Badminton and Running

A few of my friends invite me to play badminton with them a few week back and since then i play with them once every week. I thought all my running before will help me cope with the demand of playing continuously buy boy was i wrong. By the time i finished my first set my lung is on fire and my leg is wobbly. It was definitely a different thing altogether. In running one tries mostly to maintain an optimum speed over a known distance with a repetitive set of movement. But in badminton you are using all your body upper and lower with unpredictable movement which is sideway, forward, backward, jumping and all sort pathetic movement to retrieve the shuttlecock.
My body was sore and i have miss my running for 3 days.But by the third week my body began to adapt and more importantly i think my running has improved a lot. My guess is the badminton session do play a part in my VOmax improvement and strengthen my knee and calf. My current pace right now is around 6.5 min per km. Hopefully i can go faster.