Tue Sep 17, 2013 11:42 pm
There are 36 possible dice rolls, or 6 sides x 6 sides.
The least chances of how the rolls can turn out are for rolls of 2 and 12, each of which has just 1 chance. The most is 6 chances (for a roll of 7). This is because a 2 can only be rolled 1 way (1-1) and a 12 can only be rolled one way (6-6). But a six can be rolled 6 ways (1-5, 2-4, 3-3, 3-3, 4-2, 5-2). The chances for a roll get higher as your rolls approach seven and lower as your roles go beyond seven.
The way I remember the chances is to subtract one chance for every dice roll up to seven. Thus, a roll of 2 has 1 chance, a roll of 3 has 2 chances, a roll of 4 has 3 chances, and so on to a roll of 7, which has 6 chances.
After the 7 roll, the chances decline by one with each roll. Thus, a roll of 8 has 5 chances, a roll of 9 has 4 chances, and so on. You can also count the other way, adding 1 for each move up from a 2 roll or down from a 12 roll.
If you multiply the total number of chances on a given card you get 3 x 36 or 108. The combined chances on both the pitcher and hitter cards is 216. Thus, the chance of rolling a 2 in the third column on the hitter's card is 1 in 208. On average, you might see this roll about 3 times in a season (given 648 PA, i.e. 6 x 108). Thus an injury on the 2 point might result in an average of 3 injuries in a season. But the chance of rolling a 7 in the same column is 6 in 208, or about 1 in 35. You might see that roll, on average, about 18 times in a season. So a HR on the 7 for a hitter might be worth about 18 HR (assuming 648 PA). Not shabby.
This can be helpful when you want to evaluate the strengths and weaknesses of a card. For example, # BPHR on the 7 is much worse for a pitcher than a BPHR on the 3, especially in a power park.