I have solved Promotion Counting and want to ask for a simple explanation.

So, I made my own test case,

1 2

1 0

1 3

1 4.

So, obviously, there are 3 competitors who promoted to plat, and 2 + 3 = 5 promotions to gold, but for bronze to silver, we have 2 + 3 - 1 = 4. I want to know where the -1 comes from. We don’t necessarily overcount or anything. Thanks!