At first our attempts to find a game that everyone could play were unsuccessful. We began with football. We scored two broken bones within two months and all but one of the women dropped out. Then I found 20 hockey sticks for sale in a charity shop: the result was carnage on an almost military scale.

For a while our group – people with energy to burn, who wanted a fast team game to play – had nowhere to turn. Then someone introduced us to a counter-cultural import from America. Twenty-two years later, we're still playing.

There's something about Ultimate Frisbee that defuses the tensions that build up in other games. In all this time I have witnessed only two flare-ups and one serious injury: someone's ligament snapped as he was sprinting up the field (it sounded like a gun going off – when we saw him lying on the ground we thought he had been shot). Perhaps it's because this is a non-contact sport, or because we don't keep score, or because there's no referee, which means the players must decide among themselves whether a foul has occurred or a goal has been scored. Although the game can be fiercely competitive, it never seems hard to applaud the other team for a good move made at your expense.

But the most remarkable feature of Ultimate Frisbee is that it can be played at many levels, simultaneously. Duffers can mingle with seasoned players and still score some points. I have heard it described as the most aerobic team sport. The way I play – rushing mindlessly up and down the pitch – makes it feel like that, but you can do just as well by goal-hanging. The youngest person I've played with was six, the oldest 79. I've never known such a game for dragging in onlookers: many of those on our teams today are people who had watched us in the park.

The rules are similar to netball's: you can't run with the Frisbee; if you intercept the opposing team's pass or if they fail to complete it you get possession; goals are scored by catching the disc in your opponents' endzone. That's about it. As an antidote to sitting on my butt lamenting the troubles of the world, there's nothing to beat it. Except sea kayaking, but that will have to wait for another Christmas.