For professional tennis players, the coronavirus pandemic has meant canceled tournaments, lost income and frozen rankings, with the men’s and women’s tours putting their systems on hold in mid-March.

Rankings are, in many respects, the coin of the tennis realm: the determining factor in players’ ability to enter events, receive seedings and even earn certain bonuses from sponsors.

And the hiatus has created a new mathematical challenge for this global sport. As the tours prepare to resume in August, what is the best way to thaw the rankings that usually shift week by week?

The Association of Tennis Professionals, which runs the men’s tour, and the Women’s Tennis Association, which runs the women’s tour, have debated long and hard about the fairest and smartest way forward. So has the International Tennis Federation, which operates lower-level professional events and oversees the junior, senior and wheelchair circuits.

They have talked together, but their decisions are imminent and may differ. What is clear is that both the ATP and the WTA are prepared to deviate for the first time from the rolling 52-week system that has been in place since their ranking systems began in the 1970s. Golf’s world ranking system, by comparison, is based on results over two years.

Normally, tennis rankings are updated weekly by adding results from the previous week and subtracting those from the equivalent week in the previous year. Consider an example: Naomi Osaka, the Japanese star, lost in the third round of the 2020 Australian Open after winning the singles title in 2019. After subtracting the 2,000 points from her 2019 victory and adding the 130 points she earned for reaching the third round in 2020, her ranking dropped to No. 10 from No. 4.

The pandemic has disrupted that familiar rhythm. With the rankings frozen, results from April-June 2019 have yet to be subtracted, and remain part of each player’s ranking.

If and when play restarts in August, there will be a lag for the rankings and also a logjam of rescheduled events.

That creates opportunities for competitors to play and earn income, but players might be more cautious about the events they enter to avoid injury and fatigue as the season restarts.

For the men, the schedule offers five large events, including two Grand Slam tournaments, in a span of just seven weeks on two continents and two surfaces: hard court and clay.

Veteran stars like Rafael Nadal, 34, and Andy Murray, 33, are understandably skeptical that they can manage all of this, and they are concerned that the ranking system could quickly become skewed.

“It’s not safe for players to go from the semis or final in New York, quarters even, and then you’re playing on the Tuesday in Madrid at altitude on the clay court, when players haven’t competed for a very long time,” Murray said. “You’re going to have the potential where a lot of top players are not competing at many of the biggest events.”

The tours are also trying to help lower-ranked players get chances to accumulate points by adding lower-level tournaments alongside the main tour events.

Both the ATP and WTA considered unfreezing the ranking at the start of 2021 and playing the remainder of the 2020 season without points. But that option was discarded because it would essentially transform tournaments into exhibitions, a prospect rejected by events like the United States Open, which has contractual deals with sponsors and broadcasters that are linked to the tournament’s ranking points.

Another plan that was discarded was having points awarded for the remainder of 2020 that only counted toward qualifying for November’s year-end championships.

That leaves two leading options on the table, both of which would allow some of a player’s ranking points to carry beyond 52 weeks, in an attempt to reduce the impact of re-entry.

“Both are good and bad in different scenarios,” Ross Hutchins, the ATP’s chief player officer, said last month in a conference call with players.

The first option would gradually deduct points from players’ unfrozen totals as they earn points when the tour resumes. The final points from the unfrozen total would come off by August 2021.

The second, more complex option, which has been gathering momentum in recent weeks, would try to maintain the traditional system of matching up equivalent events despite all the shifting in the calendar.

That would mean, for example, that the points from the 2019 French Open, which ended in June 2019, would not be at stake until the end of the 2020 French Open, which is now scheduled to end Oct. 11.

This plan has the advantage of getting back more quickly to the traditional 52-week system. “Having a ranking which is a subsection of our current ranking is very challenging for a longer period,” Hutchins said.

For the remaining events in 2020, the plan would let players preserve their result from 2019 if it was a better finish — whether they played in the 2020 event or not.

The option is considered an attempt to protect players who cannot play in certain events because of public health concerns or travel restrictions. It would also lessen the rankings impact if the pandemic further disrupts the tournament schedule.

The rub is that it could create friction with prestigious events like the U.S. Open.

The choice would mean, for example, that Nadal, who won the U.S. Open men’s singles title in 2019, could keep those 2,000 points in his ranking even if he does not play in this year’s U.S. Open.

Though the goal, in theory, is to take the pressure off players to perform at full throttle immediately, the knock-on effect is that they could skip big events entirely without penalty. Nadal does have the major incentive of chasing a 20th Grand Slam singles title, which would allow him to tie Roger Federer’s men’s record. But under this plan, he might be even more likely to prioritize the rescheduled French Open on his beloved red clay, rather than risk pushing himself too far by competing first in New York at the U.S. Open.

If others decided to take such an approach, that could weaken the field considerably at the U.S. Open, which is scheduled to be played without spectators and with significant health restrictions in place, in a city that was once one of the global centers of the coronavirus.