söndag 6 september 2015

Tweaking summoning costs

Hi everyone!

The time has come to finally tweak the summoning costs of the PPC, in accordance to the odds of actually getting the spell off and how many points you can summon with the spell.

To let you in on how I will work this out, I've taken some time to write the procedure down for you. This is very important to me, as summoning is one of the hottest debates in the AoS game! Some think summoning is way to overpowered, while others think it should be free. The way I describe below will be the goal of this tweak - if any cost is to change later on, it will be from reports of actual gameplay and not by theoryhammering. :)


Warning, this is a long read with lots of number crunching!

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To start this off, we need to know how often you can expect to get a summoning spell off in the game. According to dice probabilities, we have the following results when rolling 2d6:

Total roll of
2 is 2.77%
3 is 5.55%
4 is 8.33%
5 is 11.11%
6 is 13.88%
7 is 16.66%
8 is 13.88%
9 is 11.11%
10 is 8.33%
11 is 5.55%
12 is 2.77%

This means that if you have a summoning spell that needs 5 or more to be successful, you have a
2.77+5.55+8.33 = 16,65% risk of it being unsuccessful, or a (100-16,65) = 83,35% chance of success!

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Now, depending on how high you rolled, your opponent will have a varying chance of unbinding your successful spell.
For example:
If you rolled a 5, your opponent would need a 6 or higher to unbind, which according to the table above is a 72.18% chance.
If you rolled a 9, your opponent would need a 10, 11 or 12 to unbind, which is only a 16,65% chance when adding the chances from the table together.

The problem is that what your opponent need for his unbinding is dependant on how high you rolled in the first place. To calculate the general odds of a spell getting unbound, we need to add all these chances together:

Unbinding on 
a 6+ is 72,18%.
a 7+ is 58,3%
a 8+ is 41,64%
a 9+ is 27,76%
a 10+ is 16,65%
a 11+ is 8,32%
a 12 is 2,77%

There is a joker in this, however, since if you rolled a 12 when casting the spell, your opponent cannot unbind it at all!

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Adding all the unbinding chances (including the joker) results in the following chance to successfully unbind a typical spell with a 5+ casting value:
(72,18+58,3+41,64+27,76+16,65+8,32+2,77)/8 = 227,62/8 = 28,45%.

So, if you do successfully cast a spell that needs 5+ to succeed, your opponent would have an average chance of 28,45% to unbind it. To this, we must of course add the actual probabilty of the spell to be cast successfully in the first place. As we've already noted above, there is an 83.35% chance of successfully casting a 5+ spell.

The total chance of successfully casting a 5+ summoning spell, including both the casting chance and the unbinding risk, is therefor: 0,8335*(1-0,2845)=0,5963 or 59,63%.

So about 60% of the times you cast a 5+ summoning spell, it will go off successfully.

Let's fast forward to me having calculated spells that succeeds on 6+, 7+, 8+, 9+ and 10+ as well:
  • a 5+ spell is successfully cast 60% of the time.
  • a 6+ spell is successfully cast 56% of the time.
  • a 7+ spell is successfully cast 49% of the time.
  • a 8+ spell is successfully cast 37% of the time.
  • a 9+ spell is successfully cast 26% of the time.
  • a 10+ spell is successfully cast 16% of the time.

What this tells us is that even if a summoning spell allows you to summon say a 200 pts unit, it will most likely only succeed 16-26% of the time, depending on if its cast on 9+ or 10+.

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The next thing to consider is how many turns you have to summon units, and if there is something else you would rather be doing with your magic, such as giving a 20 models strong unit of Grave Guard a +1 modifier to armor save from Mystic Shield, or trying to finish that annoying hero off with an Arcane Bolt.

For my calculations, I will assume that a wizard has four turns of vial summoning in a typical game, and that in the latter three of these turns it will be hard choice whether or not it's better to actually cast another spell instead. For those three turns, I will therefor halve the value of the summoning spell.

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Allright, let's calculate the simplest of the summoning spells:

RAISE DEAD 
80 pts
- Casting value of 5.
- Summons 40 pts of Undead.

One turn of full summoning where there is a 60% chance of successfully summoning a 40 pts unit:
1*0,6*40 = 24 pts.

And then three turns of summoning, still with a 60% chance of success, but where other spells could prove more useful (i.e. halving the worth):
3*0,6*20 = 36 pts.

Adding these values together would point towards a spell cost of 24+36 = 60 pts for the Raise Dead spell. That's 25% lower than what the cost is currently at, and means that if you manage to cast it only once you will have paid a higher cost for the spell than for the unit, but if you manage to cast it twice you have gained +20 pts worth of free models.

But we are not quite finished yet. The summoned unit will award victory points to the opponent when slain! How do we calculate this? I will go the easy route and take away 1/4 of the points cost for the spell to compensate for the possibility of giving away free victory points to your opponent. For the Raise Dead spell, its new profile will be:

RAISE DEAD 
45 pts
- Casting value of 5.
- Summons 40 pts of Undead.

I think this will better reflect the utility of being able to summon a unit in objective games, while making sure it's cheap enough to actually warrant some play.
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Now you know how I will calculate the upcoming tweaks to every summoning spell. Feel very free to comment on this below or on our PPC Comp discussion thread at Dakkadakka HERE!

Thanks!

2 kommentarer:

  1. please during the process of working out how expensive and how difficult a summoning spell should be take into account that at the end the undead shouldnt feel like there being punished for being the undead, coming back to life is really there thing. Taking into account prices for command groups etc

    SvaraRadera
    Svar
    1. Exactly - there needs to be a balance between how an army should function and what unbalances the game. Previously summoning spells cost too much for what they would actually do. I think that with these tweaks, we will have spells that are tactically good for a proper cost.

      Radera