We examine the result from the last post.
With a probability p of hitting a monster, the average number of attacks it takes to hit is 1/p.
On a d20 (with the mods backed out), the probability of rolling greater than or equal a particular number is:
10 = 55%
11 = 50%
12 = 45%
13 = 40%
14 = 35%
15 = 30%
16 = 25%
17 = 20%
18 = 15%
19 = 10%
20 = 5%
Examining this more closely, we have 1/p for various probabilities p:
prob = 55%, average number of attacks = 1.82
prob = 50%, average number of attacks = 2
prob = 45%, average number of attacks = 2.22
prob = 40%, average number of attacks = 2.5
prob = 35%, average number of attacks = 2.86
prob = 30%, average number of attacks = 3.33
prob = 25%, average number of attacks = 4
prob = 20%, average number of attacks = 5
prob = 15%, average number of attacks = 6.67
prob = 10%, average number of attacks = 10
prob = 5%, average number of attacks = 20
As the probability to hit gets smaller than 25% (ie. greater than 16 on a d20), the average number of attacks it takes to hit such a monster goes up considerably. To minimize combat from becoming too frustrating, it would be optimal to keep the probability to hit in the range of 25% to 50% which would correspond to the range 11 to 16 on a d20. (Less than 10 would be too easy). As one may have experienced, requiring a minimum roll of 18 or 19 to hit a monster can be very frustrating.
From the 4E DMG, the generic monsters typically have minimum defenses which scale as 12+level. So even for level 1 players fighting level 1 monsters, AC/fortitude/reflex/will are at least 13. A minion may only require an 11 or 12 to hit.
