Hey guys,

I`m working on a formula to determine the values of a bonus. The formula should create balanced boni.

I personally think that things like:
V=n-1 or V=n/2 (with n = the amount of territories within the bonus)

are not really working out to well.

A while back I created this formula:

V = T/2 + 0.05*B + 0.2*DBO + -0.2*DBW

In this formula
V = Bonus value
T = Amount of territories within that bonus
B = Amount of territories that border the bonus
DBO = Double Borders from other boni
DBW = Double borders within the bonus

The T/2 is my personal standard. It can be set to anything else.
T*(2/3) is also a good possibility for example. You`ll have to alter it to your liking. But for balanced maps I think T/2 works the best.

0.05*B because I think it is important to note that boni on the edge on the map are usually easier to defend. They have less sides they can be countered from. The amount of territories that borders a bonus makes a difference for flanking and possible routes of attack. A bonus that has more "enemy" territories around it, should be worth more than another bonus. This could make some boni very overpowered (like a 2 territory bonus in the middle of a map. It can gain quite some extra value if its territories are big). It is limited to 0.05*B and not 0.1*B or something like that to avoid boni getting to powerfull.

0.2*DBO (Double Borders Outside) because I think that if there is a territory that double borders your bonus, it should be accounted for. Double borders make a bonus harder to defend. Double borders can make such a difference that a bonus sometimes becomes unpickable. To counter this these boni get a bonus.

-0.2*DBW (Double Borders Within). If the opposite of the DBO is happening and your bonus double borders another bonus, it should be accounted for aswell. In this case your bonus becomes worth less, as it is easier to take out connected boni if they have about the same value.

After that the bonusvalues work very easily:
Values between 0.50 and 1.49 are rounded to a value of 1. and so on for every other number.

NOTES:
1. Double borders are only double borders if they belong to the same bonus. If a territory connects to two territories that aren`t from the same bonus it obviously isn`t a double border.

2. Superboni and such do not count for this formula, nor are double borders from superboni included.

3. If a territory has multiple double borders it counts for multiple double borders (as an example: Congo on the ME map double borders both South Africa and East Africa. So it counts as two DBW.
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The formula has not been tested yet, and is also not finished yet. I`m not completely happy with some values (like 0.2 for DBO and DBW, it means a bonus with a double border has a difference of 0.4 with a connecting bonus).
I also haven`t thought about territories that border 3+ territories of an enemy bonus yet. That should be taken into account as well.
Also exposed and safe territories still needs to be added to the formula. As they also make a big difference.

The biggest fear I have is that this formula neutralizes the advantages gained from bottlenecks and double borders too much. With that it would kill a part of the strategic value of this game. As I said it hasn`t been tested yet, but if it would seem to be the case then the formula needs to be altered.

I do not think this formula is perfect or finished. If some people could come up with ideas to help some of the problems that would be nice!
Thanks in advance ^^

NOTE: the formula is for designing maps, not templates :)

Edited 10/23/2016 16:33:39

too complicated. better adjust bonus values with good sense if necessary.

The only surefire way to come up with a good formula is to test it repeatedly. I would recommend starting with bigger coefficients (the numbers that multiply each variable), such as:

V = (1)*T + (1)*B + (1)*DBO - (1)*DBW

This will be wildly unbalanced, but it should give you a better sense of what each unit of the different variables is 'worth'.

I tend to think that such small coefficients like 0.05 for B will not have enough of an effect on the resulting value of V, making it much harder to get a good sense of what the best coefficient should be. Notice that with 0.05, it will only have an effect on bonuses with around 10-20 neighbouring territories. 10*0.05 = 0.5, and 20*0.05 = 1.0. It depends on whether you're rounding up or down, or to the nearest whole number.

How many maps out there have bonuses with 20 neighbouring territories?

Likewise with DBO and DBW. Try it with bigger coefficients. Who knows, you might get some interesting gameplay mechanics with big coefficients. You'll never know till you try. :-)

Once you have a sense of what the different variables are 'worth', you can adjust the coefficients down to more normal values, test it again, and keep tweaking and testing until you find a good solid combo.

Edited 10/26/2016 16:25:34

There is no well defined fitness function so it's best to just stick with something that's sort of alright. Me and zxctycxz always go for n/2 rounding up and our maps have done pretty well.

Sorry for the late repy guys, been very busy lately.

too complicated. better adjust bonus values with good sense if necessary.

I'd probably be able to do this. But there are also mapmakers who aren't good enough at WarLight to properly assign values to all boni. The formula is also to help them, its not just for me.

The only surefire way to come up with a good formula is to test it repeatedly. I would recommend starting with bigger coefficients (the numbers that multiply each variable), such as:

V = (1)*T + (1)*B + (1)*DBO - (1)*DBW

This will be wildly unbalanced, but it should give you a better sense of what each unit of the different variables is 'worth'.

I tend to think that such small coefficients like 0.05 for B will not have enough of an effect on the resulting value of V, making it much harder to get a good sense of what the best coefficient should be. Notice that with 0.05, it will only have an effect on bonuses with around 10-20 neighbouring territories. 10*0.05 = 0.5, and 20*0.05 = 1.0. It depends on whether you're rounding up or down, or to the nearest whole number.

How many maps out there have bonuses with 20 neighbouring territories?

Likewise with DBO and DBW. Try it with bigger coefficients. Who knows, you might get some interesting gameplay mechanics with big coefficients. You'll never know till you try. :-)

Once you have a sense of what the different variables are 'worth', you can adjust the coefficients down to more normal values, test it again, and keep tweaking and testing until you find a good solid combo.

You're right, I should test this with a lot a values :D
On the other hand I don't think 0.05 is too small. Right now the formula often equals the T/2 formula (which is used for most strategic maps, so its not a bad formula). For most boni with an equal amount of territories nothing changes (usually). For the boni with an odd amount of territories it sometimes give a difference. This means maps will be slightly more balanced, but aren`t too different from what is the standard at WL.

I'll try it out with different numbers, but I'm not unhappy with 0.05

There is no well defined fitness function so it's best to just stick with something that's sort of alright. Me and zxctycxz always go for n/2 rounding up and our maps have done pretty well.

True, there is no way to make a perfect function for boni. But this formula is meant to be the sort of alright thing that I stick to :p

Well, if you start the formula with T/2 and add/substract close to nothing, it will stay at T/2 after rounding :P