Needs maths lessons ===>

[Maquiladora]

Okay here is the idea. I have these unit values and i want to work out the value of all units, using the result of the 1v1 combat simulator. (attachment)

Ignore the 'ranged' values and ranged units, ignore the fact that one unit has more movement or vision than another or that one unit might have flanking (those all will be balanced manually afterwards). Use the starting point of 150 shields for a Warrior. I get some numbers but cant be sure if theyre right. Have i made a fool of myself again?

		a/d/r		firep.	armor	move	vision	cost	support
warrior		10/10/0		1	1	1	1	150	
archer		10/10/20	1	1	1	1		
hoplite		10/15/0		1	1	1	1		
samurai		20/10/0		1	1	1	1		
							
mounted archer	10/10/20	1	1	4	2		
pikemen		10/25/0		1	1	1	1		
catapult	10/10/30	1	1	1	1		
knight		25/15/0		1	1	3	2		
							
infantryman	20/35/0		2	1	1	1		
facist		25/35/0		2	1	1	1		
cavalry		35/20/0		2	1	4	2		
cannon		10/10/50	2	1	1	1		
							
machine gunner	40/30/0		2	1	1	1		
artillery	10/10/70	3	2	3	2		
tank		50/35/0		3	2	5	2		
marine		60/40/0		2	1	1	1		
paratrooper	60/40/0		2	1	2	3		
mobile SAM	10/10/80	3	2	3	2		
							
hover infantry	80/50/0		3	2	5	3		
fusion tank	65/45/0		4	3	8	3		
war walker	10/10/95	4	3	5	3		
leviathan	90/100/0	4	3	10	3

[Maquiladora]

Man, am i off my rocker? I thought it would be quite simple for someone who knew what they were doing.

[Immortal Wombat]

I'd be glad to help, but I don't have Excel so I can't run it.

[Maquiladora]

Not sure if it will work but have you tried opening it with IE? I cant tell if its just because ive got Excel installed that it works, probably.

Added to website too http://www.geocities.com/ctp2strateg...im_final_1.xls

[The Big Mc]

can't download it there seams to be a problem with your site

[Maquiladora]

Yeah sorry its yahoo blocking it i expect, go from the links page it wont do that then, but i dont know if it works in IE without excel installed.

http://www.geocities.com/ctp2strategy/links.htm

[Solver]

Nope, won't work in IE without Excel.

Here, though, is a viewer for Excel files:

http://www.microsoft.com/downloads/details.aspx?FamilyID=4EB83149-91DA-4110-8595-4A960D3E1C7C&displaylang=EN

[Immortal Wombat]

I've got it, but you can't edit the values to get the functions to run.

[Maquiladora]

Ah well thanks for trying

[J Bytheway]

Well, I can open the spreadsheet in excel, but I can't help you because I don't quite understand what it is you're trying to do...

[Maquiladora]

Okay to explain better, if a Warrior is 150 shields and we say the chance of a Warrior beating a Hoplite is 46%, i want to know the comparitive value of the Hoplite and so the compartive value of all units to one another exactly.

edit: misread posts

[J Bytheway]

Well, you could try to use odds ratios. If the probability is p the odds ratio is p/(1-p)

I doubt that the ratios you'll get will be transitive, so you probably won't be able to consistently value all units so that their relative values are related in some simple way to their victory probabilities (unless you give them all the value zero ).

e.g. Warrior vs. Hoplite - 44%, so odds ratio 80% and hoplite value 150/0.8=150*1.25=187.5

Hoplite vs. Samurai - 47%, so odds ratio 87.5% and samurai value 187.5/0.875=214.3

Samurai vs. Warrior - 57%, so odds ratio 133% and Warrior value 214.3/1.33=160.7

You don't get back to where you started at...

[Maquiladora]

Thats why i didnt like the numbers i got, i never got consistant ratios between them all. Is there any other way?

[J Bytheway]

Well... There are a few things you could try.

If you want to stick with the odds ratios you can either choose one unit (e.g. the Warrior) to be the base unit and set all of the others in relation to it, or alternatively you could retain the whole overdetemined system, and solve it via a least-squares method, to get the best possible fit.

If you don't want to do that, I think you'll have to abandon the application of these probabilities altogether and just come up with some formula based on the various values that "feels about right" to you. I can see that this would be unsatisfactory.

Personally, I favour the least-squares solution, but that is the most complicated way to proceed...

[Maquiladora]

If you want to stick with the odds ratios you can either choose one unit (e.g. the Warrior) to be the base unit and set all of the others in relation to it,

I did something similar to this on my first try i think and i ended up with snow-balling costs for later units, maybe it was slightly different what i did.

I know how least-squares method works (thanks to google) i might give that an (experimental) try.