But what if the safer place is across the field? Do you stay where you're at, or run like a fool?

The archer will aim for where he expects the target to be. It is called "leading the target." Anyone who has any experience doing things such as "going outside" is going to be moderately skilled at this. A longbow archer is presumably going to have more skill at this than the average mathematician.

Assume that the arrow travels at an average speed of 100 fps during its flight,* the archer is competent, and the target can, in fact, actually run:

The runner will be more than a few sigma archer-error away from where he appears to be heading (or his initial starting point) by the time the arrow arrives if he zigzags (or even changes his rate of travel).

The error (distribution) simply cancels itself out since it is the same regardless of where the target is when the arrow arrives.

Assuming that the archer has approximately the equivalent experience in sports as the least naturally coordinated member of SMP and has never ventured outside, I agree that it is very difficult.

How many arrows will be shot will determine the value of moving away from the archer. People are generally a bit taller than they are thick.

The archer would be quite silly to reduce the apparent size of the target by not shooting at as low of an angle as possible. Your average 6' tall man isn't 6' thick.

I am a bit out of shape and I am still twice as wide as I am thick, so emphasizing running away would be a bit foolish for a fit target.

*the longbowman is amazingly strong to maximize the likelihood that I am wrong.

fyp

I'm always amused when people realize their errors but have too big of an ego to admit it. So instead, they ramble on about something other than the statement they actually made and proceeds to talk about something else.

Me too. I pointed out quite well how the error in aiming (variance) cancels itself out.

Did you miss that part?

I stand still for getting the experience better.

I missed your bit. Were you suggesting taking an arrow to a body part just to have the experience?

If someone says "variance cancels itself out" I'm just going to stare blankly at them like they're crazy until they prove otherwise.

Nope. I figured you didn't know what you were saying. But I'll give you a chance.

The error in aim is going to be the same regardless of where the target decides to move laterally. It is therefore completely irrelevant to the question of whether the target should zigzag or not.

Try to catch up.

Ok lets try a crude study again.

If the archer makes a huge error at some significant distance due to also wind effects etc and the arrow takes 2 sec to get there at 65 m/s speed aiming in the general projected future area, that the runner was moving towards at the time he released, then the runner has 2 sec to alter that and they would be doing it anyway every 2 seconds in the way they move. If that is 1m/sec relative speed change to the left or right say out of the net 7m/sec they are running with (ie running away is the dominant approach here) then they can introduce a distance of order 2m-3m from where they were going say due to the change in velocity vector etc.

Now if the x,y coordinates of the arrow trajectory were some x=v*cos(theta)*cos(f)*t and y=v*cos(theta)*sin(f)*t and at time t=2sec the arrow is at z=human mid height level say

then the error in x ie dx due to uncertainties in v, Theta and f on the launch (from the perfect aim say of where the runner would have been without change in velocity if the archer was an AI say ) is;

dx=((cos(theta*cos(f)*t)^2*dv^2+(v*sin(theta)*cos( f)*t)^2*d(theta)^2+(v*cos(theta)*cos(f)*2)^2*df^2) ^(1/2)

For say v=65m/sec (and errors 1% in speed and 0.5 deg in angles) and assuming for simplicity without losing anything important in the argument that at the time the radial direction of runner say during a moment his speed happened to be purely radial was the line y=x ie f=45 deg and say theta was 10 deg we would have

v=65m/sec dv=0.65m/s, f=45 df=0.5, theta=10 deg d(theta)=0.5

and as a result from above

dx~0.6 m
Similarly for dy.

So basically he is off by some 0.8m say standard error from where he intended due to dx, dy the propagated uncertainties of initial parameters.

At the same time the guy has moved away from that future direction point 2-3m due to tangential speed .

So clearly the move made a difference and placed him well outside the aim/execution error range by at least 2-3 sd.

At 20-30 m the error is also about 0.2m or less say for most decent archers on moving targets. At that point the zig zag effort would have made only a small difference because the arrow comes very fast now in only 0.3sec and he would have not had enough time to change speed significantly from where it was 0.3 sec ago (if he can deliver a change of 1.5m/sec in 1 sec by a sharp turn that is only 1/2*1.5*0.3^2=0.07m in just 0.3 sec time (ie the delay between aim/launch situation and arrival)

What this means is that assuming the archer can evaluate the speed and position of the runner when real close say within 20-30 meters the aiming error is order 0.2m or less but the zig zag is only helping taking us off target by 0.07m only from where we were going. Its futile. Even at 0.1m its little effect mostly because the human reaction time is not fast enough when you have only 0.3-0.4 sec to change from where you were seen going. Zig zag is effective if you have over 1 sec to do it from the moment you change direction to the next change. Ie you need the arrow to have flight time that is comparable to the ability you have to produce a legitimate change in anticipated position through the zig zag.


This is why i said that zig-zag is not effective when real close but is important when further away than say 30-40 meters.


So the first 30 meters the priority must be to run fast. Then after 30-40 meters start zig zagging with changes in speed of order 1-2 m/sec vertically to the radial direction.

At this point zig zag makes a difference.


So the proper strategy is this in my opinion before solving it seriously or simulating it;


The first 30-40 meters run like crazy and after the first 5-10m, that you were running away from archer as fast as you could, make a turn so that your velocity vector is no longer radial. That gives the archer a moving target in 2 dimensions. So instead of the archer shooting at your back moving away radially without having to adjust for tangential speed you force them to adjust now and have to constantly rotate their bow.

That introduces a small delay in the radial progress of creating a distance after the first 10 meters but it makes the archer have to shoot a target that is moving in a manner that he needs to follow him with the bow rotating at the same time he is aiming.


After you reach 40m start zig zagging gradually devoting say 20-30% of your speed in these random left right games until you reach over 100m at which point the arrows take ~2 sec to reach you and you can be easily changing velocity by 1-2m/sec within these 2 seconds and changing position vs where you were going by 2-3 meters while his error is like 0.8 or so.


Then run to safety after 150-200m in any manner of randomness you like without losing sight connection with a fixed horizon spot to guide your randomness to not messing up your progress.


So first 10 m (2-3 seconds say) run like hell straight away towards a far point/landmark you spot instantly and then after the 10m make a turn and start moving at some 30 deg angle from prior direction towards a new landmark point to generate the tangential speed that will force the archer to keep rotating to aim at your future points. This will also give you a smaller torso cross section so what you lose in radial progress you kind of get in reduction of cross section (ie he doesnt see your back vertically). You can achieve the same result if from the start you were running in a light spiral sense aiming to turn 30 degree or so net eventually before stopping the spiral. As you reach 30-35 m (5 seconds after you made the turn ) away from archer start the zig zagging, rapidly changing direction every 1-2 seconds never missing sight of the second landmark and your general progress towards it. Keep zig zagging progressively less furiously after 150 meters (so zig zag for 20-25 seconds basically) and you are almost safe now.


Basically if you have a head start like in the movie clip there is no way in hell they get you so easily at the slow pace the archer was releasing new arrows wasting valuable early time. So head start is super important. Worse case scenario if they take 3 second to load you are only 10-15 m away when he fires the first one and its very hard to survive an expert and zig zagging is not yet even relevant. But if you have a 3 sec head start before they start loading and they take another 3 seconds to release the first you can be significantly far say 20-30 meters and the above is a decent plan.

I think your perspective of the race is in error. You're about to be lapped.

That statement is a very far cry from your original statement, which only goes to show how much you need to shy away from it because of the magnitude of the error. But don't worry. Errors cancel themselves out. I mean... ummm.. variance does.

Just misunderstand me right!

Right so I'm currently interested in pattern finding. I'm a senior at uni studying computer science and I am looking for a book (or two) to read about the general concepts / ideas / theory behind pattern recognition / finding. Doesn't need to be a cs book, and I would actually prefer if it wasn't. Also it would be ideal if it wasn't super mathy. I mean I start calc 3 (double integrals, vectors, etc) monday and have taking math 361(probability and statistics using calculus) but I hate math.

So, let me know of your favorites!

The error in aim is precisely the same as variance around the intended target. They are one and the same.

I cannot recall a single time that someone said error and variance are the same thing when they knew what they were talking about.

You've also clearly never done any serious archery. Or competitive shooting. Or sniping. Or any other outdoor activity that involves projectiles or frisbees.

So I imagine that this will be the first time you have heard the term "standard error." Cool! I haven't experienced anyone hearing it for the first time since I taught statistics!

LOL - Your intellectual failure is confirmed. You still have no idea why you're wrong, and it's hilarious! Go shoot some arrows outside for a while. You'll figure it out in a couple arrows.

I'm busy losing a bunch of money right now. Will be back soon.

I'd say this is partly true, the archer trying to hit the target the best he can induces this, but we are only talking about the archer dependent part. The total variance around the target may contain also other components. So the error in aim is directly a component in the variance around the target, but it's not all of it. Therefore the statement is only partly true, Brian.

Actually at a decent distance away, maybe 80-100 meters? It's best to stop and jog backwards, watching the archer so you can simply dodge arrows.

When playing rock-paper-scissors it's generally best not to always play leave the European Union.

PairTheBoard

Lolnationalismments?

Good luck

Can't believe my eyes, are they really leaving? Being an island must go to your head. But maybe better so, being the squeaking wheel with an odd currency.

What, someone bet the wrong side. You have been listening and/or heeding the advice of the wrong people.

Lord Nelson just got an erection. Happy times are here again.