The oldest company still in operation is believed to be Ohio-based Buckeye Donkey Ball, which was founded in 1934 and is owned by a nephew of Crosby’s, Pat Barthen. The handful of remaining companies around the country follow a common business model, taking 50 percent to 60 percent of revenue from sales of tickets priced at about $6 each. Some, like Green Mountain Donkeyball, operate fewer than 20 events a year. Others, like Buckeye Donkey Ball, hold as many as 300 and have several teams of donkeys on the road.

The game is most popular in rural communities, where the event is often a sellout, said Jessica Cordell, Crosby’s granddaughter and the owner of Dairyland Donkey Ball in Wisconsin. Half the fun is watching the school principal or the mayor fall off a donkey, she said. But, she added, “if you play in downtown Minneapolis or St. Paul, they just don’t know each other.”

Despite its popularity, donkey ball has been criticized by animal-welfare groups that say it is stressful to the animals, who travel long distances and are ridden by inexperienced players. The Humane Society of the United States, the American Society for the Prevention of Cruelty to Animals and People for the Ethical Treatment of Animals all oppose the sport. PETA’s campaigns have persuaded schools from Idaho to North Carolina to cancel events.

“Donkeys have no place in a gym,” said Kristie Phelps, a PETA spokeswoman. “They are very easily confused, and they have no idea what’s going on.”

Unlike circuses and zoos, donkey ball companies are not required to be licensed by the United States Department of Agriculture because their events are considered a competition, not an exhibition, said Jessica Milteer, a spokeswoman for the agency. Regulation of competitions is left to the states, she said. Phelps said enforcement of potential animal-cruelty violations was difficult because the companies moved from town to town and state to state.

Camie Heleski, an instructor in Michigan State’s Department of Animal Science who has studied donkey behavior, described the game as mostly harmless. “I think it is probably somewhat confusing to the donkey,” Heleski said, but no more than pony rides or novice horseback-riding lessons are to those animals. Unlike horses, she said, donkeys tend to be calm and stoic. “And if they get confused,” she said, “they just plain stop.”

Although donkey ball players are required to sign waivers before they ride and some companies say they hold liability insurance, participants have sued after being injured. In 1997, a federal jury awarded an Illinois man $110,000 after a donkey kicked him in the knee. A fifth-grade teacher in Florida settled a lawsuit last year with the Diocese of St. Petersburg after falling off a donkey in a game in 2003.