A new perspective on stars and luck

The Lucky Draw

There are both tangible and intangible elements that go into running a successful tournament. Two of the most significant considerations when planning an event are the format of the draws and the convenience of the scheduling for the participants (players, parents, coaches). The format is influenced by the number of competitors, the number of courts available, and the number of days which are to be set aside for match play. For large events with a small number of categories there are usually more who want to play than spots available, but for small to mid-size events, or large events with many categories, the number of participants per draw can vary greatly.

There are two prominent methods used to pair tournament participants and determine final placements: Elimination and Round Robin. Another approach with many variations is the Swiss System, which originated in chess. The “Lucky Draw” being proposed here applies only to elimination draws, yet it shares characteristics with other methods of pairing while overcoming some of their limitations; it makes it easy for organizers to support any number of participants while simplifying scheduling.

In tennis a “Lucky Loser” is a participant that loses in a qualifying draw but nevertheless enters a main draw, typically because another participant withdraws, or simply doesn’t show, after a draw has been finalized. While rare, lucky losers have won major tournaments; it is not rare, however, for such participants to be stronger than those selected for the main draw based on rankings, ratings, or as an alternate or wildcard.

There are a number of ways that “lucky losers” benefit organizers. Without a lucky loser, a “bye” would have to be placed, automatically advancing a first round competitor. Byes are generally reserved for seeded participants, but in the case of a withdrawal it could mean that an unseeded competitor is advanced, conflicting with rules governing competition. With lucky losers, draws do not need to be re-done, which means that schedules do not need to be re-done, which saves time and avoids confusion.

The term “luck of the draw” refers to the fact that the pairing of competitors within a draw structure cannot be controlled by the competitors; opponents are determined by chance. In The Tennis Draft I suggested a twist which introduces some participant agency in the construction of draws. The “Lucky Draw” introduces a mechanism by which participants can “make their own luck”, increase their odds of advancing, even if they lose a match. Participants and organizers benefit from this “luck generator” in other ways because “Lucky Draws” have at most one bye, which both streamlines scheduling and increases engagement, reducing the chance that competitors who get byes are waiting around for an opponent to recover from a previous match.

Structures which produce a winner via a process of elimination have been inexorably shaped by the Power of 2. This works well when all draw positions are filled, but necessitates rounds which, depending on the number of competitors, can require a large numbers of byes. When there are consolation or playoff structures, such as in Compass draws, byes propagate and strand participants without opponents, which is troublesome for organizers that wish to give participants a guaranteed number of matches.

The Swiss system allows every participant to play in every round (except for the possibility of a single bye) and reduces the number of rounds played by shuffling participants based on the outcome of previous rounds and calculating final positions based on match results, but structures that segment players into groups, including round robins, are heavily reliant on cascading and sometimes iterative sets of rules to break ties when calculated percentages are equivalent. It can be confusing for both competitors and organizers. Round robins generate too many pairings if the groupings are large, and are therefore often paired with elimination structures to play off final positions.

The “Lucky Draw” extends the logic of the qualifying “lucky loser” into main draw elimination structures. In a scenario with twenty-two participants, a “normal” elimination structure requires ten byes and produces six first round matches. Ten participants would have to wait for an opponent to play their first round match and recover. Two second round matches could be played along with the first round matches, but scheduling difficulties will proliferate. In the same scenario, a “Lucky Draw” allows all participants to play: eleven first round matches can be scheduled. To complete the second round, one first round loser is “lucky”, and this luck can be either truly random, or it can be determined based on the prior round match lost by the narrowest margin.

Lucky Draw 11–6–3–2–1

The “Lucky Draw” supports consolation and playoff structures as well, since one lucky loser advances, the “back draws” for lucky rounds simply have one less match. This means that organizers can plan and schedule a desired number of matches for all competitors, and that finishing positions can be determined without complicated tie-breaking formulas.

There are a number of interesting possibilities that arise from the dynamics of the “Lucky Draw”. Variations could include a “once lucky” rule, or a participant could theoretically lose several tight matches (mixed with match wins), and still make it to the final four. The determination of which loser in a round advances to the next can also extend across rounds, meaning that the calculation can consider the differences of all previous matches played. This consideration can even be used to eliminate or reduce indifferent play on the part of qualifiers who believe they will make into a main draw whether they win or lose (tip of the hat to Jeff).

Lucky Rounds within Lucky Draws can either follow a “feed in” pattern to avoid participants facing previous opponents, or they can be used to ‘re-balance’ the draw to ensure that the strongest players do not meet until the final and that loser brackets are as level-based as possible.

There is plenty of room for improvement in how tennis competitions are managed. Traditionalists need to consider the long term health of the sport, that everyone is busier and there is more competition for our time. The use of timed match formats is increasing; it makes sense that organizers want to offer events with definite schedule times (barring rain), but the idea of multiple timed sets conflicts with the desire for fixed schedules (unless points are aggregated across sets). When an event uses a “best of 3 timed sets” scoring format, “Lucky Draw” offers an incentive for playing a 3rd set, even if a winner has already been decided. This means no dead court time! Both the winner and the loser have incentive to play their best because every point increases their chance of being lucky, in the current round or the next.

“Lucky Draws” has been implemented in the Competition Factory and you can play around with some visualizations in the CourtHive Score Grid. I’m interested to hear your feedback. Feel free to contact me: charles at courthive.com. Thanks for reading!

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