In order for the camera to break, the puck must be slapped against the boards at the exact spot where the camera is. Pucks are dumped against the boards more than twice and fewer than 200 times per game, so a reasonable estimate is about 20 hits per game. The puck itself needs to land in a space the size of a camera lens. The size of the lens depends on whether we're talking about a regular camera or a video camera.
|This digital camera is a fair bit smaller...|
|...than this professional video camera.|
For the sake of the problem, I'll assume we're talking about regular digital camera since that is what I was looking at during the game. From the picture above, the lens appears to have a diameter of roughly 3 inches giving an area of around 10 square inches. The circumference of a hockey rink is about 500 feet with a height of about 12 feet giving area of 6000 cubic feet. Assuming the pucks are distributed uniformly over the boards (not necessarily a safe assumption), you'll have about a you'll have about a 1 in 100,000 chance that the puck hits the camera. Since the cameraman was only there about 20 percent of the time, that decreases the probability that any given hit will break a camera to 1 in 500,000. Since there are 20 pucks hit hard against the boards per game and a 1 in 500,000 chance that any given puck will hit a camera, there must be a probability of 1 in 25,000 that any given game will feature a broken camera.
At present, each team plays 82 games per year. If we consider that many of the early years in NHL history had teams playing fewer than 50 games, we can estimate that on average about 60 games are played each year. Half of these might have a camera man. That gives 30 games with a camera per team per year. On average, there've been about 15 teams each year throughout the 90 years of NHL history. From this we can conclude that 40,000 games had a camera that could have been broken.
Since there have been about 40,000 games with a camera and a 1 in 25,000 chance that a game with a camera will end a s a game with a broken camera, we can conclude that roughly 1.9 cameras have been broken. Since this is an order of magnitude estimate, any it's possible that anything up to 19 camera have been broken.
Congratulations to the winner and runner up who will receive a free copy of Ballparking: Practical Math for Impractical Sports Questions and How Many Licks?, Or How to Estimate Damn Near Anything, respectively.