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Subject: Card/Unit Balance rss

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Ross Atkinson
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I have started with the basics of creating a new game that will eventually be both a digital card miniature/unit game. I have the game mechanics roughly done on paper (though I still have some ability order to work out but that is more about balance).

What I am working on now is card/unit creation and I am having some trouble with my balancing formula. One of the mechanics of the game is each deck/army can only have a certain amount of points worth of cards/units. I have all my information inputted into a excel spreadsheet and google doc.

I am wondering if my basic formulas are even close to correct before I start some play testing. I just want some community suggestions to see if I am close before play testing to find I was heading the wrong direction.

I have 5 main variables that each unit has (Attack, Health, Speed, Range, and Dice/Turn). Each card card/unit also has its own set of abilities and categories that also have points. There is also a rarity modifier that changes the final point value by 4% for each increase in rarity. That rarity modifier is not something I am worried about however.

To make my situation even more complex I am designing the game to operate in 3 different modes (normal, easy, and quick).

Attack and Health variables are self explanatory and the same across all game modes.

Speed and Range are both the same and different in different game modes. In normal mode you move you cards/units on a board based on their speed and they can attack a set amount away based on their range. In easy and quick modes the range and speed variables are added together to determine which unit attacks first on a line. As an example all the five speed/range (five being the units speed and range added together) group will attack, then the four group, then the three group, etc.

Dice/Turn is also slightly different in the different game modes. In normal and easy mode you will select what cards to play based on a dice roll that will allow you to play card/units up to the rolled number based on their Dice/Turn cost. For example if you roll a five you could play a two and a three cost Dice/Turn Unit or a one and a four or a zero and a five. In quick mode the cards auto play as drawn from a deck after staying in your hand based on the Dice/Turn of the card. This mode is basically you clicking begin then the game auto-playing. An example of this is you draw your first card with a Dice/Turn cost of three it hits the board three turns later.

Now the formulas I use. There is no formula I am using for the cost of abilities and categories I have just assigned an arbitrary cost and am sure I will have to change it later with play testing for balance. However the cost of these abilities will always be the same across all cards/units. So if Regeneration5 costs 18 points on one unit it will cost 18 points on every other unit that has that ability. The same for categories. I have detailed categories and each has its own cost. For example I have Were, Wolf, Male, Female and Animal. I could use these to create a card/unit with Were, Wolf, Male or a card unit with Animal, Wolf, Male.

The formula I mainly want help with, and the point of this rather long post, is the balancing of the Attack, Health, Speed, Range, and Dice/Turn variables. Their current values are as follows and probably subject to an extraordinary amount of change back and forth over time.

Attack = 6 points per point of attack, Health = 3 points per point of health, Speed = 9 points per point of speed, Range = 9 points per point of range, and Dice/Turn = 400 for 0 cost with the rest of the points using the formula 400 divided the units Dice/Turn cost divided by 2.

Below is my excel formula for this where B4 is Attack, C4 is Health, D4 is Speed, E4 is Range, and F4 is Dice/Turn Cost

=SUM(B4*3 + C4*6 + D4*9 + E4*9 + (IF(F4=0, 400, 400/F4/2)))

For anyone who wants shoot me a pm with their email, I will add you to a version of this that is in my google docs so you can view the full spreadsheet formula. Though all the units I have are not added to it yet.
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Mark J
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Are you asking if we think that your specific relative weights are correct, or if the general formula is good?

As to the specific weights, I don't think it's possible to say without more information. You say that Attack and Health are self-explanatory. But, umm, not necessarily. I'm guessing that Attack is a measure of how much damage you do when you attack, and Health is a measure of how much damage you can take before you die. But, does every Attack do attack-points hits of damage? Or is there a die roll or some other randomizer? What's the nature of the formula? Like is it that you do an amount of damage somewhere between zero and your Attack number? Or that the higher the attack number the more likely you are to hit? Or what? Likewise there are many possible ways that Health could work. I guess the most common is that each hit takes away some number of Health points, and when you reach zero you're dead. But in most games you can regain health points in various ways. And there are games that use totally different formulas, like if the damage inflicted is greater than your health points, you're dead, otherwise you're unhurt. etc.

As to the general formula: The idea isn't bad. Whether it works is hard to say. Like for example, assuming that Attack is how much damage you do for every hit and Health is how much damage you can take before you're dead, and ignoring all other factors for the moment, suppose you had one unit with attack=5 and health=5, total value = 5*3+5*6=45. Another unit has attack=30 and health=1, total value = 30*3+5*1=96. Is the second unit really twice as good as the first? Sure, his first attack he'll probably take out whoever he targets. But he's a one hit wonder, because surely he'll be high on the other side's target list and quickly taken out. Likewise adding attack and range could be misleading. A unit with attack=5 and range=50 is probably much more valuable than a unit with attack=150 and range=1. The first unit could hide way behind the lines and pound an enemy before they could get close. The second unit might well never got off a shot before being killed. The difference between a health of 20 and a health of 2000 may be meaningless if the nature of the game is such that it's almost impossible to inflict more than 5 hits on one unit before the game is over. Etc etc.

That said, I may well be nit-picking. Coming up with a general rating scheme that works for all possible combinations of values in all possible circumstances may be totally impractical. Especially if you're trying to keep the scheme to a simple formula, it may be that you just come up with something that's sort of in the ballpark. Then test it with some actual gameplay. If you discover that, say, units with high health are proving much more valuable than the scoring system gives, then up the multiplier for that attribute. Etc.
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Ed Chen

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I think the only way you will find out if your formulas are ok is to playtest it.

The only thing I have to add of potential value is I've heard from several people that having perfect balance is often not desirable because it tends to make choices meaningless.
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Beau Bocephus Blasterfire
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You might want to decide what the weakest unit is and what the most powerful unit is and scale everything in between. As far as whether the numbers work out, you will need to play test to find out. I hope all the math you are doing is something that players need not repeat for themselves when they are trying to figure things out. Best of luck to you.
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Justin R
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Oman wrote:

Attack = 6 points per point of attack, Health = 3 points per point of health, Speed = 9 points per point of speed, Range = 9 points per point of range, and Dice/Turn = 400 for 0 cost with the rest of the points using the formula 400 divided the units Dice/Turn cost divided by 2.

Below is my excel formula for this where B4 is Attack, C4 is Health, D4 is Speed, E4 is Range, and F4 is Dice/Turn Cost

=SUM(B4*3 + C4*6 + D4*9 + E4*9 + (IF(F4=0, 400, 400/F4/2)))


Just one clarification note, your description of the Dice/Turn summand is ambiguous--i.e., (400/F4)/2 =/= 400/(F4/2) You should consider using parentheses in the third element of the IF statement so that you can keep it straight. Though I believe you got it right, as the latter expression in my above inequality produces counterintuitive results.
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Ross Atkinson
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saneperson wrote:
Are you asking if we think that your specific relative weights are correct, or if the general formula is good?

As to the specific weights, I don't think it's possible to say without more information. You say that Attack and Health are self-explanatory. But, umm, not necessarily. I'm guessing that Attack is a measure of how much damage you do when you attack, and Health is a measure of how much damage you can take before you die. But, does every Attack do attack-points hits of damage? Or is there a die roll or some other randomizer? What's the nature of the formula? Like is it that you do an amount of damage somewhere between zero and your Attack number? Or that the higher the attack number the more likely you are to hit? Or what? Likewise there are many possible ways that Health could work. I guess the most common is that each hit takes away some number of Health points, and when you reach zero you're dead. But in most games you can regain health points in various ways. And there are games that use totally different formulas, like if the damage inflicted is greater than your health points, you're dead, otherwise you're unhurt. etc.

As to the general formula: The idea isn't bad. Whether it works is hard to say. Like for example, assuming that Attack is how much damage you do for every hit and Health is how much damage you can take before you're dead, and ignoring all other factors for the moment, suppose you had one unit with attack=5 and health=5, total value = 5*3+5*6=45. Another unit has attack=30 and health=1, total value = 30*3+5*1=96. Is the second unit really twice as good as the first? Sure, his first attack he'll probably take out whoever he targets. But he's a one hit wonder, because surely he'll be high on the other side's target list and quickly taken out. Likewise adding attack and range could be misleading. A unit with attack=5 and range=50 is probably much more valuable than a unit with attack=150 and range=1. The first unit could hide way behind the lines and pound an enemy before they could get close. The second unit might well never got off a shot before being killed. The difference between a health of 20 and a health of 2000 may be meaningless if the nature of the game is such that it's almost impossible to inflict more than 5 hits on one unit before the game is over. Etc etc.

That said, I may well be nit-picking. Coming up with a general rating scheme that works for all possible combinations of values in all possible circumstances may be totally impractical. Especially if you're trying to keep the scheme to a simple formula, it may be that you just come up with something that's sort of in the ballpark. Then test it with some actual gameplay. If you discover that, say, units with high health are proving much more valuable than the scoring system gives, then up the multiplier for that attribute. Etc.


I think I said self explanatory as a way to just get out of explaining them. Attack and Health in this game are very basic. Attack is the damage done each turn by the Card/Unit and Health is how much damage you can take before you are destroyed.

Nit-picking is fine because it makes me make sure I have thought out things and that I have not overlooked something. I know I may have to come up with a more complex formula that scales or some such but I figured it was better starting out basic and building from there if it becomes obvious during play testing that basic will not work.

I didn't expect anyone to have some perfect formula for me to use only recommendations like, it may better to start with health worth 3 times as much as attack because from their experiences with card games it usually is worth about that much more.

random user wrote:
I think the only way you will find out if your formulas are ok is to playtest it.

The only thing I have to add of potential value is I've heard from several people that having perfect balance is often not desirable because it tends to make choices meaningless.


I know perfect balance will not work but I hope that the rarity percentage scale will help offset it enough to be viable as well balanced.

bbblasterfire wrote:
You might want to decide what the weakest unit is and what the most powerful unit is and scale everything in between. As far as whether the numbers work out, you will need to play test to find out. I hope all the math you are doing is something that players need not repeat for themselves when they are trying to figure things out. Best of luck to you.


The only problem with taking the weakest card/unit now and the strongest, is that I will be constantly adding more cards/units so these will probably eventually change. If I do it this way I think I would be worried about power creep.

No worries the complex math is all on me on the back end. One of the reasons I am using excel so I do not have to add things up myself. I find basic math in games like addition and subtraction ok but anything more complex would seem like to much to me.

JJRR_Esq wrote:
Oman wrote:

Attack = 6 points per point of attack, Health = 3 points per point of health, Speed = 9 points per point of speed, Range = 9 points per point of range, and Dice/Turn = 400 for 0 cost with the rest of the points using the formula 400 divided the units Dice/Turn cost divided by 2.

Below is my excel formula for this where B4 is Attack, C4 is Health, D4 is Speed, E4 is Range, and F4 is Dice/Turn Cost

=SUM(B4*3 + C4*6 + D4*9 + E4*9 + (IF(F4=0, 400, 400/F4/2)))


Just one clarification note, your description of the Dice/Turn summand is ambiguous--i.e., (400/F4)/2 =/= 400/(F4/2) You should consider using parentheses in the third element of the IF statement so that you can keep it straight. Though I believe you got it right, as the latter expression in my above inequality produces counterintuitive results.


Yeah I was not quite sure how to put that into words but I hoped it was easy enough to understand (400/F4)/2 is the correct way to write it mathematically.

The long formula is the exact excel spreadsheet formula and not the mathematical formula. That is why it seems a little odd.

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Jeremy Lennert
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First off: I have found that coming up with formulas for estimating how powerful a particular unit, ability, or other asset is going to be is invaluable for balancing a game, but only as a starting point. After calculating the predicted value, I make adjustments based on how I think the various parts are going to interact and synergize, then try playing with it to test my assumptions, then often make further adjustments. And the formulas tend to evolve over the course of design and playtesting, gradually becoming more nuanced as I have more examples to work from and a better understanding of the particular game's strategy.

If you are imagining that once you've created a formula you can just let plug in any numbers you want and as long as you satisfy your equation the results will all be perfectly balanced, you are likely to be disappointed.



As for your actual formula, I think Sane Person is correct that there are some pretty important details missing from your background. For example: what is the goal of the game? If you have to defend your starting area, then movement speed could be worth very little; if you have to race to contest distant objectives, then it could be critical.

Regardless, I think it's unlikely you're going to get away with anything as simple as you proposed: the utility of a stat is probably not linear, and probably not independent of your other stats (e.g. high attack value is probably more valuable on a unit that also has long range). If an attacker has a lot of freedom in choosing which target to attack--which is pretty common (as opposed to the defender choosing which target to block with)--I suspect that a unit's value will be more closely related to the product of attack and health than to their sum.

And it's unlikely that specialized abilities are going to be equally valuable no matter what unit you put them on; Regeneration will probably be better on high-health unit than a high-damage unit, for example.

If you establish a bunch of "baseline" archetypal units to fill various strategic niches and then use your numbers only for evaluating small changes to a unit that you already know is balanced, then just assigning point values to each stat and ability might be OK. But even then, you probably need different values for different archetypes.



Have you tried playing your game yet? If you haven't, you should aim to do that as early as practical--balancing is generally easier with a few plays under your belt.
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Mark J
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JJRR_Esq wrote:
Oman wrote:

Attack = 6 points per point of attack, Health = 3 points per point of health, Speed = 9 points per point of speed, Range = 9 points per point of range, and Dice/Turn = 400 for 0 cost with the rest of the points using the formula 400 divided the units Dice/Turn cost divided by 2.

Below is my excel formula for this where B4 is Attack, C4 is Health, D4 is Speed, E4 is Range, and F4 is Dice/Turn Cost

=SUM(B4*3 + C4*6 + D4*9 + E4*9 + (IF(F4=0, 400, 400/F4/2)))


Just one clarification note, your description of the Dice/Turn summand is ambiguous--i.e., (400/F4)/2 =/= 400/(F4/2) You should consider using parentheses in the third element of the IF statement so that you can keep it straight. Though I believe you got it right, as the latter expression in my above inequality produces counterintuitive results.


(400/F4)/2 = 200/F4

400/(F4/2) = 800/F4

Not sure why you break it out that way. Maybe if I knew where the formula came from it would be clear why that was more intuitive.
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Mark J
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random user wrote:
I think the only way you will find out if your formulas are ok is to playtest it.

The only thing I have to add of potential value is I've heard from several people that having perfect balance is often not desirable because it tends to make choices meaningless.


If all units are just as good in all circumstances, then yeah, I guess it doesn't matter which you pick.

Something I really like in a game is when different units are preferable in different situations, and before selecting units you have to consider the terrain you'll be fighting on, what enemy you'll be fighting, your objectives, etc. And these things change from turn to turn.

Like, one of my favorite computer games was the original Master of Orion. In that game you could build space ships with a wide variety of weapons and defenses. I was fighting an enemy with very large, well-armored, but slow ships, so I built a fleet with very large and powerful but relatively inaccurate guns. Sure, we missed the target a lot, but every hit was devastating. I won the war. Then I met another enemy with a very large number of small and fast ships. My fleet was almost useless. It was like trying to kill flies with a cannon. Sure, if I hit one he was destroyed with one shot. But I didn't have enough shots to get every one of the swarm of attackers, and most of my shots missed.
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