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Re: "How does it work?" Part 8: Skill Checks[message #204785]

Wed, 24 December 2008 07:04

incognito253

Messages:53
Registered:December 2008
Location: Ohio, USA

I noticed something about the bomb-planting formula in this how-to. When I first read it, I didn't read too far into it but it left a niggling feeling in the back of my head and after I had a good sit on the john, I took another look at it.
Quote:

Base_Chance = (Base_Chance + 100 * (Base_Chance / 25) ) / (Base_Chance / 25 + 1)

Write this algebraically and it'd be f(x)= (x+(100*(x/25))) / ((x/25)+1) where x is the original base_chance and f(x)=resultant base chance.
It's a fimiliar kind of formula with an elegant concept, where a character with a skill level of 50 (proficient but not mastered) will have a chance of success closer to that of someone with a skill of like 90 (masterful) because the gain above 50 would decline, since anyone can make a mistake. Meanwhile the gulf below 50 (proficient) grows becuase non-proficiency with this skill (bombs) tends to lead to costly errors...it's a smart concept, but unless I'm somehow missing something here the formula is not even close to what their comment states (no bonus at a base chance of 22.
I plugged in 22 to this formula, which would be as follows:

f(22)=(22+(100*(22/25)) / ((22/25)+1). So we have 22+(100*.88 / (.88 + 1) or 110/1.88 ~= 58.51, which is a 36.5% increase to the base chance. If you change the numerator section from (x+(100*(x/25))) to (x+100)*(x/25), which I thought might be the case, it decreases the result by approximately 1.5 to about 57 instead of 58.5. Either way, it doesn't seem to work out as intended.

So then I applied 1 for x. and got f(1) = 1+(100*(1/25)) / ((1/25)+1). We derive 1+4 / 1.25 = 5/1.25 = 4, which is a 3% bonus. To make this suscinct:
f(1) = 4% (3% bonus)
f(5) = 20.83333...(15.8% bonus)
f(10)= 35.*** (25% bonus)
f(20)= 55.5555555.....(35.55...%)
f(25)= 62.5% (37.5%)
f(50)= 83.333...%(33.333...%)
f(75)= 93.75% (18.75%)
f(99)= ~99.8% (.8%)

Assessment: the formula is highly elegant, except for one minor flaw: the optimum bonus is gained at approximately 22......not around 50.

Comments? Part of the formula I'm processing wrong or misinterpreting? Another function I'm missing?

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[Message index]

		"How does it work?" Part 8: Skill Checks By: Headrock on Wed, 08 October 2008 15:40
		Re: "How does it work?" Part 8: Skill Checks By: Headrock on Wed, 08 October 2008 15:42
		Re: "How does it work?" Part 8: Skill Checks By: Panpiper on Wed, 08 October 2008 16:40
		Re: "How does it work?" Part 8: Skill Checks By: Marlboro Man on Wed, 08 October 2008 16:50
		Re: "How does it work?" Part 8: Skill Checks By: Headrock on Wed, 08 October 2008 16:56
		Re: "How does it work?" Part 8: Skill Checks By: cdunigan on Wed, 08 October 2008 17:31
		Re: "How does it work?" Part 8: Skill Checks By: Headrock on Wed, 08 October 2008 19:13
		Re: "How does it work?" Part 8: Skill Checks By: FelixDrake on Thu, 09 October 2008 10:30
		Re: "How does it work?" Part 8: Skill Checks By: incognito253 on Wed, 24 December 2008 07:04
		Re: "How does it work?" Part 8: Skill Checks By: Headrock on Wed, 24 December 2008 07:32
		Re: "How does it work?" Part 8: Skill Checks By: Kaerar on Wed, 24 December 2008 08:09
		Re: "How does it work?" Part 8: Skill Checks By: incognito253 on Thu, 25 December 2008 11:52
		Re: "How does it work?" Part 8: Skill Checks By: Kaerar on Thu, 25 December 2008 12:33
		Re: "How does it work?" Part 8: Skill Checks By: Headrock on Thu, 25 December 2008 15:05
		Re: "How does it work?" Part 8: Skill Checks By: incognito253 on Thu, 25 December 2008 15:48
		Re: "How does it work?" Part 8: Skill Checks By: Headrock on Thu, 25 December 2008 16:59
		Re: "How does it work?" Part 8: Skill Checks By: BirdFlu on Thu, 25 December 2008 20:26
		Re: "How does it work?" Part 8: Skill Checks By: Headrock on Fri, 26 December 2008 01:53
		Re: "How does it work?" Part 8: Skill Checks By: BirdFlu on Fri, 26 December 2008 02:54
		Re: "How does it work?" Part 8: Skill Checks By: incognito253 on Fri, 26 December 2008 05:01
		Re: "How does it work?" Part 8: Skill Checks By: BirdFlu on Fri, 26 December 2008 12:12
		Re: "How does it work?" Part 8: Skill Checks By: BirdFlu on Fri, 26 December 2008 12:21

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