Medieval sport seems to have resembled a battle - rough, unlimited in time, and pretty vague in its rules. I don't think they did penalty shoot-outs in the Middle Ages.
What's fun for us is that quite a few of these medieval sports remain. There are tantalising suggestions in the art of the time - for instance in Gloucester Cathedral there's a 'bandyball' player shown in the east window. Apparently the dean of Gloucester challenged another couple of clergymen to a re-enactment game. I can't find out who won, though.
But if you're really interested there are some fine medieval games still being played. For instance in Siena the Palio horse race round the main Piazza still takes place, twice a year. In Florence, there's 'Calcio storico', traditional football, with a ridiculously large number of players on each side. In Pisa, the Gioco del Ponte justifies a glorious military parade - but it's a violent game between the two parts of the city, Tramontana and Mezzogiorno, with twenty men at a time trying to push their opponents off the bridge.
In Germany, Mainz has its own tradition, rather a damp one - on St John's Eve, in midsummer, the boatmen have a joust on the Rhine, using long poles to try to tip their opponents into the water.
Getting people wet is always fun. One of my friends has his own game - not a 'tradition' that the local tourist board would recognise, I suspect, but known to a good few - of organising a water-pistol siege of his house on the August bank holiday.
And here Spain and France turn out to have some really oozing, slurpy, disgustingly wet games. For instance in Prats-de-Mollo in the Pyrenees you'll find the 'bears' - villagers liberally covered with soot and oil and sheepskin, set up for the other guys to chase. They may well relate to the Jack-in-the-Green, the May Day king, but they've gone in a different direction - fun and games rather than pageantry.
There's just no excuse for the Tomato festival in Bunol, in the Spanish province of Valencia. It starts with another good game - climbing a greasy pole to get at a leg of ham. But the fun really begins when they start throwing the tomatoes.