Today I saw a forum post asking what the benefit was from a +1 to hit bonus. That seems like a very simple question with an obvious answer. Sure enough, the next post responded that a bonus of +1 to hit means that you hit 5% more often. That is a common answer and later posters all accepted it. Unfortunately, this answer is incorrect.

This is a common misconception. It is often expanded upon by saying that since you hit 5% more often, you do 5% more damage overall and effects caused by a successful hit are imposed 5% more often. These later statements would be true if the original assumption wasn’t flawed.

A bonus of +1 to hit increases your chance to hit by 5%. That is quite different from hitting 5% more often. In addition, your chance to hit does not always increase by 5%.

Let’s take the exceptions first. If you have a +7 combat modifier (from level, strength, etc) and are attacking a creature with an armor class of 30, you can only hit on a roll of 20 (which is always a hit). Therefore, you have a 5% chance to hit. If you then receive a bonus of +1 to hit, your combat modifier increases to +8. Unfortunately, you still only hit on a roll of 20. Your chance to hit is unaffected by the +1 to hit bonus. But then, the guy in our example should have been running away screaming instead of trying to slug it out.

A more common example would be at the other end of the spectrum. If you have a combat modifier of +12 and are attacking a creature with an armor class of 10, you will only miss on a roll of 1 (which is always a miss). Therefore, you have a 95% chance to hit. A bonus of +1 to hit won’t change that. No matter how many pluses you have, a roll of 1 will always be a miss.

Middle of the Road

So let’s put extremes aside. If you have a combat modifier of +12 and are attacking a creature with an armor class of 15, you need to roll 3 or higher to hit. That means that you have a 90% chance to hit. A bonus of +1 to hit increases your chance to hit to 95%. To determine how much more often you will hit, divide 95% by 90%. In this example, you will hit 5.56% more often. That’s a little more than 5% but nothing to get very excited about.

The harder the creature is to hit though, the more you gain from that +1 bonus. If you have a combat modifier of +12 and are attacking a creature with an armor class of 30, you need a roll of 18 or better to hit. That means you have a 15% chance to hit. A bonus of +1 increases that to a 20% chance to hit. That’s the same 5% increase in your chance to hit. However, in this case, that +1 bonus allows you to hit 33% (20% divided by 15%) more often!

Diminishing Returns

An obvious result is that each additional +1 bonus to hit has less and less impact on how often you hit.