A decent number of Fighter dailies have the Reliable tag: not expended on a miss. WotC seems to be roughly (and I mean that "roughly") equating Reliable power-wise with 1/2 damage on miss. Is this justified? The answer is: Reliable is slightly worse than 1/2D on miss, in general.
The math comparison between reliable and 1/2D turns out to be fairly simple. As a toy problem, imagine three abilities, a Daily Reliable one that deals D damage on a hit, a Daily 1/2 damage on miss ability that also deals D damage on a hit, and an at-will ability (used after the daily is expended) that deals A damage on a hit. We will assume that none of these abilities use different attack numbers/defenses, that the probability of a hit is h (and that of a miss is m=1-h).
The trick is to realize that calculating the average damage for a certain number of rounds amounts to summing over all possible to-hit roll sequences (with average damage). If we feed the same attack roll sequence to both Daily abilities, we can see that:
A) if the first attack is a hit, both abilities have the same result.
B) if the first attack is a miss, then everything AFTER the first hit is the same (both abilities leave you using at-wills)
Then we can see that if, over a sequence of N attacks, every attack is a miss, the 1/2D ability does D/2 extra damage over the Reliable one. This has a probability of occuring of m^N=(1-h)^N and thus increases the damage output of the 1/2D attack over the reliable one by:
m^N*(D/2).
If, instead, over a sequence of N attacks, the first one misses AND there is at least one hit, then, from the first attack up to and including the first hit, the 1/2D ability does D/2 (first swing)+A damage while the Reliable one does D damage. This has a probability of occuring of m*(1-m^(N-1)) and leads to the Reliable ability doing:
m*(1-m^(N-1))*(D/2-A) damage over the 1/2D one.
So, the first thing to notice is that if D<=2A, reliable is always worse that 1/2D on miss. Very, very roughly, D=2A throughout a fighter's career. The second thing to notice is that if D>2A, then a long enough fight will have Reliable being better than 1/2D on miss. Note that if D is only slightly greater than 2A, this fight length may well be long enough to not matter.
Reaping Strike. As an at-will ability, Reaping Strike is very nice. In the above toy model, we assumed that the at-will ability only does damage on a hit. If the fighter in question has Reaping Strike, he gets to add (average number of misses before the first hit for a fight of length N rounds-1)*(Str or Str/2) damage to A for purposes of weighing Reliable vs. 1/2D on miss. This very rapidly swings things against Reliable.
Debuffs/Effects: a potential advantage of Reliable is that is means you *will* eventually land your status effect. On the other hand, most 1/2D on miss abilities w/status effects land a reduced status effect on a miss. Then you need to weigh the benefits of a status effect *now* vs a better one later AND the possibility of the at-will landing status effects of its own (Tide of Iron is the only significant one here, although Lasting Frost+Frost weapon could also count).
The math comparison between reliable and 1/2D turns out to be fairly simple. As a toy problem, imagine three abilities, a Daily Reliable one that deals D damage on a hit, a Daily 1/2 damage on miss ability that also deals D damage on a hit, and an at-will ability (used after the daily is expended) that deals A damage on a hit. We will assume that none of these abilities use different attack numbers/defenses, that the probability of a hit is h (and that of a miss is m=1-h).
The trick is to realize that calculating the average damage for a certain number of rounds amounts to summing over all possible to-hit roll sequences (with average damage). If we feed the same attack roll sequence to both Daily abilities, we can see that:
A) if the first attack is a hit, both abilities have the same result.
B) if the first attack is a miss, then everything AFTER the first hit is the same (both abilities leave you using at-wills)
Then we can see that if, over a sequence of N attacks, every attack is a miss, the 1/2D ability does D/2 extra damage over the Reliable one. This has a probability of occuring of m^N=(1-h)^N and thus increases the damage output of the 1/2D attack over the reliable one by:
m^N*(D/2).
If, instead, over a sequence of N attacks, the first one misses AND there is at least one hit, then, from the first attack up to and including the first hit, the 1/2D ability does D/2 (first swing)+A damage while the Reliable one does D damage. This has a probability of occuring of m*(1-m^(N-1)) and leads to the Reliable ability doing:
m*(1-m^(N-1))*(D/2-A) damage over the 1/2D one.
So, the first thing to notice is that if D<=2A, reliable is always worse that 1/2D on miss. Very, very roughly, D=2A throughout a fighter's career. The second thing to notice is that if D>2A, then a long enough fight will have Reliable being better than 1/2D on miss. Note that if D is only slightly greater than 2A, this fight length may well be long enough to not matter.
Reaping Strike. As an at-will ability, Reaping Strike is very nice. In the above toy model, we assumed that the at-will ability only does damage on a hit. If the fighter in question has Reaping Strike, he gets to add (average number of misses before the first hit for a fight of length N rounds-1)*(Str or Str/2) damage to A for purposes of weighing Reliable vs. 1/2D on miss. This very rapidly swings things against Reliable.
Debuffs/Effects: a potential advantage of Reliable is that is means you *will* eventually land your status effect. On the other hand, most 1/2D on miss abilities w/status effects land a reduced status effect on a miss. Then you need to weigh the benefits of a status effect *now* vs a better one later AND the possibility of the at-will landing status effects of its own (Tide of Iron is the only significant one here, although Lasting Frost+Frost weapon could also count).
