# The Likelihood of Live Doubles Rubber in the New Davis Cup

In the new Davis Cup Finals format, each country-versus-country tie consists of three matches: two singles and one doubles. The singles rubbers are played first, so it’s possible that the doubles rubber will be “dead”–irrelevant to the result of the tie.

The Davis Cup Finals organizers aimed to make the doubles matter more, by using tiebreakers (based on sets and games won) to determine which sides advance from the round-robin phase to the knock-out rounds. It may have helped keep dead doubles rubbers interesting at first, but by the final days of the round-robin stage, teams that automatically qualified for the knock-out rounds had no remaining incentive to play doubles. Canada gave the United States a walkover, and Australia retired after one game. This was probably inevitable, but it isn’t ideal. Fans would presumably prefer to watch more tennis, and unfinished matches could wreak havoc with the tiebreaker system.

There are a lot of possible ways to restructure the event–so many that I’m not going to explore that topic today. Since dead doubles rubbers are inevitable, I’d instead like to look at how often we should expect them to occur and, given that they will occur, whether that truly sidelines doubles in comparison with singles.

Live doubles

This topic was prompted by a question ahead of this week’s podcast:

The most extreme way of handling dead doubles rubbers is simply not to play them. If we went that route, how many doubles matches would we see?

At the Davis Cup Finals last week, there were 25 ties: 18 in the round-robin stage, and 7 knock-out ties. 12 of the 25 featured a live doubles rubber: 7 of the 18 round-robin ties, and 5 of the 7 knock-outs. Using Luke’s proposed methodology, that’s roughly what we’d expect. The average tie (across all stages) had a 43% chance of reaching a deciding doubles rubber, suggesting that 11 doubles matches would matter.

Here is a list of the 25 ties, along with the probability that the two sides would split the singles rubbers. I’ve also shown whether the doubles rubber turned out to be necessary. Elo ratings didn’t do a very good job predicting which ties would require a doubles decider, even though they do give us a good estimate of how often the doubles will make the difference.

```Tie                  Decider Odds  Decider Actual
Semi: GBR vs ESP            56.2%             YES
Quarter: SRB vs RUS         54.3%             YES
Semi: RUS vs CAN            53.3%             YES
RR: FRA vs SRB              52.5%              NO
RR: ARG vs GER              51.6%              NO
RR: USA vs CAN              51.4%              NO
RR: ITA vs CAN              50.0%              NO
Quarter: GBR vs GER         50.0%              NO
RR: GBR vs KAZ              49.8%             YES
RR: ESP vs RUS              49.4%             YES
Quarter: AUS vs CAN         49.4%             YES
RR: USA vs ITA              48.7%             YES
RR: BEL vs AUS              46.1%              NO
RR: KAZ vs NED              46.0%             YES
RR: CRO vs RUS              45.7%              NO
RR: GER vs CHI              44.2%             YES
RR: ARG vs CHI              43.6%              NO
RR: FRA vs JPN              43.4%             YES
Final: CAN vs ESP           40.8%              NO
RR: GBR vs NED              37.5%             YES
RR: BEL vs COL              36.2%              NO
Quarter: ARG vs ESP         34.6%             YES
RR: SRB vs JPN              26.1%              NO
RR: AUS vs COL              10.4%              NO
RR: CRO vs ESP               7.3%              NO```

Only a few ties were near-guarantees of a singles sweep. Even with a fairly deep 18-team draw, most countries were able to bring two solid singles players, while few sides featured more than one singles elite.

This wasn’t just a fluke. I went through all World Group ties (not including the Playoff round) from 2010-18, and identified the two best singles players who appeared on court for each side. Using their Elo ratings at the time of the contest for the new best-of-three-sets format, I estimated how often we would get a deciding doubles rubber.

Across those 135 ties, the average likelihood of a doubles decider was 41%, only a bit lower than the observed rate this year. Barring some radical shift in the geography of global tennis, that gives us a pretty good idea of how frequently we should expect to see a two-match singles sweep in the new Davis Cup format.

How much does doubles matter?

When doubles matches are live, they are particularly important. Each singles rubber has a great deal of influence on each side’s chances of winning the three-match tie, but once the doubles rubber is in play, it has all the influence.

Think of this in terms of leverage, the concept I usually use for in-match shifts from one point or game to the next. Imagine two identical sides, and consider their chances of winning at each step of the process. Each side has a 50% chance of winning each rubber, which means:

• Each side has a 50% chance of winning the tie.
• Whichever side wins the first rubber will have a 75% chance of winning the tie.
• If the two sides split the singles rubbers, each side will once again have a 50% chance of winning the tie.

Now consider the leverage of each match from the perspective of the first side:

• If they win the first singles rubber, their chances of winning the tie improve to 75%. Otherwise, they fall to 25%. That’s a leverage value of 75% – 25% = 50%.
• Assume they win the first singles rubber. If they win the second, they win the tie–a probability of 100%. If they lose, it falls to 50%. Again, that’s a leverage value of 100% – 50% = 50%. (If they lose the first rubber, the math is the same, just with probabilities of 50% and 0% instead of 100% and 50%.)
• If there is a deciding doubles rubber, the pre-match probability of winning the tie is 50%. Win the doubles, and the likelihood increases to 100%; lose it, and the probability is 0%. That’s a leverage value of 100% – 0% = 100%.

Maybe you think this is excessively formal and long-winded, and you might be right. The point is, given two equal sides, the doubles is twice as important. Plenty of other sports have similar features in which certain players appear infrequently, but at key moments. Consider baseball closers, who don’t pitch in every game, only appearing late in tight games. Or NFL kickers, who only take part in a handful of plays each game, but have the potential to score on many of them.

Theory and reality

In the sample framework I’ve just laid out, the doubles rubber will be live exactly 50% of the time, and it is twice as important as each singles rubber. That isn’t exactly how it works out in real life, since the doubles rubber is only decisive a little more than 40% of the time.

Still, when the doubles rubber matters, it is always make-or-break–or, in my terms above, it has a leverage value of 100%.

I’m happy to leave dead doubles rubbers unplayed. Doubles specialists might be unhappy with such a decision, and I fear the wrath of Davis Cup traditionalists. However, this way of thinking about what’s at stake might soften the blow. In a 16- to 18-team Davis Cup structure, the teams are typically balanced enough that the doubles rubber is necessary almost half the time. And when it is, the oft-unsung doubles specialists get to play a match that is–literally!–twice as important as each ratings-grabbing singles rubber.