I wrote a quick script that recorded arrow hits to a Data window, and then cut and pasted it into a stat package and ran a few quick regressions. The idea is to separate out the individual effects of various factors, taking into account / controlling for other factors that may come into play.

This post was inspired by this study:
http://elanthipedia.com/wiki/Fletching

Except instead of frequency tables, I use regression. I convert all qualitative damage messages into numerical values based on the ordering in the table above, adjusting the scale on 1-24.

For tables 2 and 3, for those values above 12, I halved and generated a crit variable to designate that it was a "critical" hit.

Results are below


Table 1. General OLS Regression on Raw Hit values
(N=267, R2=0.1723)

Variable	Coef.	Std.Err	P-value
longbow	1.024018	.5368337	0.058
time	.1791957	.1170636	0.127
balance	-.1426173	.547773	0.795
snipe	1.838813	.679862	0.007
basilisk	3.345943	.5309098	0.000
Intercept	12.18245	4.613663	0.009

Table 2. General OLS Regression on Adjusted Hit values
(N=267, R2=0.0754)

Variable	Coef.	Std.Err	P-value
longbow	-.7728557	.4316005	0.075
time	-.1211996	.0941161	0.199
balance	.5514537	.4403954	0.212
snipe	-.6642971	.5465915	0.225
basilisk	1.315196	.4268378	0.002
Intercept	5.653249	3.709266	0.129

Table 3. Logistic regression on Crit Chance
(N=267, PseudoR2=0.0769)

Variable	Coef.	Std.Err	P-value
longbow	.6994941	.2854237	0.014
time	.1139478	.0610461	0.062
balance	-.2687256	.2875765	0.350
snipe	.917854	.3460136	0.008
basilisk	.7752528	.2779271	0.005
Intercept	.2643282	2.4129	0.913

Conclusions:
Weak Conclusion = Statistically Significant at the 90% Level
Strong Conclusion = Statistically Significant at the 95% Level

Capped Silverwood Hunter's Longbow VS. Horse Clan Composite Bow
Weak: The composite bow does on average 0.77 points more damage than the hunter's longbow.
Strong: The hunter's longbow has 0.699 (Log odds) higher crit chance than the composite bow, independent of sniping effects.

Seconds Aimed (2-16 second range)
Extra seconds aimed does not appear to have an effect on raw damage.
Weak: Each additional second aimed increases the crit chance of a hit by 0.113 (Log odds)

Nimble vs Solid Balance
No effect.

Sniping vs firing in plain sight
Sniping does not increase raw damage.
Strong: Sniping increases the crit chance of a hit by 0.917 (log odds)

Basilisk Arrows vs. Store-bought Silver-tipped
Strong: Basilisk arrows increase damage by 1.315 points on average. This effect is underestimated due to right-truncation of the dependent variable.
Strong: Basilisk arrows increase the crit chance of a hit by 0.77 (log odds).

Overall Conclusions:
Damage scaling is non-linear and multi-leveled. There is at a min, two discrete types of damage.. and I labeled them crit and non-crit for now, until I can figure it out.

If the above is true, then most types of damage modifiers increase damage indirectly by increasing crit chance instead of raw damage (e.g. weapon used, time aimed, sniping status)





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"All models are wrong, some are useful." -George C. Box

Oh god, I love stats! It made a lot more sense when I looked at the numbers too.

This may be silly or because I tend to gloss over hit messaging in general (I ultimately just want to know did I hit and am I still balanced), but how do you know that it was a critical hit? Or is it just anything above 12?

Nikpack
player of more than I should list

Climbing List:http://www.elanthipedia.com/wiki/Climbing_skill
Swimming List:http://www.elanthipedia.com/wiki/Swimming_skill

And while I am evil, I try to avoid being just plain mean.
-Z

>>This may be silly or because I tend to gloss over hit messaging in general (I ultimately just want to know did I hit and am I still balanced), but how do you know that it was a critical hit? Or is it just anything above 12?

What's classified as a "crit" is something I guessed at. For example, here is the distribution of raw hits with basilisk arrows:

Hit Value	Frequency
10	3
12	52
15	1
16	2
17	19
24	28

The distribution doesn't look like an across-the-board random process, rather something that caps at 12 and 24. So my guess is that there is a discrete category of "random" hit that caps around 12. And then another category that I will call crit, that caps at "24" (apocalyptic).


Here is the same table of hit values for store-bought arrows.

Raw Hit	Frequency
7	2
8	1
9	13
10	20
11	12
12	59
13	10
14	6
15	9
16	5
17	2
18	3
19	8
20	2
21	4
22	1
23	1
24	4
Total	162

Again most values in the first range 0-12 seem to cap at 12, but the difference is the values above 12 are more random.

I don't know if there's been previous info on this before (maybe someone can c/d) but my guess on what is happening is that the attack is determined to be a critical hit or normal. If it's normal the attack value is converted to a hit between 0-12 with probability proportional to its hit power. If it's a crit, the attack is converted to a hit between 13-24 in the same way, but with a reduction penalty.

I know I'm not getting the whole picture because there are some intermediate hit values such as "17" which are are happening too much to be a result of the process above.

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"All models are wrong, some are useful." -George C. Box

My guess would be that limb damage caps at 12, but it wasn't really clear from your post exactly what your process was. To do this the right way, you should really only count first shots that happen to hit vital areas. Or hunt something much harder.

Ok, but you really need to consider the limb shot thing too, that the primary thing that's skewing your data.