| The Math
Step 2: The likelihood that x number of consecutive games will all include hits. Again, it may be effective to think of this with simple whole numbers before proceeding to the specific DiMaggio numbers. Let us assume an excellent player, like our hypothetical 1/3 Lajoie-type guy. That hypothetical player gets a hit in 80.2% of his games, but for illustration purposes, let's say he gets a hit in exactly 80% of his games, four out of every five games. What are his chances to hit in two consecutive games. Simple enough. It is four-fifths to the second power, 16/25, or 64%. In any given sequence of two games, he will hit in both games 64% of the time, he will hit in neither game 4% of the time. He will hit in one of the two games 32% of the time. His chance of hitting in any given three game series looks like this:
His chance of hitting in all three games in any given three game series is 4/5 to the third power, or 64/125, or 51.2% |
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His
chance of hitting in all 56 of any given 56 game series is, therefore, 4/5
to the 56th power, or .00000374, or about 4 chances in a million, or
about one chance in every quarter of a million opportunities.
As opposed to our hypothetical player, DiMaggio in 1941 actually had a probability to hit in 81.1% of his games, not 80%. That tiny variant approximately doubled his chances to 8 chances per million, or about 1 chance in every 125,000 sequences of 56. |
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