Think of it this way:
THACO - opponent AC = number you need to hit your opponent
So if your THACO was 15 and your opponent's AC was 0, you would need 15 - which is why the THACO number is 15!! If your opponent's AC was 4, you would need 15 - 4 = 11.
The only time your to-hit roll affects damage is when you roll a natural 20 (also known as a critical hit). In this case you ALWAYS hit your opponent, and damage is doubled before any modifiers are added.
In all other cases to-hit rolls do not influence damage.
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