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Discussion Starter #1
Hi, I'm Wolf and new here *woof*. I am 23 years old and have always loved the idea of archery and though I've never had enough resources and time to really get into it :( I've taken whatever chance I could get at local medieval festivals that take part annually to shoot with real bows, and with a friend I made two makeshift survival-style bows out of bamboo sticks and some rope (using shop-bought arrows). I favor traditional archery and longbows, and have always dreamed about crafting my own bow and arrows following the example set by Primitive Pathways' channel on Youtube. I hope someday soon I manage to get into it, but with my work right now things are looking pretty bleak. All I can do is daydream even though I live on the edge of town and would have relatively little trouble finding materials I guess (plenty of oak and hazel around here).

But to get on point, I am also really into forum role-playing and am currently working on a combat system and need some help with my ranged weapons mechanics. Specifically bows. I am going to present my case and ask for opinions on people here because for all my effort I don't really have a feel for archery and this system is supposed to be realistic - not so much like Dungeons and Dragons etc. so if you know nothing of tabletop RPs it doesn't matter (doesn't hurt either if you do). I really need some expert opinions. The system is supposed to be simplistic and based on percentage chance boosted by one's Ranged Warfare rank, relative to distance. Here goes and thank you in advance *howl*




Finally decided the formula to be default chance + 1/2 warfare rank, dropping per 5% after passing the 0% mark for default chance. It seems close to realistic I think. Professional marksmen were able to hit targets up to 200 meters far I think. There were longer shots, but those were just shooting into approaching armies and hoping for a random hit based on the sheer mass of soldiers.

I was asking to look at it from a logical point of view. The comparisons looks alright... btw I'll talk in meters now. Dunno why I used feet for the game. I guess the imperial system has some sentimental value, and makes things sound authentic because it's old. But I have to keep using a ft to m calculator to even think straight lol *woof* (next RP definitely using meters)

Right now a complete amateur has 100% chance to hit targets that are up to 5 meters away, which seems legit. Even an idiot couldn't miss that. At 15 meters he has fifty-fifty chance, which also sounds, well sound. And he absolutely can't hit anything farther than 120 meters, and even that's with practically no chance. So he probably shouldn't shoot at anything farther than 90 m, where he still has a usable 30% or so.

A trained yet ordinary/average soldier or city guard archer can 100% hit things up t0 22 meters, has fifty-fifty at 80 m and can't hit anything beyond 140 m. Effectively his shots pay off up to about 110 m (roughly 30%).

On the other hand, elite units such as veteran sharpshooters and the like have 100% chance to hit targets up to 40 m away and fifty-fifty chance at 100 meters. Their maximum hittable range is 155 m, making their payoff threshold around 125 m (30%).

And finally, true masters of the bow can't miss anything closer than the 60 meters mark and have a fifty-fifty chance as far as 120 m. With a maximum hittable range of 175 m, their 30% distance is at 145 m.


Personally I wouldn't fire at anything that I have less than 20-30% chance of hitting, so that's why the above logic. What bothers me is the far side of the field. Supposedly archers in medieval times were expected to hit things as far as 200 meters (or am I wrong?). But according to this table even the greatest archers here can't hit someone more than 150 meters away. Not to mention that even so, a 5% chance sounds very low. Too low. It would take Warfare of over a hundred to even reach 200 m with a 5% chance... that would be 650 ft, so it would take 150 Warfare (aka max) just to have 5% chance to hit someone at 200 meters yeah. Wow. Shouldn't a legendary archer get like, 15% at least on that range? And then there's the fact that this person would have 50% chance to hit at 155 m, which in turn sounds a bit OP. But if he has 15% at 200 m somehow, that would increase his chance further at 155 m.

This last bit feels weird to me. How do I give more chance on the far side without increasing the short values, especially the 100% threshold which seems far enough as it is. A logarithmic scale would mean having to make a huge table to write down values for every possible Warfare lvl, whereas now you can easily and quickly calculate those just looking at the reference points. You apply your 1/2 Warfare rank at 400-415 where the default has 0% for the first time, and from there it falls off by 5%. Things were improved when I changed the falloff from 10% to 5%, maybe I should decrease it further? Like 2 or 3? This would just slightly reduce the maximum 100% chance mark and slightly increase the maximum overall range, so maybe it wouldn't help after all.



Of course, this table is for longbows and assuming you are trying to hit one specific target the size of a human being. If you wanted to fire beyond your chance to hit, but you were firing into an oncoming group of enemies then the chance would surely need to be significant. I mean that's large scale warfare 101. No one's aiming at individual angry barbarians in a horde, unless they really have a score to settle with one. You fire in their general direction... So assuming I accept the table as it is, I need to somehow provide for this other possibility. Maybe boost the chance by 5% for each additional target?

So let's say you are a veteran marksman with 60 Warfare firing into a group of 10 enemy infantry soldiers that are about 160 meters away. This gives you exactly 0% chance to hit (being right outside your range). But for each of them (not counting the first one) you get a +5% bonus, totalling 45% chance to hit someone (or should we count the first one too if we are already at 0% and aiming at a group? so 50%).

Then, let's say one of them is the leader... You would also technically have a 10% chance to hit him. One out of ten. Of course, all of that assumes they are moving close enough together to count as a group. We could say that this math applies for as long as they are not more than 10 ft from each other, represented by 2 squares on a map. Then for each 10 ft we could reduce the value of the 5% bonus per each down by 1%, giving you only a 1% bonus if they are walking 40 ft apart which would be a very wide formation (12 m). So a 9% (or 10% if we count them all) bonus to hit someone. Anything more and they can't be considered a group. You'd have to pick one target and at that range they'd probably sidestep lol.

Oh and it's a fantasy medieval game. The longbow is supposed to be the average english longbow I guess. And for shortbows I reckon it would probably do to reduce maximum range by... 30% or 50% even? And the just adjust the math from the longbow. I know this is probably one of the weirdest threads you've ever gotten here, and I apologize if this is out of place. I am just so unsure :/
 

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I'm only a few months into archery, but I have extensive gaming experience, and a physics degree. It seems like if you want realistic, you could go at this a different way.
An amateur can fire an arrow +/- 5 degrees of aim point left to right, and with a vertical accuracy of +/- 5 degrees, we'll say, and a Grandmaster of the bow can hit within 1 degree left/right and 2 degrees vertically.

At 30 feet, a 6' tall and 2' wide man occupies 1.15 degrees of angle horizontally, and 11.31 degrees of angle vertically. The amateur has a 1.15/10 chance horizontally, and 11.31/10 (so, 100%) chance vertically to be on target. This works out to 11.5% chance to hit at 30 feet for a total amateur, with the numbers chosen.

At 300 feet, the same man occupies 0.38 degrees horizontally and 1.15 degrees vertically. Our amateur has (.38/10)*(1.15/10)=0.4% chance to hit. Our Grandmaster however, has a (0.38/1)*(1.15/2)=21% chance to hit. (if you pack a group of people close together such that they're all within the same angular hitbox, even the amateur's chance can go up greatly)

This makes the chance to hit purely geometrical. You then have to decide how much space your target takes up (what if the man is crouching) and what the accuracy of your archer is based on his skill. This also makes it not too hard to add in windage or target motion as they're just extra multiplicative factors. I could make you up an excel sheet that lets you play with the numbers and shows you your full table for chance to hit based on range and skill. I could even include boxes for you to quickly calculate chance to hit for any size target, or include other factors. Easy to round to the nearest 5% too.

I think bowmen were required to be able to fire an arrow 200 yards, but not to hit a given person at that range. As you said, they're firing into an army. Today, Olympic shooters with technology unthought of when bows were used as weapons of war, shoot at 70 meters, and the best in the world consistently hit within....a square foot? less? I'm not totally sure. I think a legendary bowman would have a reasonable chance to hit out to 100m, maybe 150 depending on your definition of 'reasonable'.

Assuming a maximum skill of 150, each skill point should reduce the error inherent in an archer's shot by some amount. It wouldn't have to be the same amount in both axis, and it wouldn't have to be linear either. You lose out on easy calculation, but you gain in realism, and you also gain in the ability to easily, consistently, and logically apply other modifiers like wind, motion, target behind cover, groups of targets close together, etc. By getting rid of easy calculation, you prevent your players from metagaming the math as easily too.

Let me know if you're interested. I love to mathcraft games out.
 

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I'm sure someone with more experience with field archery will know better. But just skimming, and looking at your examples in the middle. I think your estimates of % chance to hit are highly optimistic, especially a single target at middle to extreme range using traditional gear.

I see complete amateurs miss a 16 inch target face at 5m at the range... no wind and they aren't in combat! For the same person, 20 meters and up hitting a target is pretty lucky, 50 would be blind luck.

I wouldn't give anyone a 100% chance to hit anything and you could probably drop your higher ranges in half for the more skilled archers. Accuracy drops off ridiculously fast with range. Archers at the Olympics don't hit all the time at 70m, even with specialized modern equipment, sights, clickers, stabilizers, no rampaging barbarian hordes! I think in "hit things at 200m", the things they're talking about are enemy formations or literally broad sides of barns. :)
 

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So I put together a spreadsheet, comparing my aiming accuracy with the accuracy I need to hit a target at range. The results are...well, it's hard to hit far targets, let's put it at that. This isn't even accounting for judging wind, distance, or movement. This is purely "how precisely can I aim my bow, and if I can aim that precisely, how often will I hit my target at range?"

Short version is, your accuracy starts very high, and over the course of maybe 30 meters will go from 80% to 50%. It's very sensitive to numbers, but percent chances aren't that high. It's very much slanted to the extreme upper end. A the difference between a skill of 150 and 145 at, say, 70m, is greater than the difference between a skill of 0 and 115 at the same distance, with a linear progression of accuracy. So, you suck, and your effective range is maybe 50m until you get to 140 skill. I doubt that's what you want.

I'm going to work on a way to make it a bit more realistic and balanced for a smoother progression. By adding not the square, but the square root of your skill (times an improvement factor for how much each skill point helps your accuracy) the chart looks a lot smoother. When I change the target size however, it looks totally wrong again. Probably because real archers don't hit randomly within their hitbox--their shots group towards the center, in general, which would tend to improve their hit chance...dunno yet. I'll keep playing around until I find something that's both balanced for the game, somewhat realistic, and usable for a variety of situations/targets.
 

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Our local club used to always put out a point blank target . It was one of the tougher shots for many. Kill zone shots were the exception . You need experience with every range you will shoot for any degree of proficiency . As was stated earlier, nothing is 100%.
 

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It may not work with your system, but I could see where your skill determines the die you roll being a way to level up. This is a basic theory without any math that perhaps Lucidish could work with. A d4 has say 1, miss left, 2 miss high, 3 miss right, and 4 is a hit. This goes all the way up to a d20 where 20 is a hit, but 19-16 or so are missing only by inches (and still hitting) but 1-3 or so is missing by a couple feet.

There are two different aspects in hitting a target. There's chosing where to point the bow, and then executing the shot. You could have 2 different die rolled. One determines aim, and the other determines shot execution. Both together result in final arrow placement. Keeping a directional aspect would allow for realism of errors compounding or slightly correcting depending on luck. As an archer levels up each of these the odds of getting the center or very close increases. I guess if you want to always use the same die, then you could use ranges of numbers to represent fewer, larger boxes. The key is that as skill increases and more boxes are added, the ones closer to center are smaller than the ones farthest away.
 

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That chart is not even close to reality, especially with a longbow. What your math isn't taking into account is the amount of arrow trajectory guess work being done by the shooter. Plus what you believe certain skill levels can do is way off the mark. In the days of the English longbow being used as a war weapon it wasn't much like what you see in a store now. They didn't have fiberglass to make it more efficient and their arrows were heavy wood. No carbon or aluminum. The draw weight was a minimum of 80lbs or more. It wasn't really intended to be a aim and hit a single target type weapon. Not like what we have now. It was primarily to create rain of arrows on an army with the occasional lucky hit if aimed.

If you want realism, grab a bow and go to a real tournament and take notes of the distances shot at and their success rates. Your numbers will get squashed down to about 1/4 or less of what you've got and it won't be linear by any stretch. Out past 50 with a long bow and the success rate drops to about 30% for the average shooter on a human sized target. Even the better shooters will be hard pressed to keep it above 80%. Past 70 and hits become pretty sparse for just about anyone. Change the bow and the hit factor can rise but you would need to have a good understanding of what makes a bow more inherently accurate one over another. Longbows are on the lower end of that spectrum.

However, most people that would play this game aren't archers so you could put up what ever you want and they'd be none the wiser. Worked for L Anderson. He fooled a lot of people with his BS antics.
 

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Discussion Starter #9
Alright first of all: That's a ton of help already from all of you guys! Thank you so much!

@Lucidish your experience and degree are evident from your replies. That's incredibly powerful math right there, but I fear it may be too much for me. Now, if this was a roleplay revolving around archery then I'd embrace what you're suggesting right away. I mean, it would call for such an amount of detail and factors. But it is not; this system I am making is supposed to be lightweight and inspired more by Amber Diceless RPG than D&D and the crew. I should also remark that the game in question has been ongoing for quite some time... Almost three years, in fact! *howl* And we're only 50% of the way as of last week! :D Additionally, it was pretty freeform posting until now so I can't suddenly introduce anything too complicated or I might lose even my most loyal players lol.

All of your other tips helped me alot, too. Not just you, but @Soopy and @redribbon too. And those are some good points from you, @ranchoarcher. As for you, @bjaurelio, I think I see where you are going with your idea but I'm unsure of it. I don't doubt Lucidish could take it and make something amazing with it, but once again I fear it would end up too complicated for my needs *woof*

I am looking for realism, but I must also strike a good balance between it and simplicity. So I set the default values (which were unrealistic at first, you were all right on that) and then went to compare how people would do at Warfare ranks of 30, 60, and 90. These are for the average army marksman, an elite sharpshooter with special training, and a grandmaster archer. The math needs to be relatively simple because my players will probably be anywhere in between these ranks, and they won't always be rounded to tens. Someone might have 27 or 51 and I need to be able to quickly come up with their % chance to hit at any given range. I'm not really into making a table to cover all ranks from 1 to 100, which brings me to... Max level isn't 150. I just stated that on the old table it would take rank 140 in order to have a 5% chance to hit a target at around 200 meters - but this doesn't matter because like you all agreed, you can't really expect anyone to hit a human-sized target at that range - unless there were a hundred people standing in a group, in which case you are simply required to fire the arrow far enough and hope for the best. No, looking at the table I think the rank cap should be 100, just to round it up. Maybe push it to 120, so that the following logic applies (and let me know if this makes sense to you): If an average soldier is ranked 30, then an elite is twice as good with 60, and a legendary marksman is even twice as good as the elite at 120 - though most grandmasters will stagnate around 100. 120 will be a bit more room for those once-in-a-generation heroes.

I made a new table, lowering the starting chances and slightly adjusting the scaling logic. First of all, everything is based on the default values so they must be foolproof. I am ok with them being slightly optimistic, but let me know if it's still too much. Now, you take the default value and then add 1/2 of your Warfare rank and that's your chance for any given distance. I left the percentages topping over 100% just to make that math visible. From the closest distance, 5-15 feet (1.5-4.5 meters), your chance degrades by 5% for each step in distance (and the steps are roughly by 5 meters). However, once you hit 50%, your chance starts falling off by 10% for each subsequent step. That is how it works, right? The chance to hit falls off more the farther you go, so up close it falls off slowly at first. I think of this as a compromise between linear and non-linear scales.

I believe it still needs some adjusting but I wanted to hear what you guys think of the new table. Closer to target, I hope? With this, looking at 100 meters, an elite archer has 10% to hit a man while a grandmaster gets 40%. Things like wind speed and target running I'll take into account when they happen. For example I imagine someone running around would halve your chance to hit regardless of what it would be.




Finally, that's all assuming we are aiming at somebody specific. If we're firing into a crowd of people, which we almost always are if it's a long distance shot, then how should things work? Can you dissect what I wrote earlier about that? Because I still feel it's on the right track:

Of course, this table is for longbows and assuming you are trying to hit one specific target the size of a human being. If you wanted to fire beyond your chance to hit, but you were firing into an oncoming group of enemies then the chance would surely need to be significant. I mean that's large scale warfare 101. No one's aiming at individual angry barbarians in a horde, unless they really have a score to settle with one. You fire in their general direction... So assuming I accept the table as it is, I need to somehow provide for this other possibility. Maybe boost the chance by 5% for each additional target?

So let's say you are a veteran marksman with 60 Warfare firing into a group of 10 enemy infantry soldiers that are about 160 meters away. This gives you exactly 0% chance to hit (being right outside your range). But for each of them (not counting the first one) you get a +5% bonus, totalling 45% chance to hit someone (or should we count the first one too if we are already at 0% and aiming at a group? so 50%).

Then, let's say one of them is the leader... You would also technically have a 10% chance to hit him. One out of ten. Of course, all of that assumes they are moving close enough together to count as a group. We could say that this math applies for as long as they are not more than 10 ft from each other, represented by 2 squares on a map. Then for each 10 ft we could reduce the value of the 5% bonus per each down by 1%, giving you only a 1% bonus if they are walking 40 ft apart which would be a very wide formation (12 m). So a 9% (or 10% if we count them all) bonus to hit someone. Anything more and they can't be considered a group. You'd have to pick one target and at that range they'd probably sidestep lol.
 

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I'll see if I can turn my spreadsheet math into a table and progression that you can calculate in your head. To answer one of your questions, if you increase your range to target by 2x, your chance to hit (just considering how precisely you can aim a bow, not including the factors of judging distance and such, which probably have a bigger impact) decreases by a factor of 4. Increasing by a factor of 3x reduced your hit chance by a factor of 9. This is what's called an inverse-square relationship. That's not accounting for the fact that as your range increases, you need to arc your arrow more, which means your cross-section to hit shrinks as well since the arrow is coming down from above more than coming in from the front. Also, you have to estimate range, and you can only estimate to what, maybe +/- 10% or so? That's an additional factor that probably influences accuracy more than the others.

tldr; Yes, range impacts to hit % more than anything else, and it gets worse as you go farther faster than linear--proportional to distance squared, at least. However, no matter how bad you are, as long as your target is within range of your bow, there's *some* chance to hit. Maybe make your table go down to 1% chance instead of 0%. This comes into play later for groups.

As for a group, I think if there's more than about 5 or 10, the chance isn't based on adding 5% per target, but on how closely they're spaced. If you aim for the center of the group, and the group is big enough that your arrow won't land far to the left or right of the group as a whole, then the only factor (aside from ranging your shot correctly) is how densely the group is packed. If there's only an inch between each target, you're guaranteed to hit something, since it's basically one big mass, right? If you have a small group, say 3 individuals, your chance to hit could be argued to be 3x your chance to hit one target. This means when you're shooting at a group, if it's tightly spaced, you could just take your chance to hit a target at that range (minimum of 1%) and multiply by the number of targets in the group. If the group happens to be a tightly-packed army...well, you'll hit something won't you? If it's a more loosely spaced army, maybe you have only half the area filled by targets, and the other half is empty space, so your chance to hit is your base chance per target times the number of targets, times the density (1/2, in this case).

Base chance has a minimum of 1% at max range of bow
Chance goes down as you stated before
Chance is improved by warfare level as you stated
Density of a group of targets is expressed as a decimal from 0.1 (sparse) to 1.0 (shoulder-to-shoulder)

So, chance to hit at a given range = (base chance + 1/2 Warefare level) * number of targets * density of targets
 

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Discussion Starter #11
Hm. Yes, that does make a ton of sense.

Combat encounters would take place on a battle map where the grid is made up of 5x5 ft squares, meaning that a medium-sized being (human) occupies 1 such square. So we're assuming that's the closest that targets will be standing next to each other. So how far to look? Should I grant bonuses to hit % only for adjacent targets? Those that are standing right next to each other? Or maybe up to 1 square apart (10 ft)?

The 1% min chance is a good idea. I will make it so *woof*
 

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If I'm 5 feet from the next guy, that's maybe 1/3 coverage. You could be generous and say you get a .5 multiplier if targets are adjacent...that's more of a balance question. When you start getting down to the finest units your game allows (in this case, a single grid square) you sometimes have to stop considering reality at that point--you could say that two targets in adjacent 5 foot squares will be considered to be soldiers standing shoulder-to-shoulder, for instance. It's not the player's fault that the squares are 5 feet big.

It may be best to divide your rules into rules for attacking a specific target, and rules for firing into an army. A specific target works as we have now with a base chance plus half warfare level. Firing into an army/group gives you a flat percent based on density. Or maybe 5* your chance at that range, up to 50% chance (or whatever chance corresponds with the army density). The 5* your base means that if you're right at the limits of your range, you don't get the full 50% chance because you may not even get the arrow there.

So, at 290 feet, using your table, if trying to pick off a specific individual, you get a chance of 1% for amateur, 5% for soldier, 30% for marksman, 55% for master. If you're just firing your arrow into the oncoming horde because there's so many, you get 5% for amateur (he probably won't get the arrow in that area), 25% for soldier (He usually can shoot that far, but sometimes not. After all, he likes swords more), 50% for the marksman (he's not good enough to have a better chance to hit a specific individual, so he's limited by the density of the army) and still 55% for the master, because he doesn't care that there's more targets, he's still better off taking out a specific one).

This means that if the Master wants to try to take out an officer at 350 feet, he has a 30% chance of doing so, but if he misses, he'll likely miss by just a little, and thus won't hit anyone else. Or, he can just throw an arrow in there and take his 50% chance to hit somebody, anybody. His choice. This offers your players a strategic choice that's still easy to understand, and keeps them limited by their range/level somewhat, but makes it feasible to pepper an army with arrows at long range, as realism would encourage. You only need to be able to describe the density of an army, and that's the upper limit of chance to hit by firing a random arrow. It's up to you whether you want to make them specify an area they're firing at, and then you define the density of soldiers in that area, or if you want to not worry about that kind of specificity.
 

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Discussion Starter #14
Thank you, Lucidish. Everyone here was very helpful but you most of all. I believe I now have enough understanding to finish what I started *howl*
 

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Read Sir Arthur Conan Doyle’s The White Company for an historical take on what a master archer was capable of.

You’ve also left out the matter of equipment — you’ll want to match up bow draw weight to the strength characteristic adjusted by the draw length (a function of height and draw style/release technique).

Similarly, the materials and skill of the bowyer and fletcher should factor in somewhat.
 

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Discussion Starter #16
@WillAdams - True, those things should factor in and I would surely do so if I were making a game that's oriented around archery. But I am not, and archery here is just one of many things you can do and as such I cannot afford to go into that much detail. I will have to assume that everyone has a roughly ideal weapon and only make distinctions between longbows, shortbows, and crossbows *woof*

Thanks for the read recommendation. I'll try to study it sometime ;)
 

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Discussion Starter #18
I'd be interested to hear what you decide to go with. And you're quite welcome--it was fun to work on and think about.
I'll make sure to send you a link to the entire finished product when it's done (probably at least a week; I am working on other aspects of the system too). You deserve nothing less ;) *howl*
 
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