Saying be patient doesn't work, because the numbers never do catch up unless you have an extremely long battle. In a 5-round battle Wail wins in terms of damage every single time once you're past the extreme early game. If you go longer than that Dirge can start to catch up, but how many battles do you have that last that long? Here's some #'s that I cut out of my original post to prevent people going TLDR. I have a ton of #'s below, but in the last example with a L12 Sovereign and 8 Death Shards you would need to have a ... NINE ROUND BATTLE before Dirge did more damage than Wail. And your opponents are alive for those entire nine rounds, beating the crap out of you - instead of being instantly dead the way they would be if you just cast Horrific Wail. For less than half the mana expenditure, even.
•Early game damage, L3 Sovereign, one death shard. The current winner in terms of both damage per combat and efficiency is Contagion. Changing damage would bring Dirge into first place in that category but still be dead last in efficiency. Changing mana costs would have Dirge tied with Contagion for damage but still be slightly less efficient. Calculations below.
◦Currently Dirge does (3 Base) + (1 per Shard) = 4 maximum, targets will take 1-4 points on cast and then 1-4 per round thereafter with an average of 2.5. Assuming the battle lasts for five rounds total this yields four ticks of damage (initial plus three DoT ticks) averaging 2.5 each for a total average damage of 10 per unit. Dirge also costs a staggering 64 mana to cast, an extremely steep cost for the early game Sovereign. Damage per unit of mana is (10/64) = 0.156.
◦Contagion is identical to Dirge except it only has a base of two damage. So (2) + (1) = 3 max. However since it casts faster you get one more tick out of it, so five ticks of 2 avg dmg comes out to 10 for the battle. Contagion is much cheaper to cast than Dirge, coming in at 18 mana. Damage per unit of mana is (10/18) = 0.555
◦Horrific Wail does (Level x 3) frontloaded flat damage with no ticks, doing an average of 9 damage per unit. It's mana cost is higher than Contagion, coming in at 24, for a cost of 0.37 mana per point of damage.
◦Adding damage to Dirge would yield an average of 3 dmg x 4 ticks = 12 dmg per unit with a cost of 0.187 mana per. It is now first in damage but still last in efficiency.
◦Changing the mana costs would change the efficiency of the current Dirge and Wail spells to 0.500 and 0.140 respectively, making Dirge less efficient than Contagion but much more so than Wail. Wail's dmg is all still frontloaded however, giving it a significant advantage thereby.
•Little later in the game we have a L7 Sovereign with four death shards. This is only really possible if you are actively converting other types to death. Currently Horrific Wail is now solidly in first place with both the most damage (completely frontloaded as well) and the best ratio damage per mana expended. Changing damage values for Dirge would bring it slightly ahead of Wail. Changing mana costs would put Dirge between Contagion and Wail in terms of efficiency. Calculations below.
◦Mana costs and damage values now include bonuses from Path of the Mage. This is important for the DoT spells, since they still can do a single point of damage.
◦Currently Dirge does 11 maximum (it rounds up) with 6 average damage. Four ticks is 24 damage with a damage per mana of 0.50.
◦Contagion does 9 max with 5 avg damage. Four ticks is 20 damage, with a damage per mana of 1.48. ◦Horrific Wail does 32 damage with an average damage per mana of 1.77.
◦Adding damage to Dirge would yield an average of 9 dmg x 4 ticks = 36 dmg per unit with a cost of 0.562 mana per. It is now first in damage but still less than 1/3 as efficient as the competitors.
◦Changing the mana costs would change the efficiency of the current Dirge and Wail spells to 1.00 and 0.50 respectively, making Dirge less efficient than Contagion but much more so than Wail.
•Extending this idea, lets try a L12 Sovereign with 8 death shards and Evoker II. Now eight shards is a lot, to have this many you have to have aggressively expanded and taken them from your neighbors, then converted most or all of them to death shards. Horrific Wail is now doing almost 75% more damage than its competitors, all completely frontloaded, and for a fraction of the mana cost.
◦Currently Dirge does 22 maximum with 11.5 average damage. Four ticks is 46 damage with a damage per mana of 0.95.
◦Contagion does 20 max with 10.5 avg damage. Four ticks is 42 damage, with a damage per mana of 3.00.
◦Horrific Wail does 72 damage with an average damage per mana of 4.00
◦Adding damage to Dirge would yield an average of 19.5 dmg x 4 ticks = 78 dmg per unit with a cost of 1.21 mana per. It is now first in damage but still incredibly inefficient.
◦Changing the mana costs would change the efficiency of the current Dirge and Wail spells to 1.91 and 1.12 respectively, making Dirge still be less than 2/3 as efficient as Contagion, but still better than Wail.