Max hit vs average hit

[Kalafai]

okay, so...

 

Max.   Avg.
1      1
2      1.5
3      2
4      2.5
5      3
6      3.5
7      4
8      4.5
9      5
10     5.5
ect...

 

Am I correct in assuming a steady variance between hits averaging the median here?

 

with a max hit 30 averaging 15.5, then getting it up to 31 with yer fighter torso/bandos only gets your average to 16, meaning a 3% increase in damage, yes?

[1230abcz]

Well, that's assuming it's a perfectly normal distribution. I'm fairly sure it's skewed to the right, in that most of your hits will lean towards the higher end of the damage spectrum, so your average hit will be a bit higher.

 

If your case does apply, then a max hit of 30 would imply that your average hit would be (30+0)/2=15, not 15.5.

 

Also, Runescape damage doesn't really work that way. Your average hit with a torso would be increased by 1, not .5, because +4 str entails an extra hit per hit you inflict. Considering no one really knows the facts, that's as far as I can go. You'd have a 3.33% increase in damage, but that's only if your max is 30. If your max is 1, you'd gain a 100% increase in damage, and if your max is 100, you'll have a 1% increase in damage.

 

Sorry if the the above text was confusing. In conclusion (transitions that take you back to 6th grade, lol), your average will be increased by 1 hit. A 3.3% increase is misleading, as your max hit will always change.

[The_dmt1234]

torso/bcp looks cool, so it wins. end of story.

[Zaaps1]

No, you are not considering the fact that your equipment and target will change as well.

[Kidd_Varrow]

Well, that's assuming it's a perfectly normal distribution. I'm fairly sure it's skewed to the right, in that most of your hits will lean towards the higher end of the damage spectrum, so your average hit will be a bit higher.

 

I agree. It seems to me like I hit for higher numbers more often than lower numbers. Btw, this would mean it's skewed to the left.

 

If your case does apply, then a max hit of 30 would imply that your average hit would be (30+0)/2=15, not 15.5.

 

No, he's right. Assuming equal probability of all possibilities from 1 to 30, the expected value (or average) is (1 + 2 + 3 + ... + 30) / 30 = 465 / 30 = 15.5.

[Kalafai]

.... Your average hit with a torso would be increased by 1, not .5, because +4 str entails an extra hit per hit you inflict...

That'd be giving it a min hit of +1. I do believe you are much further off than I.

 

 

No, he's right. Assuming equal probability of all possibilities from 1 to 30, the expected value (or average) is (1 + 2 + 3 + ... + 30) / 30 = 465 / 30 = 15.5.

Also, to simplify, but not prove, n/2+.5, as per observation of the ratio.

 

I'm still hitting a lot of 8s and such as often as 2s and maxes with my whip, and just watching without tally, it seems pretty even distribution to my eye*.

 

 

*99.9th percentile in pattern recognition for my qualification. Maths would be better still, thought take some 20 odd times as long.

[Bladewing]

I took data on damage distributions for about 8000 hits. The data indicated uniform distribution.

[Kalafai]

wohoo! Now I just need to divine the nature of the to hit roll, watch for the data gathering on monster attack/defense levels, and I can finally solve the problem of defense to offense efficiency!

 

 

Or just will the formula to myself.

 

...

 

*head explodes*

 

Or get a friend and take hit/miss distributions with various attack values and armour values at the duel arena... unless someone has already done that... in which case that's good, because I have no friends.

[Kidd_Varrow]

.... Your average hit with a torso would be increased by 1, not .5, because +4 str entails an extra hit per hit you inflict...

That'd be giving it a min hit of +1. I do believe you are much further off than I.

 

 

No, he's right. Assuming equal probability of all possibilities from 1 to 30, the expected value (or average) is (1 + 2 + 3 + ... + 30) / 30 = 465 / 30 = 15.5.

Also, to simplify, but not prove, n/2+.5, as per observation of the ratio.

A mathematical proof of this result:

 

The mean of a set of n values is defined to be the sum of the values divided by n. Since the sum of the integers from 1 to n is n(n + 1) / 2, the average of these values is thus:

 

n(n + 1) / (2n) = (n + 1) / 2 = n/2 + 1/2.

 

Sorry, I'm feeling a little mathy tonight. :geek:

[1230abcz]

Well, that's assuming it's a perfectly normal distribution. I'm fairly sure it's skewed to the right, in that most of your hits will lean towards the higher end of the damage spectrum, so your average hit will be a bit higher.

 

I agree. It seems to me like I hit for higher numbers more often than lower numbers. Btw, this would mean it's skewed to the left.

 

If your case does apply, then a max hit of 30 would imply that your average hit would be (30+0)/2=15, not 15.5.

 

No, he's right. Assuming equal probability of all possibilities from 1 to 30, the expected value (or average) is (1 + 2 + 3 + ... + 30) / 30 = 465 / 30 = 15.5.

 

 

Yea, skew left. Vocab fail there. And also, I took 0 into account as well. I'm assuming 0's are important in the calculating average hit. Do the math again, and you'll get 15, not 15.5.

[Kalafai]

hmmm... no, I do believe min hit is 1. I'll see it better as Kalafai becomes something of an attack pure as she levels up. But I never see 0s at all on no miss opponents with Time Kitten.

[lagatag]

The minimum hit FOR MELEE is definitely 1. I'm only assuming this because at Kuradals dungeon + Ferocious Ring, I never hit below 5 (well, except for 0's, but those are misses). If it were possible to hit 0 (not miss, which also shows up as 0 for melee), then the minimum hit would be 4 at Kuradals dungeon with the ferocious ring.

 

I would say that this applies to ranged as well. I'm not sure about magic, because missing with magic results in a splash, but I've also landed a hit for 0 damage. This could mean either magic has to have 2 hit rolls (spell success, then hit success?), or it is possible to just do 0 damage with magic. The KB doesn't really offer any insight into this other than saying you can fail to cast the spell, which results in a splash. But that could still mean either there is a second hit roll to determine if you're spell hits the target, or that if the spell is successful then you do hit the target, but can just hit it for 0 damage. It could even mean both. Testing at Kuradal's dungeon+ferocious ring would likely resolve the issue of whether 0 is a hit or miss, but I've never used magic there, or seen anyone maging there.

 

 

I would also say that you are more likely to hit for higher damage. I hit for 20+ a lot more than I hit for under 10.

[Grimy_Bunyip]

So what's your thought on average hit based on a target's hp level?

because inevitable you'll need to knock out a monster, and all damage you hit over the remaining hp is lost

Clearly for a monster of high hp, wasted damage should average out to [Max Hit]/4, but it gets kinda obnoxious for monsters of lower hp

this is just a thought I've been having, any chance you have any thoughts on it as well?

[Kalafai]

It is defenetly not waisted on monsters of lower HP, since all the more chance to one hit them.

 

And I've never counted damage for killing blows, just too much to go wrong there.

[sees_all1]

I did a test with 2 lvl 3's a while back. No equipment bonuses. A was hitting on B, with the defensive style. B had auto retaliate off.

 

Max hit was 1, Min hit was 0.

I forget the data I had, its in a thread around here somewhere (in general discussion, I'll repost here if I can find it again).

My conclusion was that 0 is a valid hit for any strength level, but I didn't test any strength bonuses.

 

Please remember that hitting a 0 naturally would be just as likely as hitting your max, and its very difficult to differentiate between the attack failing and the hit succeeding with 0, especially if your max hit is VERY high.

 

Anyhow, if you toss out attacks failing / succeeding, your average hit should be Max / 2.

[knight10071]

Too tired to comment on the math, however, I am pretty certain that the minimum hit isn't 0.

The reason I think so, is that you can SGS spec and hit 0, but still be healed. The explanation would be that you "rolled" hit, then "rolled" 0. Also, with magic, it's visible (splash vs hit) and I doubt it would be different with melee/ranged.

Why you never hit below 5 in Kuradal's is simply explained by assuming that the check for the damage addition is "rolled" 1 or up, instead of "rolled" hit.

[NastyJenny]

You can hit 0 with magic in Kuradal dungeon with ferocious ring... i mage dragons there when get as task