
Heroscape Strategy Articles Heroscape Strategy Articles with discussions. Including Order Markers, Units, Game Play, etc. 

Thread Tools  Search this Thread  Display Modes 
#1




Fun with math or Why high variance can be a good thing
One thing that may initially seem counter intuitive to a lot of people is how different distributions can have a large effect on damage calculations even when the expected averages are the same.
To demonstrate this, let's take a look at the amount of damage inflicted on a unit with 4 defense when being attacked by figures who have different ways of achieving an average of 2 skulls. In order from the least variance to the most it would like this: 1. No Variance  Assume a fictitious unit which didn't have to roll any dice and always got 2 auto skulls Average damage on a figure with 4 defense: .790123 2. Low Variance  Sharwin  1 auto skull and 2 dice Average damage on a figure with 4 defense: .864198 3. Normal Variance  A figure who rolls 4 dice Average damage on a figure with 4 defense: .932099 4. High Variance  Zetacron or a Minion (2 dice with skulls doubled) Average damage on a figure with 4 defense: 1.061728 5. Very High Variance  A fictitious figure who rolls 1 die and quadruples skulls Average damage on a figure with 4 defense: 1.333 In all cases, the average damage is 2 skulls, but the figure with very high variance does a whopping 69% more damage then the one with no variance. What's the point of all of this? I'm not sure, but I thought it was interesting. 
#2




Re: Fun with math or Why high variance can be a good thing
I'd rather have low variance (and hence high precision) in my attacking damage, at least lower than the variance in my opponent's defense. Let them throw blanks first!

#3




Re: Fun with math or Why high variance can be a good thing
Very well thought out. Maybe this is why I prefer figures like Zetacron, the Minions, Snipers and Migol. I love taking chances! I would like to see a figure get one attack die that quadrupled, that'd be fun. Of course that sort of power would quickly become over powered if you added height, glyphs or any other attack bonus.

#4




Re: Fun with math or Why high variance can be a good thing
Sounds like a perfect candidate for a special attack.

#5




Re: Fun with math or Why high variance can be a good thing
Quote:
Of course I'm a sucker for high variance unitsD20 powers are my favorite abilites in the game. 
#6




Re: Fun with math or Why high variance can be a good thing
Thanks for the responses.
A couple more points: The difference in average damage between high variance and low variance goes up when the defense goes up relative to the expected number of skulls. Attacking a Raelin backed Q9 with a figure with 2 average skulls is much more successful with a very high variance figure then a low variance figure. At the other extreme, if attacking a hero with zero defense, there would be no difference in average damage calculations. So does that mean that higher variance always does at least as much average damage as low variance? No, which brings me to the second point. The above calculations all assume that the defending figure has at least as much life left as the highest possible attack. Clearly, if attacking a figure with only 2 life left, rolling 4 skulls 50% of the time is a waste. To sum up, if attacking a figure who has as much life left as your maximum attack, the higher variance figure will do at least as much, and often much more average damage as the low variance figure. The amount of extra damage goes up in proportion to the strength of the defender versus the expected number of skulls. One more thought, average damage aside, other strategic considerations come into play. There may be times where you'd rather have a higher chance of doing some damage at the expense of a lower average damage amount. 
#7




Re: Fun with math or Why high variance can be a good thing
Nice analysis. But one nitpick.
Quote:
For example, lets look at your mythical figure that quadruples skulls rolled. True, he has a 50% chance to roll 4 skulls. And a figure that rolls 4 normal dice only has a 6.25% chance to achieve the same number of skulls. However, that same mythical figure has a 50% chance to roll ZERO skulls. And again, with 4 normal dice, there is only a 6.25% chance of no skulls. Having said that, you do caveat your statement with "higher average damage" Interesting and thought provoking.... The future of scape is players like us who support a community like this  with new maps, scenarios and events. Playing scape. Not buying scape... QuickSetUp Map Thread The Principles of War 
#8




Re: Fun with math or Why high variance can be a good thing
This discussion illustrates why the Stingers are so good. They have variable variance. Against squad figures, it is best to use the normal attack of 3. Against heroes (especially heroes with high defense), it is better to increase the variance of the attack by using Stinger Drain.

#9




Re: Fun with math or Why high variance can be a good thing
Good analysis. Note that the results flip when we talk about defense.

#10




Re: Fun with math or Why high variance can be a good thing
Quote:
The auto 2skuller, on the other hand, has a 40.7% chance of no wounds, a 39.5% chance of one wound, and a 19.8% chance of two wounds. What he was saying is average damage, so the better the defense, the better the highrisk one stacks up. at six defense, the chance to wound is the same for both figures, and higher than that it substantially favors high risk. (In other words, the caveat was there for a reason.) 
#11




Re: Fun with math or Why high variance can be a good thing
By definition. But this is a cool post, +rep to you. I think most people don't like high variance for this reason. The highest variance are all d20 powers and those usually have a low power rankingbecause in the right situation they may be your only hope/deadly but usually they are just too high risk.

#12




Re: Fun with math or Why high variance can be a good thing
Actually I would argue that the D20 powers generally are very low variance, just in the opposite direction. Mindshackle comes to mind immediately; there is a 95% chance that you will fail that roll. That to me is low variance. Obviously it changes greatly depending on the power; Isamu has a high variance ability because it could go either way easily.
Vary interesting thread. In forest dark or glade beferned
No blade of grass shall go unturned Let those who have the daylight spurned Tread not where this green lamp has burned. 

Thread Tools  Search this Thread 
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Variance and Power At Odds?  Jexik  HeroScape General Discussion  17  May 2nd, 2009 10:18 PM 
High Risk/High Reward attacks  Onacara  Custom Units & Army Cards  9  March 2nd, 2009 03:20 PM 
Walmart nonsightings (a good thing).  nyys  Sightings and Sales  9  December 24th, 2008 11:47 AM 
Are Licensed Properties a good thing in Heroscape?  Tiak  HeroScape General Discussion  159  October 26th, 2007 04:54 PM 
Price Match....what a beautiful thing! (A Walmart Story)  archangel1021  Sightings and Sales  18  October 8th, 2007 10:32 AM 