 100 spots higher, that player went 9-1 with the only loss coming from Peter Gojowczyk's five-set win over Jo-Wilfried Tsonga. At the US Open, in the same categories, the records were 6-5, 9-3, and 8-0.

Based on those numbers it seems that big upsets are only slightly more likely, while small upsets are pretty close to equally common.

The Conclusion
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.

The reason I believe upsets no more likely at Davis Cup than the US Open despite the drastic change in environment is because Davis Cup participation is optional. The only players who typically get chosen to play in Davis Cup are the ones who aren't carrying any injuries and want to help their country. On the world tour, participation in some events in mandatory, so some players show up with injuries and no desire to win, and simply lose in the first round and go pick up their pay check. Since that never happens at Davis Cup, it balances out some of the upsets that are created by the unique environments that make Davis Cup so much fun.

*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.