Math-hammer request

[minigun762]

Can anyone who is bored go through and find the probability of a Daemon Prince successfully using Warptime against the main forms of Psyker defense and compare the respective killing power of the DP?

 

I'm thinking you can use MEQs as the baseline for killing. For the defenses, Eldar Runes, Librarian's Hood, Space Wolves fancy item (the 3+), Tyranids Shadow of the Warp and Deathleaper's -LD ability.

[Cale]

Do you want the results in terms of probabilities or expected return?

 

And do you want the WT DP compared to a regular 4 swing DP or a 5 swing Khorne DP, and do you want to look at the DP charging or in a subsequent round?

[minigun762]

Do you want the results in terms of probabilities or expected return?

 

And do you want the WT DP compared to a regular 4 swing DP or a 5 swing Khorne DP, and do you want to look at the DP charging or in a subsequent round?

 

You read my mind Cale, I was going to compare it against the KDP as a baseline.

 

My brain usually works better in terms of expected returns, normally with MEQ as the target since that is fairly common.

 

I don't really care about charging one way or another, the results should be similar enough either way.

[Zhukov]

I'll do it later this weekend (sunday I think), if nobody else wants to do it.

 

Warn me if somebody else already does it!

[Cale]

Alright:

 

The baseline is a charging Daemon Prince with a Mark of Khorne. Six swings, threes to hit, and twos to wound:

3.33 kills on average.

 

A charging Daemon Prince with Warp Time has five swings with an 8/9 chance to hit and a 35/36 chance to wound for a total of 4.32 wounds on average, presuming he passes. If he fails, he has five swings with a 2/3 chance to hit and a 5/6 chance to wound for a total of 2.78 wounds on average.

 

Normally, this Daemon Prince has a 91.67% chance of getting the power off successfully, meaning that he does 4.19 wounds on average.

 

Under the effects of Runes of Warding, the Daemon Prince has exactly a 50% chance of successfully casting Warp Time, meaning that he has a total expected return of 3.55 wounds.

 

Under the effects of a (ld 10) Psychic Hood, the Daemon Prince has a 91.67% chance to pass his psychic test 58.33% chance to get past the Psychic Hood, for a total of a 53.47% chance of getting the power off successfully, meaning that he has a total expected return of 3.60 wounds.

 

Under the effects of a Runic Staff, the Daemon Prince has a 91.67% chance of passing his psychic test and exactly a 50% chance of getting past the Staff, for a total of a 45.84% chance of getting the power off successfully, meaning that he has a total expected return of 3.49 wounds.

 

Under the effects of Njal's Runic Staff, the Daemon Prince has a 91.67% chance of passing his psychic test and exactly a 1/3 chance of getting pas the Staff, for a total of a 30..56% chance of getting the power off successfully, meaning that he has a total expected return of 3.25 wounds

 

 

I'd do Shadow in the Warp and the Deathleaper, but I don't actually have those rules memorized. Let me know the relevant bits, and I'll work those up for you, as well.

 

 

If the Daemon Princes were not charging, the variations you would see between the Khorne Prince and the various Warp Time prince results would be slightly larger.

[minigun762]

Just to be an ass, the other potential issue to factor in might be the increased damage inflicted by multiple PotW tests.

[Cale]

I can do expected returns from PotW, too.

 

Taking a Psychic test normally (which includes under the effects of Runic Weapons, Psychic Hoods, and the Deathleaper by itself, since none of these affect the probability of getting a PotW result) a DP has a 1/16 chance of getting a PotW result and a 5.56% total probability of taking a wound after saves (presuming it doesn't have a Mark of Tzeentch). The expected return in terms of wounds per psychic test, is, therefor, 0.0566

 

Under the effects of Runes of Warding, the probability of getting a PotW is 37.5%, which means that the expected return against the Daemon Prince in terms of wounds is 0.33--about six times higher than without the Runes of Warding.

 

Under the effects of Shadow in the Warp, the probability of getting a PotW is 14.81%, which means that the expected return against the Daemon Prince in terms of wounds is 0.1317

 

 

As for the Deathleaper and Shadow in the Warp:

 

Shadow in the Warp by itself affects a Daemon Prince's expected return in exactly the same way as Runes of Warding.

 

The Deathleaper reduces the probability of the Daemon Prince successfully casting Warp Time to 58.3%, 72.2%, or 83.3%, with an even distribution. This leaves the DP with a total expected return of 3.88 wounds.

 

If we factor in both the Deathleaper and Shadow in the Warp, the Daemon Prince has a 37.5%, 25.9%, or 16.2% chance of successfully casting warp time, again with an even distribution. This combination leaves the DP with a total expected return of 3.19 wounds

 

Again, these are presuming a daemon prince with Warp Time but without a Mark of Tzeentch. They presume a turn on which the Daemon Prince is charging, and a target with T:4 or less and Ws:6 or less and no invulnerable save.

[minigun762]

Thanks Cale. Its actually kinda reassuring that even with all the crap out there, Warptime Princes still manage to get the job done.

Oddly enough, it also shows me that a KDP isn't quite as bad as people make it out to be and given the cheaper cost and lack of any chance to hurt yourself it coudl be a viable option.

[Cale]

I basically agree on both points, and I've been using Khorne DPs for a long time, now. WT does do better damage when you get it off, but I find that the extra 15 points often let me do something useful, like possess my vindicator, and that failing that psychic test irritates me in a manner that is way out of proportion to how much it actually matters.

[Zhukov]

Thanks Cale for having this done, I assume its correct haha.

Some important things miss in here though I think, which are great advantages of Warp Time:

 

Against vehicles which you hit at a 6:

-Warptime: 5x 0.3055= 1.53 hits, a 16% of no hit at all

-Khorne: 6x 1/6 = 1 hit, a 33% chance of no hit. (5/6)^6

 

So against vehicles who moved so fast that you hit them on a 6, Warptime is a very big improvement (~84% chance of at least getting 1 hit, against the ~67% chance of khorne getting at least 1 hit)

 

Against T6 Models (so MC's mainly) with WS 6 or lower:

 

-Warptime: 5x 8/9 x 3/4= 3,33 wound

-Khorne: 6x 2/3 x 1/2= 2 wounds

 

Against T6 Models with WS 7 or higher:

-Warptime: 5x 3/4 x 3/4= 2,81 wounds

-Khorne: 6x 1/2 x 1/2 = 1,50 wounds

 

Against T8 Models (so C'tan or Wraithlord?):

-Warptime: 5x 8/9x 11/36 = 1,36 wounds

-Khorne: 6x 2/3x 1/6= 0,67 wounds.

 

This shows nicely what I think is the biggest pro for warptime: It helps greatly against other MC's.

 

Other benefits:

-Apart from the general improvement on averge damage, it also lets you counter really bad rolls. (only hitting 1 or 2, or throwing multiple 1's on to wound). The overall chance of getting a really poor roll is greatly reduced by warptime.

-You cant take MoN and MoK, so if you want your prince to be more killy and more survivable: Warptime is there as an option if you want MoN or MoT (or MoS)

[Cale]

It's true that, if Warp Time goes off, your probability/return curve really humps up towards that top end, with a very low probability of getting the particularly bad rolls.

 

It's also true, though, that under the effects of psychic hosers, the Warp Time Prince has a much more widely spread probability/return curve than it does otherwise. The difference between getting warp time off almost every time and getting it off about half the time means that your prince is going to do significantly better than the Khorne prince about half the time and significantly worse than the Khorne prince about half the time. Its better performance is further above the khorne prince's performance than its worse performance is below it, but you're still looking at performing worse than a khorne prince about half the time if you're facing anti-psycher measures.

 

 

That said, it is certainly important to remember how much Warp Time helps against those fast-moving vehicles. I didn't do that math because it wasn't requested, but you're right in saying that the difference is significant.

[minigun762]

Nice information as well Zhukov. I called out MEQs as the baseline since they seemed like an appropriate yardstick to start with.

 

However vehicles and MCs (both of which are heavy in the current meta-game) are prime targets for our DPs, if not the preferred targets so again its very useful to know how valuable those rerolls can be.

[Ashe Darke]

It's almost a given that in 40k re-rolls are ideal. There's a few exceptions. First Rank FIRE! Second Rank FIRE! is one where the increase in the number of shots is better than a re-roll. Rapid fire range is the same but at full range the extra shots give you 2.5 more shots.

 

But in this case it's either a single extra attack on one guy or re-rolls on everything and this is one of the times where re-rolls just win every time as they're so invaluable. When you're used to re-roll and you don't get it it's horrible. One of my Princes today peril'd trying to cast it and got a 6 and four 1's for his rolls to hit in combat :P But because I had my re-rolls in later rounds and his MC didn't I won that combat.