jatrax is on the right track. for manual focus sports photography you really need to know the sport. I shot a lot of sports in school for yearbook etc. I used a 135 2.8 a 1.4 tc and 400 iso film (sometimes pushed to 800). max speed on the body was 1/500. i would stop down to f4 if light allowed and shoot at 1/500 if possible. I would read the play for football and prefocus on where i thought the next play would go and wind off one or 2 shots. managed to get some very good ones (ie guy snagging the ball out of the air while he was off the ground. but there was luck involved along with planning. It got way easier when i got aq bulk back and motor drive so i could hit 3-6 frames per play
Like Boriscleto said action photography existed long before AF came along. you just need to look back at some of the old 70's sports illustrated covers to see what could be done
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stopping down a little with a longer lens gives more forgiving DOF so if you use the 200 shoot f8 or so, there will still be sufficient isolation at f5.6 to f8 on a 200
1970's SI cover, an iconic shot done most definitely with a manual focus lens (though also with a motor drive and bulk film back guaranteed )