If there were still darkrooms you could get a foot in the door of sporting picture agencies, I know, because I did :0)
I got my break because I was a student at college, and was already photographing sailing events, then I introduced myself to a professional photographer who had been hired to cover the event...from that I got a work experience with Allsport (now getty), from that I had a job straight from college with the biggest sporting picture agency in the world...I worked in the darkroom, was up to my arm pits in E6 and c41 chemistry mon-fri but at the weekends I was able to get press passes for lower league rugby and football, and got coverage in the nationals etc..I was also a wire tech, processing, scanning and sending off images...I was also a studio tech, and second photographer whenever I could get time away from the darkroom. And during the london marathon all the wannabee snappers get press passes and access of just go to different parts of the course, and if you get images in the sets then you were laughing...I also got to shoot rugby internationals at Twickenham and advertising shoots with Beckham, so it wasn't just smelly chemicals and windowless rooms
Now your way in would be a a wire tech/computer operator...where you could shoot for the first 10 mins and then wire the pros images back
As for starting off, first you need a strong folio of images, there are thousands of rugby and football matches going on every sat and sunday morning in parks and fields up and down the country go to those and get your experience there...the action is slower and easier to follow...get in touch with your local leisure centre and see if you can photograph the sports that go on there from athletics to trampolining to judo photograph it all and get good at it...submit images to the local papers give cards out to parents etc
Usually you'll only get press passes if you know someone or are working on behalf of someone and they'll make the application for you...or you'll need evidence that you have a client but for all of the above you need a folio
If you're good enough agencies will hire you on a freelance basis...and after a while you might get to join the inner sanctum of being a staffer....but remember there are a lot of other photographers out there who are better than you, work harder then you, know more people and have more experience that you.
So unless you have the energy and enthusiasm to work all the hours you can, and sit in the rain on a Saturday afternoon in the middle of winter in the rse end of nowhere getting freezing cold and wet, then find another area of photography, cos it's not all premier league and F1 :0)
Go out there and get shooting :0)
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