I was replying to this guide earlier on, and it got me thinking about why I tend to build Death Prophet the way I do. Is there a best way to do it?
It's quite tricky as you really want many early levels in Crypt Swarm, at least 1 level in Silence (for ganks) and at least 1 level in Witchcraft to make your level 1 Exorcism suck less. The mana cost reduction and speed increase of Witchcraft also make it very enticing for many players - it's really quite useful.
Ok, so lets oil up TheXyrusOmeter, cos it's maths time!
Lets look at why I usually go with this build...
Early game nukes and magic damage are pretty much king - they tend to secure the kills, deal the serious harassment and generally run the show. They often fall off the side of a cliff late game as they don't scale however.
Mana pools and regen are also a big issue early game - unless you've got access to a mana battery like Keeper of the Light or Sacrifice then you have to be pretty careful to get value from it. Clarity potions might be better, but they generally force you to play more passively if you want their benefit.
We can summarise these two things into one number by working out their "Damage Per Mana Point" - this gives us a very good idea of their general efficiency, and lets us work out good ways of levelling.
Here's the info on Crypt Swarm by itself:
Lvl \ Dam \ Mana \ DPM (Damage Per Mana)
1 \ 100 \ 105 \ 0.95
2 \ 175 \ 120 \ 1.46
3 \ 250 \ 140 \ 1.79
4 \ 300 \ 165 \ 1.82
Ok, hopefully that makes sense to you. We can also see an interesting feature of Crypt Swarm - the scaling is a bit out, almost all other nukes are waaaay more mana efficient at level 4 than at level 3 - this barely scrapes it. Obviously level 1 sucks, but we should expect that.
Ok, next up, lets bring Witchcraft into that mix, it reduces the cost of your other two spells by 10/15/20/25.
Hero Level 2-3
Level 1 Crypt Swarm with Level 1 Witchcraft:
100 damage now costs (105-10) mana = 1.05 DPM
Level 1 Crypt Swarm with Level 2 Witchcraft:
100 damage now costs (105-15) mana = 1.11 DPM
Level 2 Crypt Swarm with Level 1 Witchcraft:
175 damage now costs (120-10) mana = 1.59 DPM
Hero Level 5
Level 3 Crypt Swarm with Level 1 Witchcraft:
250 damage now costs (140-10) mana = 1.92 DPM
Level 1 Crypt Swarm with Level 3 Witchcraft:
100 damage now costs (100-20) mana = 1.25 DPM
Level 2 Crypt Swarm with Level 2 Witchcraft:
175 dam costs (120-15) mana = 1.67 DPM
Hero Level 7
Level 1 Crypt Swarm with Level 4 Witchcraft:
100 damage now costs (100-25) mana = 1.33 DPM
Level 4 Crypt Swarm with Level 1 Witchcraft:
300 damage now costs (165-10) mana = 1.94 DPM
Level 3 Crypt Swarm with Level 2 Witchcraft:
250 damage now costs (140-15) mana = 2.00 DPM
With both skills maxed you reach an eventual efficiency of 2.14 DPM. Peak efficiency is actually 2.17 with Level 3 Crypt Swarm and level 4 Witchcraft.
Quick summary of those last few levels:
3CS+3WC = 2.08
4CS+2WC = 2.00
3CS+4WC = 2.17
4CS+3WC = 2.07
It's pretty clear that getting Crypt Swarm levelled over Witchcraft is far more efficient than levelling Witchcraft first. This also tends to play out in game experience - having a single more powerful nuke is generally better than more, less powerful ones. You don't generally get to cast many when ganking, and higher burst damage is generally more scary and decisive than more frequent weak damage (it gives people less reaction/movement time).
There may be circumstances where you need Silence earlier (i.e. you think either set of supports will gank mid), but generally speaking, this is most efficient early Death Prophet build:
What about not taking DP ult at lvl 6? Most mids start moving around the map after maxing their nuke and having their ults, so you can't really take the enemy mid tower very easily before that. Also the lvl 1 Exorcism is kind of weak and maxing Witchcraft before taking ult lets you have a more powerful ult and more efficient Crypt Swarm. I think some players used this build in TI.
The issue you run into with this mentality is that you wont be able to take a tower until lvl 7, or worse 8, or even worse 9 depending on how far you neglect your ult. The fact is that if you take your ult at level 6 you achieve a higher gank ability that can easily transition to a tower, or at least most of a tower.
At lvl 6 you should have at least one level of Witchcraft making Exorcism have 7 spirits each with 1 attack per second (no increase of attackspeed and a BAT of 1 so dps = (1 + IAS)/BAT) at an average damage of 55.5. This means your ult is dealing roughly 1 * 55.5 * 7 = 388.5 damage per second at lvl 1 (hero level 6) and damages towers. Compare that to a lvl 3 Crypt Swarm + lvl 3 Witchcraft that only deals 50 damage per second and doesn't damage towers. Level 1 Exorcism doesnt really suck, it just sucks compared to lvl 2 or lvl 3 with lvl 4 Witchcraft (999 dps and 1498.5 dps respectively). Now you do have to take into consideration the unruly nature of the damage being dealt and the fact that the damage is reduced by armor so those numbers are most likely slightly lower, but still much grater than maxing CS and WC.