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Yesterday, in Edmonton, at a baseball game two of my friends caught a home run, in separate plays during the game, and I am wondering where to begin in analyzing what the probability of this happening was? They were sitting beside each other. This happened at the Telus Field which has a capacity of 10, 000. The field dimensions: Left: 340 ft (100 m) Centre: 420 ft (130 m) Right: 320 ft (98 m)

Unfortunately, I don't think these dimensions include the seating area (I found these dimensions on wikipedia). How can I approach this problem?

To constrict the problem a little, I try to define the possible landing areas of the ball as squares with sides, roughly the diameter of the ball, which fill the area of shape representing the total possible landing positions. This shape would extend out from the batter's position following the foul lines into the stands, the distance between the lines increasing as you travel further from the batter. I am not including the area outside of the foul lines, and the grid of squares representing the possible positions would extend into the far reaches of the stands. I am assuming that the baseball is 3inches in diameter. Probabilistically, would I need to know which area of squares is landed on most frequently? And would I need to know their exact seating positions?

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I don't think the restrictions help much. You have to take account of each pitch. Given the pitch, what is the probability that it will be hit? If it is hit, what is the probability that it will go fair? If it goes fair what is the probability that it will be hit into the seats for a home run? Then given that it is a home run inot the seats what is the dsitribution of the location that it will land? This will no tbe uniform. Lefthand hitters are more likely to hit the ball to right field and right hand hitters to left field. –  Michael Chernick Jun 16 '12 at 16:51
    
So if you model it as non-uniform with distribution dependent on lefthanded or righthanded then you may want to say where the two seats were located. –  Michael Chernick Jun 16 '12 at 16:51
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This is very complicated. Obviously we know it is unlikely from observing baseball games. For example I have gone to many games and rarely had a ball come close enough to my seat that I could reach for it. So even to get 1 ball in a game is rare and this is almost like getting 2. But where a baseball will get hit is very complicated. It depends on whether the batter is a right or left handed hitter, the pitcher and the type of pitch and other things. To answer this with a probability estimate would require modeling the process for individual picthes and then to look at all the pitches thrown in the game, proably more than 200 pitches. It is even rarer than what I am saying because I am think of balls hit in fair or foul territory and you are restricting it to home runs which only accounts for about 1/4th of the seats.

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Is it the case that I would need to gather significantly more information before being able to come up with any reasonable estimate? –  Kurt Jun 16 '12 at 16:41
    
More information or more assumptions would be needed . I think you might be able to get home run distributions from major league baseball. Statistics on average number of home runs per game could be obtained. Of course for this to happen you need at least 2 home runs in the game. Given the breakdown of right and lefthand hitters and location distributions for home runs you can determine (1) probability of 2,3,4 ... home runs in the game and (2) the probability of a home run hit to your spot by left and right hand hitters. –  Michael Chernick Jun 16 '12 at 19:01
    
Then you should be able to get an estimate that this outcome would occur. –  Michael Chernick Jun 16 '12 at 19:01
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