Author Topic: Simplified attack/defense rating for comparison purposes  (Read 1276 times)

Zelc

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Simplified attack/defense rating for comparison purposes
« on: September 07, 2015, 08:59:31 AM »
I'm surprised we haven't developed a system to summarize a unit's attack and defense stats. It takes a long time to type out A(5) 5/5, D 2/2. I think it'd be nice to summarize that as something like 10 attack 4 defense.  Here's a system for doing so. The purpose is a simplified system to refer to similar types of units generally against a benchmark of the A(5) 5/5 D 2/2 stats. This rating does not to capture the different nuances of different attack and defense stats (i.e. counter matchups), nor does it capture one-time effects like charge bonuses, impact hits, etc (although you can say this unit has X attack, and Y attack on the charge).  It's not intended to serve as a replacement for point costs and the formula.

Update 1: tweaked numbers on the skew
Update 2: tweaked numbers on skew again

Defense Rating:
Step 1: Add up the defensive skill and toughness.
Step 2: Adjust for skew. Add 0.25 if the skew is 2, and add an additional 0.5 for every difference above that.

Examples:
D 2/2 = 4 + 0 = 4 DR
D 1/3 = 4 + 0.25 = 4.25 DR
D 0/3 = 3 + 0.75 = 3.75 DR
D 1/4 = 5 + 0.75 = 5.75 DR
D 3/3 = 6 + 0 = 6 DR


Attack Rating:
Step 1: Add up the offensive skill and power.
Step 2: Adjust for skew. Subtract 0.25 if the skew is 2, subtract 0.25 + 0.5 = 0.75 total if the skew is 3, and subtract an additional 0.75 for every skew above 3.
Step 3: Adjust for dice. If number of dice is greater than 5, add 0.5 x (number of dice over 5). If number of dice is less than 5, subtract 0.5 for 4 dice, and subtract 1 for each die below that.

Examples:
A (5) 5/5 = 10 + 0 + 0 = 10 AR
A (5) 6/5 = 11 + 0 + 0 = 11 AR
A (5) 4/6 = 10 - 0.25 + 0 = 9.75 AR
A (5) 3/7 = 10 - 1.5 + 0 = 8.5 AR
A (8) 5/5 = 10 + 0 + 1.5 = 11.5 AR
A (3) 6/5 = 11 + 0 -1.5 = 9.5 AR
A (4) 4/7 = 11 - 0.75 - 0.5 = 9.75 AR


The Vanilla Swordsmen has 10 AR and 4 DR.  "Balanced" unit stat lines seem to be 8 AR and 2 DR, 9 AR and 3 DR, 11 AR and 4.5 DR, and 12 AR and 5 DR.
« Last Edit: September 10, 2015, 02:19:17 PM by Zelc »

Kevin

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Re: Simplified attack/defense rating for comparison purposes
« Reply #1 on: September 07, 2015, 10:14:49 AM »
Good call!  I really don't think you need to adjust for skew.  If you really want to do so, you're a full order-of-magnitude too much!  Like the multiplier should be around .05 or maybe .1. 

I would put in an adjustment to reflect hit points, though.  Here's something quick-and-dirty:

-0.5 if it has 8 or fewer hit points.
+0.5 if it has 12 or more hit points.
+1 if it has 15 or more hit points.
+0.5 if fearless


Again, I'd take out the skew adjustment from the attack rating (or make it a lot smaller).   I'd also make the dice adjustment a flat 0.5 per die above or below 5.
However beautiful the strategy, you should occasionally look at the results. - Winston Churchill

Zelc

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Re: Simplified attack/defense rating for comparison purposes
« Reply #2 on: September 07, 2015, 10:48:57 AM »
I'd take out the skew adjustment from the attack rating (or make it a lot smaller).   I'd also make the dice adjustment a flat 0.5 per die above or below 5.
Adjusting for skew for defense is really important:
Against A(5) 5/5, D 1/4 and D 3/3 both average 0.56 damage. You'll note both of them are 6 DR.

Adjusting for skew on offense and for dice are also important. The reason it's a full -1 for 4 dice -> 3 dice is because that's usually when 1 dice is worth as much as 1 attack stat against a 2/2 stat line. Obviously the flat addition/subtraction isn't perfect, but it gets close.

Against D 2/2, A(3) 6/5 averages 1 damage. It's 9.5 AR, which gets it right between A(5) 5/5 (1.25 damage) and A(5) 4/5 (0.83 damage).
Against D 2/2, A(5) 4/6 and A(4) 4/7 both average 1.11 damage. A(5) 5/5 averages 1.25 damage. You'll note A(5) 5/5 is 10 AR while the other two are both 9.5 AR.


Maybe skew should be .25 points, with an additional +/-1.25 if defense is 3 or above, or if offense is 3 or below.

EDIT: Ok I tinkered with it some more :).


Quote
I would put in an adjustment to reflect hit points, though.  Here's something quick-and-dirty:

-0.5 if it has 8 or fewer hit points.
+0.5 if it has 12 or more hit points.
+1 if it has 15 or more hit points.
+0.5 if fearless
I didn't want to do hit points because there are so many variations and Courage makes a huge difference :). While hit points have an effect on offense and defense, I'd much rather track them in a separate rating. Haven't thought about how I want to do that.
« Last Edit: September 07, 2015, 11:07:16 AM by Zelc »

Kevin

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Re: Simplified attack/defense rating for comparison purposes
« Reply #3 on: September 09, 2015, 11:57:10 AM »
Quote
I'd take out the skew adjustment from the attack rating (or make it a lot smaller).   I'd also make the dice adjustment a flat 0.5 per die above or below 5.
Quote
Adjusting for skew for defense is really important:
Against A(5) 5/5, D 1/4 and D 3/3 both average 0.56 damage. You'll note both of them are 6 DR.

Except that you're assuming that you'd spam 5/5 units no matter what you're facing.  Put me up against Undead or Wuxing and I'm going to be filling my army with as many power 6 and 7 units as possible.  Put me up against High Elves or even Carthage and I'm going for skill 6+.  So in practice, no a 1/4 isn't close to being as good as a 3/3.  (Except maybe in Ravenwood if the opponent expects a bunch of Elves but faces a tree.)
« Last Edit: September 11, 2015, 06:35:45 AM by Kevin »
However beautiful the strategy, you should occasionally look at the results. - Winston Churchill

Zelc

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Re: Simplified attack/defense rating for comparison purposes
« Reply #4 on: September 10, 2015, 02:17:11 PM »
I could remove the extra 0.25 bonus for a defense of 4+ and cap the increase at 0.75 for skew on offense, but I think the rest of the system accurately reflects the value of skew.

BubblePig

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Re: Simplified attack/defense rating for comparison purposes
« Reply #5 on: September 10, 2015, 11:14:38 PM »
You do have to draw the line somewhere, but from a metagame standpoint certainly 1/4 in a faction that has 3/1 units is a whole lot more of a bargain to me than 1/4 in a faction with a bunch of 1/3, 2/3 etc. (and conversely the 3/1 units are also a better bargain) depending on how much choice the opponent has to skew his attack profile in response.