The Davis Cup is an international men’s tennis competition that is one of the oldest and most prestigious team events in the sport. It was founded in 1900 by Dwight F. Davis, a Harvard University tennis player, hence the name “Davis Cup.” The tournament is contested annually between more than 130 nation teams and is highly regarded by players and fans alike and is run by the International Tennis Federation. It provides an opportunity for players to represent their countries and compete as part of a team, which is a unique experience in a sport largely dominated by individual competition. The tournament has seen some of the greatest players in tennis history, including names like Rod Laver, Bjorn Borg, John McEnroe, and Roger Federer, all vying for the prestigious Davis Cup title.

This blog will explain why the Davis Cup is a special case when it comes to calculating Nation ranking and shows how well the bespoke ranking method was designed. It will also link to a research paper investigating the performance of the ranking method (Kelley, 2024).

The Competition Structure

The competition structure of the Davis Cup often slightly changes from year to year to adapt to the nations taking part in the different levels of the competition and to improve the structure in terms of organisation and participation. A major change to the format occurred in 2019 and since then it has had a structure close to that illustrated in Figure 1.

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Figure 1. The Davis Cup competition structure (adapted from Kelley, 2024).

The Davis Cup competition starts with a qualification stage. There are three levels to this, Finals, World Group I Play-offs and World Group II Play-offs, each with 24 nations that play a single tie. The winners and losers progress as shown in Figure 1.

The Finals section of the competition structure consists of a group stage followed by knockout rounds. Six groups consisting of three nations that play in a round-robin format. Eight nations qualify for the knockout stage starting at the quarterfinals. Winners of the quarterfinals automatically qualify for the following year’s Finals and all other nations begin the following year in the Qualifying round, from which two wildcards for the Finals are selected.

The World Group I and World Group II sections are single tie knockouts. Winners and losers progress to the qualifying round of the next year as shown in Figure 1.

The World Group III, IV and V sections split nations into groups based on location with similarly located nations group together where feasible. The groups contain around six nations and typically they play a round-robin format followed by knockouts to determine regional winners and promotion places. Nations that finish lowest in the round-robin in Group III and IV are relegated to Group IV and V respectively. A number of nations in Group III, IV or V will not be promoted or relegated and will remain in that group the following year.

Rankings are very important to the competition structure. The draws that determine which nations play in each tie in almost every section of the structure use the rankings to seed teams. Seeding is commonly used in tennis and other sports to ensure top teams or competitors do not play each other early in the competition and knock each other out of contention. Nation rankings are also used when The International Tennis Federation need to adjust the position of a nation within the competition structure. For example, this may be required because a nation is unable to compete in a year and one or more nations need to be moved to ensure the correct number of nations in each section.

Nations can have very different progressions through the Davis Cup competition compared to each other. Even if nations finish the year at the same point in the competition structure, there are many routes they could have taken. For example, in Figure 1 we can see that there are four ways a nation can finish the year in World Group I Play-offs:

1. Qualifying -> World Group I -> World Group I Play-offs
2. World Group I Play-offs -> World Group I -> World Group I Play-offs
3. World Group I Play-offs -> World Group II -> World Group I Play-offs
4. World Group II Play-offs -> World Group II -> World Group I Play-offs

A nation could play six ties if it progresses from Qualifying to the Final at the Finals. A nation could play more than six ties in Group III-V. Any nations that play in Group I or Group II will play exactly two ties in a year.

Producing a ranking method that works with such a structure is not trivial. It must perform fairly throughout the various levels of the competition structure, with nations playing knockout and/or round-robin ties depending on their level and with some nations playing three times as many ties than others. Nations that finish the year in the same position in the competition structure should receive a similar number of ranking points regardless of their starting position and route.

Davis Cup Ranking Design

The Davis Cup rankings are explained on the Davis Cup website. Within a single year, a nation earns ranking points in the following ways:

1. Stage Points – awarded at the start of the year based on the nation’s starting position in the competition structure.
2. Win Bonus – awarded for each tie won. The value is dependent on the level of tie within the competition structure.
3. Rank Bonus – awarded if the nation beats an opponent ranked in the top 32. The value increases for higher ranked opponents.
4. Away Bonus – 10 points are awarded if a nation wins a tie away from home – the single-tie knockout rounds have a home nation that chooses the surface and venue of the tie which is a major advantage.

A nation’s overall ranking is determined by using the current year total and a percentage of the previous three years (75%, 50% and 25% respectively) added together. The values awarded for Stage Points, Win Bonus and Rank Bonus are shown in Table 1.

Table 1. The points awarded in the Davis Cup. In addition to the values in the table, Nations receive 10 points for winning an away tie.

Rank and Away Bonuses have historically been part of the Davis Cup ranking method and were included in part because of that. An away bonus is absolutely justified given the advantage home nations have in the single-tie knockout rounds where they can choose the playing surface. The rank bonus rewards the winner of high-profile ties. Both are relatively easy to understand, interpret and justify.

The choice of Stage Points and Win Bonus values is less easy to understand. The values of the Stage Points descend relative to starting position, but not consistently. The Win Bonuses available do not show a consistent pattern with the most points available for those playing in the Finals or in Group III-IV, at opposite ends of the competition structure. We can only really understand why these values are used if we look at how they work together.

Figure 2 considers nine positions within the competition structure that a nation can finish the year in. These are the nine finishing positions that can be easily differentiated. Figure 2 shows the range of points a nation can achieve if they have finished in that position.

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Figure 2. The range of points a nation can achieve in one year when finishing in one of the six locations at the end of the year; Finals (winner, runner up or losing semi-finalists), Qualifying, World Group I Play-offs, World Group II Play-offs, Group III, Group IV and Group V.

Figure 2 shows how well designed the Davis Cup Ranking method is. For each finishing position, the range of points is quite narrow which means that any nations with the same finishing position will have achieved a similar number of points. Comparing adjacent finishing positions, we can see that each higher finishing position has a clearly higher range than each lower finishing position. In addition, the gaps between adjacent ranges are small, showing an almost continuous possibility of achieved points. These design successes are achieved despite the multiple potential routes to each finishing position – multiple combinations of stage points and bonuses are contributing to the potential range for each finishing position.

Performance

The performance of the Davis Cup ranking method was compared with the Elo rating method by Kelley (2024). The Elo rating method is used in many games and sports and originated in games such as Chess. The FIFA international rankings in football use a method based on Elo rating. The following criteria were used during the comparison:

1. Finishing Order Correlation – Accurately reflect the annual competition finishing order.
2. Skill Level Correlation – Accurately reflect a participant’s skill level – this concept is not possible in reality but can be tested when competitions are modelled with results dependent on participant skill level.
3. Responsiveness – React quickly to a participant if their competitive standard changes – for example an improving team, through improved coaching, players or investment, should be able to improve their world ranking in a short time relative to their player careers.
4. Protection – Include short-term protection for participants – this is to reduce the pressure on athletes to compete every year, allowing for sufficient recovery times from injuries and allowing for breaks in play that may include paternity leave.

Kelley (2024) presented results generated using a simulation of the Davis Cup competition and found that the Davis Cup ranking method performed well against each criterion. It also found that a standard Elo rating method was unusable because it’s Responsiveness was not good enough. An adapted Elo rating method showed some improvement but did not out-perform the Davis Cup ranking method.

Conclusion

The Davis Cup has a complex competition structure and has a unique bespoke ranking method. On the surface, it is hard to understand the design of the ranking method until you see how it works in practice. The results presented here show how well designed the ranking method is when considering the potential range of points available for each finishing position. Kelley (2024) showed how well it performs in practice, using simulated results. The ranking methods bespoke design allows it to work well for nations playing at all levels of the competition structure, either at the top playing in the Finals or at the bottom playing in the regional Groups.

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References

Kelley, J., 2024. Using simulations to compare the current Davis Cup ranking system to Elo. PLoS One. Last accessed 24/02/2024 from: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0298188