Here is a short description of a few sports which were done in medieval towns.
JAVELIN-THROWING WITH LEFT AND RIGHT ARM
It was important to be good at throwing the javelin, or spear, if you were fighting in a battle. If one arm was hurt, you had to throw with the other arm. Therefore, people practised throwing with both left and right arm.
Throw as far as possible. First throw with one arm, then use the other. Add up the results. Compete in shooting at a target.
ARCHERY
The medieval longbow was a much-feared weapon. Both noblemen and citizens practised at shooting with a bow-and-arrow.
Shoot at a target from a suitable distance. You can also shoot at a model of a bird which has been nailed to a pole.
There is more information about medieval backgammon, skittle games and sports in two booklets published by Kalmar Läns Museum.