Monday, February 16, 2015

Archery – Field Experiment

My current house-rules for archery are based on a combined mathematical model and game simulation program (link). This is the fruit of quite a bit of analysis on the archery game (search the blog for "archery", you'll find lots of posts). The most important observation is this: shooting man-to-man and shooting at an army are totally different tasks (the former may be impossible to hit, while the latter impossible to miss, at the same range).

This is based on some pretty good data in Dragon #58, originally from the book Archery, on hit rates for Grand Masters at different ranges (think: top-level fighters with several bonuses). Not having specific hit data, my model for beginning bowmen (1st level fighters?) was very roughly estimated by recent GNAS scoring, and guessing they're maybe one-tenth as accurate as Grand Masters. The table below recaps the expected hit rates from both the game rule model and the bivariate normal physics simulation. But were those reasonable assumptions?



Obviously, the only way to approach this scientifically is to run a test in the field (like, an actual field). At the end of August I visited my folks' place in Maine and got out my very old bow and arrow kit and set up a target to see whether my own accuracy broadly matched this math model. The equipment is a 30-year-old Bear compound bow with a 28" draw at 60 pounds (with no maintenance ever having been done in those 30 years; in fact, it spent several winters in an outdoor shed), shooting 32" target arrows. I made a 2-foot radius target (to match the old GNAS competition), and took a series of 10 shots each from 10, 20, and 40 yards distance (to match the increments in the prior D&D model). Due to time constraints, I didn't take any practice or warmup, and I haven't done any shooting in at least several years (and I've never done it with this target size or range).

Now technically the first thing I did was set up the target and several bales of hay in back of a metal trailer and shoot one flight of arrows that I had to start with. Each of these shots went entirely through the target, hay, into the side of the trailer, and entirely shattered from head to tail. So I didn't count those, and had to go down to the Kittery Trading Post to get another batch of arrows. Later that afternoon, I was back with this setup:



Here are the two flights of 5 arrows each, shot from 10 yards. I easily hit all ten times, although several of the arrows flew entirely through the target. Notice that even on the second set of 5 my accuracy was noticeably improved, grouping the arrows closer to the center of the target.




Here are the  shots from 20 yards. Again I hit the target all 10 times -- although more of the arrows are disappearing through the target. I think I started getting a fuller draw at this point, because on the second set of 5 every one of them flew entirely through the target.




At this point I started shooting from 40 yards away (from way down in the field, actually). Here I only got 2 arrows out of 10 to actually go in the target. Generally I was aligned correctly, but my shots were mostly falling low/short, although I'm sure that would improve if I got more practice and got the ascension right.




So, an admittedly small sample size, with very old equipment and an unpracticed shooter, but that's all I could accomplish on the particular day. Let's compare the results to our prior model:

That's not a perfect match, but the numbers do seem to moving in generally the same direction. Based on my experience that one day, I really couldn't miss an immobile target of that size from 10 or 20 yards distance. From 40 yards I was hitting a bit less than predicted for a "3rd class bowman", but I'm pretty sure with a little more practice at that range I could start doing much better than that, likely above 30%. (As a comparison, the next day I spent most of the afternoon shooting from 30 yards, and I felt like I nearly couldn't miss once I had the range down; over about 100 shots I missed only 2 or 3 times, for a 97-98% hit rate. The house rule game model would predict a 55% success rate, and the physics-model simulator about 48%.)

Generally it seems like with a little practice, my hit rates are better than predicted, which could be due to a number of factors: (a) I underestimated the skill of GNAS 3rd-class bowmen, (b) I have better equipment than that used for the base data (the Archery book was published in 1894), (c) I'm a better archer than expected -- seemingly the least-likely hypothesis.

Coincidentally, a neighbor's son who is entering high school as freshman came over the next day with his own archery equipment, and it was kind of stunning to see how the equipment and style has all changed completely in the 30 years since I got my own bow. His bow is much lighter and smaller (half the draw weight) with a bunch of built-in sights and range-finders and whatnot. Shooting is done with a bent left arm (whereas I need a big leather guard to prevent injury) and a loose grip, letting the bow fall out of the hand loosely on a cord after the shot (whereas my heavier bow would likely break my wrist if I tried that). Plus a trigger-button release is used, whereas I mostly chewed a hole through a leather glove and my fingers over the afternoon. He took a few shots and obviously had much greater accuracy than I was getting, which speaks to the rapidity of how much the discipline can change due to technology in a fairly short time.

Anyway: What we clearly see in the experiment is that hit rates may be 100% at close ranges, and then very rapidly drop off to near-zero with just a few doublings of range. Even if I could practice more at the 40-yard range, I'm sure that shooting from 80 yards out at a single man-size target would be practically impossible for me. But the flip side is that it would only take a few doublings in target size (4 or 8 men deep or wide) and I'd be back to automatically hitting on almost every shot. So in broad strokes the math does seem to be winning, and generally predict the overall dropoff in accuracy from shooting at a small target at distance.

Got any more data?


30 comments:

  1. If you haven't seen this yet, you should check out: https://www.youtube.com/watch?x-yt-cl=84503534&v=BEG-ly9tQGk&x-yt-ts=1421914688

    He's definitely a high level archer and he doesn't use modern style mechanics in his shooting. It's pretty amazing.

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    1. I did see that, and I honestly love it and it's amazing. I also saw some pretty believable criticism (see "skepticallypwnd"), like to these tricks he's skipping a full draw/impact and prepping the arrows in special ways, etc. Still: super impressive.

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  2. I was going to mention Lars Anderson as one of my two things also. The other is that I went shooting in October at 25 30 40 and 50 yards. I was using a 60# wooden competition recurve with heavy aluminum arrows (wrong weight of arrow). With these arrows and shooting high I could barely reach 50 without overshooting by a great distance - also I was on a slope facing down hill. At 25 and 30 I had no problem. 40 I was about 60% iir. But this was four months ago and I didn't write anything down... So I could be way off

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    1. Thanks, that seems pretty compatible!

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  3. I love this sort of stuff- equating real-life to fantasy game statistics. Two take-aways from your experiences I would have would be the almost automatic hit at close range (i.e. the sort of range you would normally see in, say, a dungeon room) and the need to analyze for a moving target instead of a stationary one. Maybe another reason to take a thief in a party- if he can move silently, hide successfully, and get into that all important close range, an auto-kill using a bow would make sense. Cool stuff.

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    1. Right, I agree. I've totally removed the normal penalties for shooting into groups at close range for exactly those kinds of observations. Which is nice, because it does give the players (incl. thieves) more tactical options.

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    2. Yes, but shooting into a group of moving people is very, very different than a stationary target. A typical recurve or longbow is shooting an arrow at around 150 to maybe 200 feet per second, where somebody with a gun will hesitate to fire into the same melee with a bullet moving 2,500 feet per second.

      Even the psychology of it is different. It's a lot like a 100 yard shot in golf. Most people have no trouble hitting a ball that far with even a 7-iron. Make the same shot over a water hazard, and a significant number of people suddenly hit short and in the water.

      I'm sure there's a real psychological thing where you are focused on trying not to hit something, so it makes it more likely you'll hit it.

      Remember that bow hunting is dependent on stealth and taking a shot before the deer knows you are there and moves. Granted, hunters are going for a humane, 1-shot kill at about an 8" circle on the side of the deer. But one of the problems that hunters actually have is the deer's reaction time is fast enough, that they can actually react to the sound of the bow (because it travels faster than the arrow), and turn what looks like a clean shot into a complete miss.

      I would imagine trying to shoot somebody at the line of scrimmage after the ball has been snapped. The quarterback might be an easy shot, he's relatively stationary and unprotected, but for the guys locked in melee combat in the front line? I wouldn't want to take that shot.

      In my 5e rules, I give disadvantage on the shot into melee. If the shot misses, the other die is the attack roll against whatever (whomever) the cover was. If there are multiple possibilities, then determine randomly. I don't know how realistic it is, but it feels more realistic to me.

      Ilbranteloth

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    3. Hey Randy: That was my expectation until I saw a bunch of SCA videos with team skirmishes where the archers were firing quite freely into melees (and getting head shots seemingly at will). One observation is that there wasn't quite as much chaos as I might have expected (people forming lines to protect themselves, etc.). Another is that the archers were picking their shots with some care (not full rapid fire). See here.

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    4. Hi, Delta - I may have seen different videos, but most of the shots I saw were for the outliers, somebody moving to enter the combat, etc. Either that or too fast to really see what was happening.

      But as much as they are attempting to simulate the real thing, it's a very different thing when you might accidentally hit your ally with a rubber-tipped arrow vs. what could be a killing blow.

      Even in the sword fighting, the same thing applies. These aren't people actually fighting with their lives on the line.

      Regardless, my approach is from a different angle. It's not so much a question of whether you CAN do it (as it's quite possible in my campaign), it's just a question of whether it's harder. In other words, if the base archery shot probabilities are calculated based on good conditions: no cover, no concealment, and a clear, stationary target, then attempting to shoot at a target that is in the midst of melee would be more difficult. What the appropriate penalty might be is certainly up for debate, but I just think it's harder.

      In my game, targeting somebody in melee imposes the 1/2 cover penalty - disadavantage on the attack, and a +2 to their AC.

      However, a well trained archer (that is, with the Archery Fighting Style), doesn't have disadvantage when somebody is behind cover, and they have a +2 to hit with any shot. In other words, the good archers don't have a penalty at short range when shooting into melee compared to others.

      Fighters, Paladins, and Rangers select a Fighting Style feat at 1st level. Others can gain them, by purchasing a feat. I like the approach, because it fixes a problem I see between 5e and AD&D - the fact that fighters aren't better at hitting things anymore since everybody has the same proficiency bonus, but it keeps it within a narrow field of expertise. If you're a better archer than everybody else, it's because you've put your training into that. You can gain additional Fighting Styles as time goes on.

      I think this reasonably represents that targeting a creature in melee is harder than a target in the open. But if you're well trained, you can do it with almost no penalty. The reality is that you still have a -2 penalty compared to an open target (because your +2 is offsetting the extra AC of the target due to cover), but I think a 10% penalty for shooting into melee as a well trained archer is reasonable.

      PS - the head shots don't really surprise me. In melee, that's the least obscured part of the target. More so, as an archer, you're really targeting about a 3"-6" diameter target. For example, when hunting, you're not trying to HIT the deer. You're trying to KILL the deer in one shot - a shot through their heart.

      For the moment, it's still very hard to get that precise a shot in my game. It would be too deadly otherwise. But I'm still considering how best to simulate it.

      On the other hand, in hunting that requires you to be hidden, and the target stationary. But there are plenty of opportunities for that to happen in the campaign. I'd call it a critical hit, it's just a question of how easily you can get it.

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    5. I think there's a big difference between shooting (you don't fire a bow...) rubber-tipped arrows instead of potentially killing your ally. More importantly, in the videos I've seen, most of the shots I could actually see were for outliers - targets that were entering the melee, or just outside the group.

      Regardless, it's really a factor of working from the opposite direction for me. It's not a question of whether it can be (or is) done. It's a question of whether or not it's harder to do.

      Is shooting a moving target that is randomly partially obscured/covered by other creatures (some of which are friendly) more difficult than shooting a stationary target in the open?

      If the answer is yes, then there should be some sort of penalty to the attack. People take cover for a reason. Duck Hunt is difficult for a reason.

      Does that mean that a well-trained archer can't overcome these penalties? Of course not.

      I've modified Fighting Style feats a bit in my 5e campaign. They all grant the character a +2 to hit with that particular Fighting Style. This is because in 5e fighters aren't better at hitting things any more than other classes.

      The Archery style replaces sharpshooter, but negates the disadvantage for shooting a creature behind cover.

      (1/2 cover in my campaign - +2 AC, others have disadvantage attacking you). Melee combat grants you 1/2 cover. 3/4 cover increases the AC bonus to +5.

      So a character with the Archery Fighting Style has the same chance of hitting a target in melee as anybody else has when shooting at a target in the clear.

      I think that's reasonable. It shows the greatly increased skill of a fighter that has specialized in archery.

      PS - the head shots don't surprise me at all. They are the most visible targets, and protected by the least amount of cover. In addition, an archer is targeting a 3" - 6" circle whenever they shoot. So a head isn't a big deal. I would guess that hitting a head is second to hitting a torso in terms of difficulty. A torso is not only larger, but moves less than the head. But the head is limited in its mobility in regards to the torso. Hitting an arm, on the other hand, is probably harder, since it moves more, and more quickly. A hand is really difficult because it's even more mobile than the upper arm.

      I'm still tweaking the deadliness of arrows in the campaign. A hidden archer within 30 yards should get a high percentage of critical hits if they remain undetected. The best defense (and the one most commonly used) is armor. It might not prevent damage, but would certainly convert a number of those critical hits to just hits. Of course, most folks would at least be disabled with a solid hit with an arrow.

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  4. How high are your ceilings? An inability to "arch" your shot will limit indoor/subterranean range.

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  5. I've been thinking about ranged attack accuracy myself recently, and I think it's important to realize that accuracy under firing range conditions bears very little resemblance to accuracy under combat conditions. I know there are lots of studies of e.g. police incidents that indicate that the miss rate for firearms at a range of 10'-20' is staggeringly high. There is a HUGE difference between shooting at a target in a relatively calm environment, and shooting at a living being in the midst of combat. And if you're far enough away from the enemy that you can take your time and set up your shot calmly, the time of flight may be such that accuracy suffers significantly when shooting at an individual target. Unfortunately I'm not aware of any data for combat archery accuracy...

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    1. It's a real problem for assessment. The best analogy I've come up with is documentation from SCA fights where combat archery is allowed, and I have to say that I was surprised that it seems a lot more accurate than I expected. This is among the reasons that my house rules got tweaked to be a lot more permissive about mid-melee shooting (although harsher about range penalties): http://deltasdnd.blogspot.com/2014/04/a-model-of-archery-for-d.html

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  6. Many years ago I could hit a rabbit or squirrel on the run at about 20 yards with a selfbow, recen tly I had chance to use my brother-in-law's compound bow and out of 5 shots I lost 2 arrows and only 2 struck the target true. No archery for 25 years has me very rusty.

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  7. I don't see how this relates to D&D since I don't see how you could qualify your ability and your target was inanimate.

    The target in Battle as opposed to a select animal or individual is a crucial distinction and flaw with Bow fire in D&D. Ive said before that I'll happily stand 70 yards from someone while they try to hit me with an arrow.

    The most important distinction (and it's never mentioned) is whether the target is aware he is being fired at or not. My rule is that you can only fire at a target who is aware of you at short range.

    In battle this again become unimportant because the target can never know from where he is being fired upon so the bow again becomes very powerful.

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    1. I think you mean "you can only fire at a target who is unaware of you at short range"? I can kind of sympathize with that, because I've also seen it written how important that is in reality. But adjudicating that awareness in a D&D melee seems like a real hassle -- I'd prefer it just be subsumed by the whole surprise/AC/Dex core mechanic.

      Other than that, if you look at "The Model" (link), you'll see that those other concerns are accounted for, in that the in-game D&D archer is being given a total of about +12 bonuses to hit here for the static-target case. Accounting for battle conditions simply means not giving them that bonus, and then you're back to standard D&D with about 50/50 to hit at close range. The real point here is "what should be done about range modifiers?", and the results seem consistent: about -8 per doubling of range.

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    2. --I think you mean "you can only fire at a target who is unaware of you at short range"?--

      No, the point of my rule is that at short range the speed of an arrow is sufficient to make the target's awareness irrelevant. At medium and long ranges I have decided it is impossible to hit an aware target.

      By 'aware target' I do not mean an animal moving in a straight line (which could be hit at long distance). I mean an intelligent target who is watching the bowman.

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    3. Oh I got you; that's reasonable, thanks for the clarification. My own house rule currently on the books is that you just can't shoot at an individual over 40 yards (you might say I'm assuming awareness and non-helplessness), although you can shoot at a random member of a large group.

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    4. I would say that a target displaying Kent's "awareness" is actually performing a parry maneuver: focused on the shooter and the shot, devoting movement to dodging that attacker. Any attacks against him in melee would distract him from his dodging of the shot, so he needs to pick which attacker he's going to defend against. If your game has a simple "full defense" option, maybe he's scampering around generally making himself hard to hit. In either case, because he's devoting so much attention to defense, he must have lower or no attack capability that round (if he can declare defensiveness and also get normal attacks, why would any character ever not do that? And so we must assume that kind of mixed defense/offense middle stance must be subsumed in the regular attack roll vs. AC).

      Then is the target is actually able to see the arrow coming, and where is he going to dodge? This would be better modeled by the shot having random variance in where it lands based on the attack roll, and the defender simply choosing where he will go knowing only that the attacker probably was trying to shoot at him. Imagine a situation where a hundred arrows from a hundred archers are pouring down: how will this man dodge all of those arrows? Instead, he must be in a place when they all land, and whichever arrows hit that place must hit him. He can't turn himself inside-out and slip into a sideways dimension to avoid them all.

      But if you want to use a typical attack roll instead of determining grenade-like scatter, I'd just use the existing parry or full defense rules.

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    5. I could see that from a far enough distance. A fastball and slap shot is around 100 mph, or a penalty kick in soccer about 80 mph.

      In the case of the penalty kick, it's 12 yards, and the goaltender has to commit to the direction before the ball is even kicked. If they guess right they can make small adjustments. 20 yards for the baseball pitch, and the same thing applies, small adjustments can be made (including a check swing), and an attempt (often failing) to avoid being hit by a pitch.

      Some outfielders throw close to 100 mph as well, and that's a 60-70 yard throw. Easy to avoid provided you're watching it and making the attempt.

      A recurve bow shoots an arrow around 150 mph, and a longbow somewhat less than that, between the 100 and 150 mph. Crossbows are about 200 to 350 fps (up to 240 mph), which might extend the distance that you would have difficulty dodging the bolt.

      In the midst of melee, however, it would be a bit more difficult to avoid. Perhaps you could aim for a specific target as you recommend, Delta, within 20 to 30 yards, but I'd still do it with disadvantage. That is, you can select a specific target, you just might miss. Perhaps at 10 yards you'd be OK, but the reality is that even at 10 feet somebody with a gun is usually pretty hesitant.

      All this is very interesting the more you think about it. I'm thinking the shooting into melee is a random target IS the way to go, for nearly any range. So what effect does this have on the other most common ranged attack...spells?

      One could argue that the targeting system for spells is different, in that they act as having a homing capability. But fireball has always had that "unless it strikes something else first" clause.

      Ilbranteloth

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    6. Hi, Randy: See above for how my thoughts were like yours until I saw some SCA skirmish videos. Nowadays I don't give any penalty for shooting into melee at close range.

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  8. Now you need to start incorporating combat conditions. Your stats so far would work well for an archery tournament.

    It doesn't take into account light conditions.

    It is against a stationary target. It would be quite different if the target was moving and even more different if the target was aware. The target can be both proactive (trying to fake the archer out) and reactive (dodging the arrow when in flight, moving shield). Try looking up stuff about martial artists trying to dodge and catch arrows.

    Combat would make the situation different as well: being rushed because something(s) is trying to kill you; talking and coordinating with your party; having to be aware of your surroundings so nothing takes you by surprise; looking for and identifying targets; being attacked by ranged attacks yourself; etc.

    There are lots of statistics about police officer accuracy. e.g.
    http://www.cops.usdoj.gov/pdf/Deadly-Force-Statistical-Analysis.pdf
    http://www.theppsc.org/Staff_Views/Aveni/OIS.pdf

    There is a famous(too strong?) experiment called the Tueller Drill that determines how far an officer has to be from a knife weilding opponent to be able to draw and shoot safely and the distance is about 20 feet. Less than that the officer gets stabbed. This would be similar to a sword weilding fighter charging an archer with arrow in quiver.
    http://en.wikipedia.org/wiki/Tueller_Drill
    The link to the original article is in the notes.

    Keep it up!

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    1. Yeah, actually: if you look at the last post (here), under "The Model", you see that I'm giving the D&D game archer here a total of about +12 bonuses for the target-shooting case. (Namely: +4 for target size, +3 for target null dexterity, +3 for shooter unmoving/unthreatened/aiming, and +2 for 20th-century equipment.) And then the results do line up nicely with both the "Archery" documentation and the bivariate normal physics simulator.

      So if you just back those out what you're left with is the standard D&D hit mechanic at close range against an uncooperative opponent (as one uses for swordplay, of course; about 50/50 for an unarmored opponent if they don't get initiative and close on you first). The residual conclusion is that the real change needed in core the system is to use something on the order of -8 to hit per doubling of range.

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  9. First thought: you're a better archer than I am.

    Second though: I suppose the ideal test would be to have multiple archers of differing skill levels do a static test to provide a baseline, then do a run through a Hogan's Alley firing at multiple pop-up targets with scoring for time and accuracy to see how the scores correlate to skill, but that's hard to set up.

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    1. But it would be awesome!

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    2. Or a football game with a paintball gun?

      Ilbranteloth

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  10. Given that your shots at 40 yds were mostly short, it looks as though this is a systematic error that could be fixed once you had a proper feel for the range/elevation relationship. That could make a significant difference in hit probability. It would have been useful to measure dispersion about the centre of the impacts at different ranges and distance from the centre of the group to the point of aim. You would want a much larger target so you know where the "misses" are going. For practical hit probability, a man-shaped and sized target would make sense.

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