Elf smacking in numbers - Optimizing Piling On usage

[Carnis]

Calculated this for our league forum. Might as well translate it here as well:

MB/Piling on statistics on AV7

Basic damage on a knockdown vs armor 7:
15/36 to pass armor *9/36 KO, *1/6 CAS
=> 225/1296 chance of KO or worse, 90/1296 chance of CAS.

Baseline then: 225/1296 or 17,3% / and 90/1296 or 6.9% KO+/CAS+ per knockdown.

MB PO player can improve this by:
Odds of getting a KO+ | CAS+
+180/1296 | +96/1296 = +13,9% / CAS +6,9% by using MB.
+6075/46656 | +2790/46k = +13% / CAS +6% by using PO to reroll armor.
+4725/46k | +2250/46k = +10% / CAS +4,8% by using PO to reroll stuns*.
+1890/46k | +756/46k = +4% / CAS +1,6% by always using PO to reroll stuns.

This is a local maximum for maximal removal chance with the following odds:
Total KO+ chance: 27270/46k = 58,4%
Total CAS+ chance: 12492/46k = 26,8%

Notice how rerolling stuns without MB available is the least efficient. Even then, the PO player has 41% odds of removing opposing player. The odds increase is minor, because it is the rarest event, where piling on can be used beneficially.

For maximizing CAS, knockout rerolls with PO may be beneficial:

Odds of getting a KO+ | CAS+
225/1296 | 90/1296 = KO+ 17% / CAS 6,9%, base
+180/1296 |+96/1296 = 13,9% / CAS +7,4%, using MB
+6075/46656 | +2790/46k = +13% / CAS +6%, using PO to reroll armor
+4725/46k | +2250/46k = +10% / CAS +4,8%, using PO to reroll stuns*
+1890/46k | +756/46k = +4% / CAS +1,6%, always using PO to reroll stuns
-2475/46k | +1650/46k = -5,3% / CAS +3,5%, using PO to reroll KOs*
-1134/46k | +324/46k = -2,4% / CAS +0,7%, always using PO to reroll KOs

Local maximum for casualties:
Total KO+ chance: 23661/46k = 50,7%
Total CAS+ chance: 14466/46k = 31%

The last tradeoff -2,4% KO+ for a +0,7% increase in CAS is probably suboptimal.

Optimal elf-hunting PO usage:
Always use MB (+14%/7%).
Always reroll stuns (+14%/6,4%)
Always reroll armor (+13%/6%).
Always reroll KO*, but not without MB available (-5,3%/+3,5%).

Odds then:
Total KO+ chance: 24795/46k = 53,1%
Total CAS+ chance: 14142/46k = 30,3%

*whilst MB is still unused

The odds of damage for each strategy in a table in odds and in percent:
P% = opponents chance to be prone, S% = chance be stunned, etc..

Code: Select all

        Prone/1296 Stun/46k KO/46k CAS/46k P% S% K% C%
AV7:       756     11340    4860   3240    58 24 10 7
MB7:       540     12636    7884   6696    42 27 17 14
MBPA7:     225     17901    11169  9486    17 38 24 20
MBPAS7:    225     11286    14778 12492    17 24 32 27
MBPASK*7:  225     13761    10653 14142    17 30 23 30
MBPASK7:   225     14895    9195  14466    17 32 20 31

AV7 = BASE DAMAGE
MB7 = USE MB
PA7 = USE PO ON ARMOR
PAS7 = USE PO ON ARMOR/STUN
PASK*7= USE PO ON ARMOR/STUN, AND KO* IF MB IS AVAILABLE
PASK7 = ALWAYS USE PILING ON, IF NO CASUALTY

Odds ratios for best strategies versus no skills:

Code: Select all

          Prone Stun  KO  CAS  KO+CAS
Default:  1     1     1   1    1
MB7:      0.72  1.13  1.7 2    1.82
MBPAS7:   0.29  1     3.2 3.85 3.41
MBPASK*7: 0.29  1.25  2.3 4.28 3.12

Odds of knocking down and killing Blodgers with different skillcombinations with 2die blocks (and 3DB for MB/PO, a common skill/die combination with big guys):
KO+ | CAS+ (odds below).
Odds of opponent [T = Standing P = Prone, S = Stun, K = Knock, C = CAS] after being blocked in percent.

Code: Select all

                   KO+        CAS          T% P% S% K% C%
No skill:   11/36 *225/1296  |*90/1296   = 69 18 7  3  2
Frenzy:  627/1296 *225/1296  |*90/1296   = 52 28 11 5  3
Tackle:     20/36 *225/1296  |*90/1296   = 44 32 14 6  4
MB:         11/36 *405/1296  |*186/1296  = 69 13 8  6  4
MBFrenzy:627/1296 *405/1296  |*186/1296  = 52 20 13 8  7
MBTackle:   20/36 *405/1296  |*186/1296  = 44 23 15 9  8
MBPiling:   11/36 *27270/46k |*12492/46k = 69 5  8  10 8
3D MBPO:   91/216 *27270/46k |*12492/46k = 58 7  11 14 10
MBPOFrenzy:627/1296*27270/46k|*12492/46k = 52 8  12 15 13
MBPOTackle: 20/36 *27270/46k |*12492/46k = 44 9  14 18 15

[Marlow]

This is a local maximum for maximal removal chance with the following odds:
Total KO+ chance: 27270/46k = 58,4%
Total CAS+ chance: 12492/46k = 26,8%

Interesting. I never realised it was quite so high.

[Smeborg]

Marlow - yes, it's very high. You can't get better against an AV7 opponent than a 58.45% chance of a K.O. result or better. You get the same odds against AV8, AV9, AV10 if you also have Claw!

However it looks better than it is, because you have to knock down your opponent first. In a developed Elven team, you can expect plenty of Block+Dodge+Sidestep, not to mention Fend, which will in most cases prevent Piling On. And if the Elves are hiding, you may only get one Blitz per turn after the first.

Against an undefended player you get (say) a 3/4 chance of knocking him down.
Against a player with Block or Wrestle ou get (say) a 5/9 chance of knocking him down.
Against a player with Block/Dodge you get (say) an 11/36 chance of knocking him down.
Against a player with Fend you get no chance to pile on (ignoring Grab and Juggernaut).

So you actually get a wide range of odds from 9.5% to 44% (K.O. result or better). Still rather good, but low enough for the "win first, die later" strategy of the Elven teams to work often enough.

Carnis - I will admit that I rarely re-roll a K.O. result unless it is a "dead" turn, or the match is already decided. Getting players off the pitch is good enough for me.

[Carnis]

Against an undefended player you get (say) a 3/4 chance of knocking him down.
Against a player with Block or Wrestle ou get (say) a 5/9 chance of knocking him down.
Against a player with Block/Dodge you get (say) an 11/36 chance of knocking him down.
Against a player with Fend you get no chance to pile on (ignoring Grab and Juggernaut).

Carnis - I will admit that I rarely re-roll a K.O. result unless it is a "dead" turn, or the match is already decided. Getting players off the pitch is good enough for me.

My last table actually acknowledged the problem of getting knockdowns, and it covers everything except the case of the undefended player (Block, Blodge, Fend are covered in the last table). I'll admit I've never played against player who can prevent MB/PO with fend, whilst mb/po denial with block/dodge and positioning is commonplace. And indeed, the odds run all the way from: 10% KO or worse with MB to 33% with a 3skilled tackle/MB/PO against a blodger.

I also rarely actually get to reroll KOs. Lately only my norse team (with 3 MB/PO combined with 2 frenzy and one frenzy/tackle) and usually only after the first 4 or so turns. Or my last game with halflings.. Rerolling KO'd halflings (when MB is up) gives you 52% CAS, which is ace .

[Baduk]

I find this topic offensive

[mattgslater]

And at least a touch unsportsmanlike!

[quozl]

That's interesting - I hadn't realised how similarly effective MB is compared to tackle when hitting elves with dodge!

You're less likely to get them down, so it's less of a sure thing, but if all you're doing is using your 1 blitz a turn to hit a wardancer, you're almost as well off hitting them with the MB guy as the tackle guy.

I had a game with my underworld - one blitzer had block, MB, claw, piling on, and the other had Block, tackle.
There were 2 opponent AG5 witch-elves. I hit them with the tackle guy, but this shows I actually should have hit them with the MB/PO guy for sure instead.

Thanks.

[DoubleSkulls]

A while ago I did most of the skill & Av combinations

http://slobb.doubleskulls.net/injury.php