NAF block dice fairness test

The dice of Zeus always fall luckily. Sophocles

Dice are funny things. If you play games a lot, especially wargames, you get use to how fickle they can be. In Blood Bowl, "Nuffle" the god of luck, has cost me more game than I care to remember by punishing me for daring to roll dice. Some people have mad rituals around dice and how they roll them, change them after they roll low, blow on them for luck etc. For me a dice is a random implement and so superstition has no place at my table. I do though, often wonder, if any dice are truly random, especially custom dice.


So I decided to test a set of NAF Blood Bowl dice by rolling them a thousand times and seeing how far they deviated from what would be expected by randomness.


A simple test but one that should highlight any potential problems with the fairness of the dice.


I decided to set the measure of statistical significance
at 5% (p-value >= 0.05). That would mean that the actual dice outcomes would have to deviate by 5% or more from the expected outcomes for the test to indicate a potential problem. I figured 5% over 1000 rolls should be safe enough. 


Test results

Outcomes	Total	Expected	% diff
Pow	171	166.67	2.60
Pow!	160	166.67	-4.00
Skull	162	166.67	-2.80
Pow/Skull	163	166.67	-2.20
Push	344	333.33	3.20
Check	1000	1000	0.00

Conclusions

The dice all stayed within the 5% threshhold and so from this test, I am pretty sure, the NAF Blood Bowl block dice are safe to use.

Rolling more dice would provide a greater degree of certanty, so the results would be safer after 10,000 or even 100,000 rolls but even at 1,000 the results seem pretty sound to me.

Blood Bowl Zombie vs Skeleton resilience comparison

....it ain't about how hard you hit, it is about how hard you can get hit and keep moving forward, how much can you take and keep moving forward. That's how winning is done! Rocky Balboa (2006)
 

I was talking to Lycos at the Chelmsford Bunker Bowl in October 2011 and we got to discussing the undead team, in particular my loathing of the over-costed Skeletons. They used to cost 30K but recently (in Blood Bowl terms) moved to 40K for the addition of "Thick-Skull".


So Lycos, NAF president and all round good guy (he got my vote again this year), said that he always takes at-least one Skeleton in his Undead team. He explained that he took them mainly for the increased movement but also because they are just as resilient as a Zombie due to the "Thick-Skull" skill.


I, on the other hand am a Zombie guy, sure he is only movement 4, but he is a top drawer meat shield and foul bot. I personally never go near Skeletons unless I am playing Khemri.


So I thought I would have a quick scan over the numbers and see what comes out.


The challengers

1. Skeleton AV7 with Thick-Skull
2. Zombie AV8 

Percentage chance of breaking armour for each

1. Skeleton 41.67%
2. Zombie 27.78%

 Percentage chance of getting a KO of better for each

1. Skeleton 11.58%
2. Zombie 11.58%

 Percentage chance of getting a injury for each

1. Skeleton 6.95%
2. Zombie 4.63%

So the conclusion is, that if you are looking at the narrow band of getting a KO or better then the Zombie and Skeleton come out identical. However, in regards to both Stunned and Casualty results, the Skeleton is 50% more likely to be on the receiving end than the Zombie. Is that increased Stunned and Casuality rate worth the trade for the increased movement value? Not in my books, but then I have won exactly zero NAF tournaments and Lycos has a houses full of trophies.

GF9 Menoth Battlefield in a Box for £17.50 (off topic)

I just came across this deal on Amazon for the GF9 Menoth Battlefield in a Box.

They originally retailed for £50 but now you can get the Menoth (and unfortunately only the Menoth one) for £17.50.

Link below...

http://www.amazon.co.uk/Battlefield-Box-Protectorate-Menoth-Warmachine/dp/B003NTQWX4/ref=sr_1_4?ie=UTF8&qid=1325766458&sr=8-4

They are pretty good quality and come pre-painted. We had all 4 of the GF9 set (Cygnar, Menoth, Cryx and Khador) at Tanelorn and I have just today picked one up for the Chelmsford Bunker. I can highly recommend them.

Get yourself a nice late Christmas present, it will liven up your battlefield and make Menoth players go weak at the knees.

Heavy Warbeast survivability

"None of you seem to understand. I'm not locked in here with you. You're locked in here with ME!"  Rorschach

First off, Warbeast are more complicated than their Metal Mickey counterparts. Animi (plural of Animus?) and lots of other tricks make these results a little less solid than the Warjack set. 

The Animus "Bump" is a perfect example. If you hit the Skorne beast Tiberion once with "Bump" up, you get pushed away 3". This would prevent any further attacks. There are way to prevent "Bump" working but it all gets complicated. I decided to ignore "Bump" for this test.


On top of that, Warbeast are more expensive than Warjacks because of Fury mechanic and the extra utility they usually bring. 


I feel you would be better served comparing the Survivability rating within faction, rather than across faction.


That being said, on with the test.




Test:


How many hits would it take to destroy different Beasts per cost point of the model?
To explain further, if a model costs 7pts and needed 7 hits to be destroyed, then the survivability rating would be 1.00.

Assumptions:

1. Attacking model has Mat 6, P&S 17, and can perform as many melee attacks as needed to complete the job.
2. All defensive buffs the Beasts possess are up (Spiny Growth, Warping etc).
3. Things that occur in melee, like Unyeilding are on, but things that break the combat, like the animus "Bump" are off.

Example: 


I do not want to get into hot water with PP for publishing a list of Def, Arm, Pt cost and Damage boxes for its models and so will give as an example the Legion Carnivean, whose rules are freely available as part of the Quick Start Rulebook.
The Carnivean has Def 11, Arm 20 (with Spiny Growth), has 30 boxes and costs 11 points.
He will be hit 83.3% of the time by MAT 6 and will take 4 damage on average when hit by P&S 17.
This runs to 3.33 damage taken per attack and so the Carnivean will be destroyed after 9.00 attacks.
The Carnivean costs 11 points and so dividing 9.00 by 11 gives you the value 0.82, it's survivability rating.




Results: 


Table 1.1:

Rank	Faction	Model	Survivability
1	Skorne	Sentry	1.33
2	Circle	Feral	1.24
3	Circle	Ghetorix	1.22
4	Skorne	Archidon	1.17
5	Skorne	Tiberion	1.09
6	Skorne	Gladiator	1.04
7	Skorne	Cannoneer	1.00
8	Circle	Pureblood	0.99
9	Legion	Angelius	0.95
10	Legion	Seraph	0.94
11	Skorne	Bronzeback	0.91
12	Circle	Wold Guardian	0.86
12	Circle	Stalker	0.86
14	Circle	Shadowhorn	0.84
15	Minion	Blackhide	0.83
16	Legion	Carnivean	0.82
17	Minion	War Hog	0.81
18	Skorne	Rhinodon	0.77
19	Circle	Gnarlhorn	0.75
20	Troll	Earthborn	0.74
21	Skorne	Molik Karn	0.73
22	Troll	Blitzer	0.72
22	Troll	Mauler	0.72
22	Minion	Road Hog	0.72
25	Circle	Woldwarden	0.71
26	Circle	Megalith	0.69
27	Troll	Mulg	0.68
28	Legion	Scythean	0.67
29	Troll	Bomber	0.65
30	Minion	Ironback	0.61
30	Legion	Typhon	0.61
32	Legion	Ravagore	0.60
33	Troll	Rok	0.59
34	Legion	Proteus	0.55
35	Minion	Swamp Horror	0.53

The table 1.1 shows the outcomes for each Warbeast up to Domination releases.

• Skorne take the Khador role and are dominant in this category with half the top 10.
• A big surprise however, was how good some Circle models appear to be, 3 of the top 8 are Wolfs.
• Trolls seem a bit lame but if you factor in Krielstone bearers. They get quite a bit better.
• Legion have problems and the Flying models have clearly the best Survivablilty, followed by the Carnivean (due to it's Animus).
• Minions came off badly.
  

Conclusions:


Skorne has the clear advantage in this catergory, but for the rest, good Def seems to be better than good Arm.