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I somehow viewed 15-12 as winning four of every seven.

Use the common denominator and you won't have this problem. Example below:

The common denominator of 15-12 is 3, which reduces down to 5-4. which is 5 out of nine. OR divide the number of games won by the total number played to get the winning percentage -- 15 divided by 27 same as 5 divided by 9 (common denominator, again, 3).

Equals 55.56% as ComptrBob reported.

Hope you find this helpful and useful for future reference.