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  #1  
Old September 18th, 2009, 09:22 PM
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Half-Wounds: Reducing Variance in Wounds Dealt Per Attack

Original Post:
A lot of people love the simplicity of the wound system, especially in that it requires very little bookkeeping. One downside though, in my opinion, is the all-or-nothing nature of wounds.

I would like to consider using a hit point system in my home games that would reduce variance in the amount of damage inflicted per attack, but I'm not sure how to do so while keeping bookkeeping to a minimum.

Has anyone tried a hit point system with HS and does anyone have any suggestions?

Thanks


Killer, Simple Idea:
Quote:
Originally Posted by rouby44 View Post
In order to decrease variance in number of wounds inflicted per attack, do the following:

Rule 1.
Wound markers now represent half of a wound.

Rule 2. When rolling attack or defense dice, count all blanks as half of a skull or shield, respectively (do not apply half symbols to special powers such as Stealth Dodge).

Rule 3.
When a squad figure receives a half wound, place one wound marker on the tile that that figure occupies. When a hero receives any number of wounds or half wounds, place them on its army card as per the official rules.


That's it! It's amazingly simple and requires no extra bookkeeping, complex formulas, or transformations, yet it achieves the goal of reducing the extreme variance in wounds dealt per turn that I set out to do.

Example 1:
Attack Dice: 3
Result: 1 Skull, 1 Shield, 1 Blank
Total Attack: 1.5

Defense Dice: 3
Result: 1 Skull, 2 Blanks
Total Defense: 1

Wounds dealt: 1.5 - 1 = .5

Resolution:
One wound marker is placed on a defending hero's army card or on the space that a defending squad figure occupies.

Example 2:
Attack Dice: 5
Result: 2 Skull, 1 Shield, 2 Blank
Total Attack: 3

Defense Dice: 3
Result: 1 Skull, 1 Shield, 1 Blank
Total Defense: 1.5

Wounds dealt: 3 - 1.5 = 1.5

Resolution:
Three wound markers are placed on a defending hero's army card or a squad figure is destroyed.

Last edited by rouby44; September 19th, 2009 at 03:02 AM.
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  #2  
Old September 18th, 2009, 09:57 PM
Warlord Alpha Warlord Alpha is offline
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Re: Has anyone experimented with hit points instead of wound

Very interesting idea. You would have to do something crazy with Atk/Def/Life stats for it to work, though.

The easiest way I can think to do it would be to just multiply everything by a factor of 10. So, Charos would have 90 life, 50 defense, and 50 attack.

You would probably need to simulate it on a computer or something, because that is some serious dice rolling, but you see that that would be a way to do it. Maybe you could do like triple it or something, and you get less precise but then you can realistically roll it.
_______________________________

That is really the only way I can think to do it without having to do all kinds of re-balancing.
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  #3  
Old September 19th, 2009, 01:11 AM
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Re: Has anyone experimented with hit points instead of wound

Quote:
Originally Posted by Warlord Alpha View Post
The easiest way I can think to do it would be to just multiply everything by a factor of 10. So, Charos would have 90 life, 50 defense, and 50 attack.
Unfortunately, it's not quite that simple. Multiplying all attack, defense, and life values by a constant like you suggested actually changes the distributions of average damage inflicted per attack and chance of at least one wound. An example will help me explain this a lot better:

Consider the average amount of wounds inflicted with 3 attack versus 3 defense: it's .75 wounds.

If we double the attack and defense values, we get 6 attack and 6 defense, but the average amount of wounds inflicted in this scenario is 1.28, which is not equal to .75(2).

Quote:
Originally Posted by Warlord Alpha View Post
You would probably need to simulate it on a computer or something, because that is some serious dice rolling, but you see that that would be a way to do it. Maybe you could do like triple it or something, and you get less precise but then you can realistically roll it.
Yes, I think there probably is a way to deduce a formula for converting attack, defense, and life values into a hit point system, but it won't be as simple as just multiplying. I'll have to think deeper about how to do this...

One interesting dimension that can be added via a hit point system is that of variance
or consistency. For instance, two units could have the same average attacking power, but one might produce attacks that hover very near to their average while the other unit's attack power varies to a greater extent from turn to turn, but averages out to be the same as the first unit's.

Here's how that might work: Let's say that in order to determine damage dealt for Unit A, your forumla is (D10) + 11. In other words, you roll a 10-sided die once, and then add 11. So in this case your average attack would be 5.5 + 11 or 16.5.

For Unit B, your attack formula is 3(D10) for an average attack of 16.5

So the average attack ratings are the same, but Unit A's rolls will have a lower standard deviation. In other words, their individual attacks will be more similar to each other than Unit B's attacks will be.

Quote:
Originally Posted by Warlord Alpha View Post
That is really the only way I can think to do it without having to do all kinds of re-balancing.
I'm afraid a lot of re-balancing would be in order, but I'm up to the challenge. I've already done a lot of that anyway (see link in sig - Official Units Revisited - for how I currently play HS at home with friends).

Last edited by rouby44; September 19th, 2009 at 02:35 AM.
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  #4  
Old September 19th, 2009, 01:40 AM
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Re: Has anyone experimented with hit points instead of wound

Ok, I think I've got a pretty killer and simple idea.

In order to decrease variance in number of wounds inflicted per attack, do the following:

Rule 1.
Wound markers now represent half of a wound.

Rule 2. When rolling attack or defense dice, count all blanks as half of a skull or shield, respectively (do not apply half symbols to special powers such as Stealth Dodge).

Rule 3.
When a squad figure receives a half wound, place one wound marker on the tile that that figure occupies. When a hero receives any number of wounds or half wounds, place them on its army card as per the official rules.


That's it! It's amazingly simple and requires no extra bookkeeping, yet it achieves the goal of reducing the extreme variance in wounds dealt per turn that I set out to do.

Example 1:
Attack Dice: 3
Result: 1 Skull, 1 Shield, 1 Blank
Total Attack: 1.5

Defense Dice: 3
Result: 1 Skull, 2 Blanks
Total Defense: 1

Wounds dealt: 1.5 - 1= .5

Resolution:
One wound marker is placed on a defending hero's army card or on the space that a defending squad figure occupies.

Example 2:
Attack Dice: 5
Result: 2 Skull, 1 Shield, 2 Blank
Total Attack: 3

Defense Dice: 3
Result: 1 Skull, 1 Shield, 1 Blank
Total Defense: 1.5

Wounds dealt: 3-1.5 = 1.5

Resolution:
Three wound markers are placed on a defending hero's army card or a squad figure is destroyed.

Last edited by rouby44; September 19th, 2009 at 02:33 AM.
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  #5  
Old September 19th, 2009, 04:07 PM
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Re: Half-Wounds: Reducing Variance in Wounds Dealt Per Attac

There is no way to reduce the variance of attacks without the figures being rebalanced. Some figures value(or lack of value) comes from its variance. For instance with zero variance an attack of 2 would be exactly the same as an attack of 1 with double-strike(Omnicron Sniper).
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Old September 19th, 2009, 05:13 PM
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Re: Half-Wounds: Reducing Variance in Wounds Dealt Per Attac

Quote:
Originally Posted by Sisyphus View Post
For instance with zero variance an attack of 2 would be exactly the same as an attack of 1 with double-strike(Omnicron Sniper).
I don't follow.

If an attack has zero variance, that means it is always produces the same result.

An attack of 2 dice, would always produce the mean result (1 skull), and I don't see how that is equivalent to rolling one attack die with Double Strike, because the latter result will vary.
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Old September 19th, 2009, 05:24 PM
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Re: Half-Wounds: Reducing Variance in Wounds Dealt Per Attac

Quote:
Originally Posted by rouby44 View Post
Quote:
Originally Posted by Sisyphus View Post
For instance with zero variance an attack of 2 would be exactly the same as an attack of 1 with double-strike(Omnicron Sniper).
I don't follow.

If an attack has zero variance, that means it is always produces the same result.

An attack of 2 dice, would always produce the mean result (1 skull), and I don't see how that is equivalent to rolling one attack die with Double Strike, because the latter result will vary.
average skulls with two attack = 0.5 * 2 = 1
average skulls with 1 attack double-strike = 0.5 * 1 * 2 = 1

variance skulls with two attack = (1 - 0)^2 * 0.25 + (1 - 1)^2 * 0.5 + (1 - 2)^2 * 0.25= 0.5
variance skulls with 1 attack double-strike = (1 - 0) ^2 * 0.5 + (1 - 2)^2 * 0.5 = 1


The average number of skulls is the same in each case but the difference in variance is why in general an attack from an Aubrien Archer is better against low defense squads and and attack from an Omnicron Sniper is better against high defense heroes.
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Old September 19th, 2009, 05:25 PM
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Re: Half-Wounds: Reducing Variance in Wounds Dealt Per Attac

Quote:
Originally Posted by Sisyphus View Post
For instance with zero variance an attack of 2 would be exactly the same as an attack of 1 with double-strike(Omnicron Sniper).
One other thing I should point out is that abilities such as Deadly Strike (and Shields of Valor, Stealth Dodge, Lethal Sting, etc.) would still applied within the half-wound system, but their affects are based only on dice that show actual symbols, not on any blanks rolled.

For instance, if a Minion with Deadly Strike rolled 1 skull and 1 blank, the net result would be 2(1 skull) + .5 skulls for a total of 2.5 skulls.

And yes, I see that this does change the distribution of possible attacking outcomes for the Minion, and so in the sense that his point-cost is based upon that distribution, his value has been changed - I think that is the point you were trying to make.

But changing that distribution of outcomes is the entire point of the half-wound system. It is a very subtle effect, applied universally, and shouldn't drastically affect the value of any particular unit.
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Old September 19th, 2009, 05:47 PM
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Re: Half-Wounds: Reducing Variance in Wounds Dealt Per Attac

Your title says "reducing variance in wounds dealt per attack" so that is what I am assuming you are trying to do. I just don't understand WHY you want to do this.
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Old September 19th, 2009, 06:03 PM
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Re: Half-Wounds: Reducing Variance in Wounds Dealt Per Attac

Quote:
Originally Posted by Sisyphus View Post
Your title says "reducing variance in wounds dealt per attack" so that is what I am assuming you are trying to do. I just don't understand WHY you want to do this.
Basically, I just want dice rolls to tend towards their average expected result more closely than they currently do (but not too much) and thus make figures perform more consistently.

This consistency is reflected in the standard deviation of a unit's attack and defense rolls. I know you have thorough understanding of the concept of standard deviation, Sisyphus, but for those who might be following this thread that do not, standard deviation is the average amount by which scores differ from the mean. For example, take two different data sets:
Data Set A has scores of 5, 6, and 7. The mean (average) score is 6, and the standard deviation is 2/3, because that is the average amount by which scores differ from the mean of 6. For the math behind this, check the spoiler.
Spoiler Alert!

Data Set B has scores of 3, 6, and 9. The mean is still 6, but the standard deviation has jumped up to 2, because that is the average amount by which scores differ from the mean of 6.
Although this example was exaggerated for purposes of illustration, Heroscape dice rolls are more comparable to Data Set B than Data Set A, and I want to make them more like Data Set A.

This gives a slight nudge to the skill factor and takes away a little bit of the luck factor in determining a game's outcome. This is just the personal preference of my play group, and I only advocate it for people with similar play styles to us.
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Old September 20th, 2009, 10:32 AM
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Re: Half-Wounds: Reducing Variance in Wounds Dealt Per Attac

Interesting idea but it does negate the flagbearers' abilities that count the symbol side (or blank side) as a skull or a shield.

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Old September 20th, 2009, 11:21 AM
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Re: Half-Wounds: Reducing Variance in Wounds Dealt Per Attac

Anything to make my Groks last longer!

In all seriousness, this is a pretty neat idea, but it seems like it will make combat resolution take longer, and it will make the fight, in general, take longer.


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