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Complex Potential
Soliders Of Eve The Church.
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Posted - 2008.03.09 10:42:00 -
[1]
Hi guys
I've been putting some thought into what the 'perfect' orbit speed would be, and I figured it would probably be the fastest you can go at optimal range while still being able to physically track the target.
WARNING: Maths ahead.
Now here's the thing; how do you work out that top speed out? Eve's game mechanics mean that it treats the tracking on both the orbiter and orbitee (you know what I mean) exactly the same, so for this calculation, let's pretend we are sat still and our target is whizzing around us. The speed he goes at would be equivalent to you whizzing round him.
Assume he's in a perfect orbit at distance 'D' m from you moving at speed 'V' m/s and your gun is tracking him, moving at a rate of 'R' rad/s (radians per second which is what eve quotes tracking in, quite handily).
Now because he is in perfect orbit, V is actually the transversal velocity because there is no radial component.
so in the case of Eve these 3 variables are mathematically linked simply by
V = D*R
Where V is the transversal, D is the optimal range and R is the tracking speed of your gun.
Let's take the case of a Megathron with Neutron Blaster Cannon IIs and Void ammo. Assuming you have your opponent webbed and at optimal range, what would be the fastest you could orbit?
Well, you'd know D because that's your optimal range given in the weapon info and you'd also know R because that is your tracking also given in the weapon info.
So, with my skills, the Blasters have an optimal of D = 6750m and R = 0.03518 rad/s.
Therefore V = D*R = 6750*0.03518 = 237.5 m/s
If your ship moves any faster than that your guns physically couldn't move around fast enough to keep up with the target.
This obviously just gives an estimate because is does not acount for sig radius and other stuff like that, but it's interesting that the numbers come out sounding reasonable.
Conversely, you could use the above formulae to find the closest orbit distance based on your ship's top speed and gun tracking.
ie. D = V / R
where V is your ship's top speed and R is your tracking (both known).
I've had a play and it seems to come out ok for the most part.
I tried it with a Raptor, using 125mm railguns with spike ammo and orbit distance of 20km. It predicts a 'perfect' orbit speed of 531 m/s.
How realistic this is, I'm not sure. Maybe Raptor pilots can orbit at 20km at 5000 m/s and still hit with spike ammo, but I'd be willing to bet not very often.
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Ogul
Caldari ZiTek Deepspace Explorations Interstellar Alcohol Conglomerate
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Posted - 2008.03.09 10:56:00 -
[2]
Edited by: Ogul on 09/03/2008 10:58:14 You have completely ignored optimal range, falloff and the ratio of your target's sig radius to your turret's sig resolution.
Additionall, your tracking being higher than your target's angular velocity does not mean you will hit. The ratio between those two numbers just determines the hit chance.
--- This is a war declaration, issued from your alt corp. It is used to gank people in high sec. |
Glassback
Body Count Inc. Mercenary Coalition
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Posted - 2008.03.09 10:59:00 -
[3]
Check your opti range and use that as "Keep At" range.
Orbiting using guns means they will miss more often.
G.
LinkedIn
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Marine HK4861
Caldari Radical Technologies
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Posted - 2008.03.09 11:19:00 -
[4]
Your calculations are correct, the problem is your one assumption that you're in a perfect orbit.
You can't affect the Signature Resolution/Signature Radius part of the equation except by using smaller guns or a target painter, so it effectively becomes a constant.
Unless you're fighting a heavily webbed target or a stationary missile boat, you'll never be able to maintain your optimal range and hence the part of the tracking equation that deals with Optimal and Fall off will keep flicking on and off.
Another issue would be setting the exact speed in-game, although you could probably get close.
The final problem is whether you have better tracking than the target. If he has better tracking than you, he'll be able to hit you more easily at your perfect orbit speed, to say nothing of his friend in another ship outside of your perfect orbit speed (and has relatively lower transversal) or missile ships.
The way EVE PVP works, there's little point in going at anything below your maximum possible speed in combat.
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Complex Potential
Soliders Of Eve The Church.
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Posted - 2008.03.09 11:19:00 -
[5]
Originally by: Ogul Edited by: Ogul on 09/03/2008 10:58:14 You have completely ignored optimal range, falloff and the ratio of your target's sig radius to your turret's sig resolution.
Additionall, your tracking being higher than your target's angular velocity does not mean you will hit. The ratio between those two numbers just determines the hit chance.
And you have completely ignored half my post which stated that it was just a prediction, not taking into account sig radius and other stuff. This was more a thought experiment rather than an exact answer.
I'm perfectly aware of what factors effect tracking, but sometimes a simplified model can help us to understand a more complex system. This is a fairly standard methodology I had to apply during my Maths degree, but I dont suppose you have one of those?
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Complex Potential
Soliders Of Eve The Church.
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Posted - 2008.03.09 11:22:00 -
[6]
Originally by: Marine HK4861 Your calculations are correct, the problem is your one assumption that you're in a perfect orbit.
You can't affect the Signature Resolution/Signature Radius part of the equation except by using smaller guns or a target painter, so it effectively becomes a constant.
Unless you're fighting a heavily webbed target or a stationary missile boat, you'll never be able to maintain your optimal range and hence the part of the tracking equation that deals with Optimal and Fall off will keep flicking on and off.
Another issue would be setting the exact speed in-game, although you could probably get close.
The final problem is whether you have better tracking than the target. If he has better tracking than you, he'll be able to hit you more easily at your perfect orbit speed, to say nothing of his friend in another ship outside of your perfect orbit speed (and has relatively lower transversal) or missile ships.
The way EVE PVP works, there's little point in going at anything below your maximum possible speed in combat.
Thanks for the constructive comments. This was more the idea of why I posted this up. I'm always interested in the differences between real life and Eve mechanics. How closely the two can be put together never seems to match up that well.
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Marine HK4861
Caldari Radical Technologies
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Posted - 2008.03.09 11:28:00 -
[7]
Originally by: Complex Potential
I'm always interested in the differences between real life and Eve mechanics. How closely the two can be put together never seems to match up that well.
If it were real life, the orbiting ship wouldn't have any tracking problems as the target ship is always in the same position relative to its guns.
The only problem then would be how fast and how close it could go, to affect the target ship's tracking.
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Kazuo Ishiguro
House of Marbles Zzz
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Posted - 2008.03.09 11:36:00 -
[8]
When considering range, you're OK within optimal but beyond that you hit less frequently. Tracking is different. Any transverse motion at all reduces your chance to hit (unless your target is an anchored object). There is no positive threshold for tracking within which turrets can 'keep up' and always hit an orbiting target, despite what the tracking guide says about turrets being able to 'keep up'.
I refer you to the hit chance formula: http://wiki.eve-dev.net/Tracking
Let me know if you still have any questions. My research services Spreadsheets: Top speed calculation - Halo Implant stats |
Ogul
Caldari ZiTek Deepspace Explorations Interstellar Alcohol Conglomerate
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Posted - 2008.03.09 11:53:00 -
[9]
Originally by: Complex Potential
And you have completely ignored half my post which stated that it was just a prediction, not taking into account sig radius and other stuff. This was more a thought experiment rather than an exact answer.
I'm perfectly aware of what factors effect tracking, but sometimes a simplified model can help us to understand a more complex system. This is a fairly standard methodology I had to apply during my Maths degree, but I dont suppose you have one of those?
I really like your ad hominems attacks. Let me return the favour.
If you know what factors effect tracking your "maths degree" should enable you to apply them to the correct expression (which is of gaussian shape inside optimal range as far as I remember).
Your simplified model does not predict hit chances (or anything else), it just produces a "perfect orbit speed" out of thin air (disregarding a shockingly large number of relevant details). However, there is still a chance I might be wrong and lack the appropriate degree to understand your maths that consists of multiplying two numbers.
--- This is a war declaration, issued from your alt corp. It is used to gank people in high sec. |
Marine HK4861
Caldari Radical Technologies
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Posted - 2008.03.09 12:56:00 -
[10]
Originally by: Kazuo Ishiguro There is no positive threshold for tracking within which turrets can 'keep up' and always hit an orbiting target, despite what the tracking guide says about turrets being able to 'keep up'.
There is however a maximum speed you can orbit at optimal distance, where you'll have the best chance of hitting.
This was what the OP was trying to work out, not the highest transversal you can go where you'll always hit, which as you've pointed out, is impossible unless you're both stationary.
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Akita T
Caldari Navy Volunteer Task Force
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Posted - 2008.03.09 13:24:00 -
[11]
Edited by: Akita T on 09/03/2008 13:35:42 ___
To answer the OP's question : the perfect orbit speed is zero. Due to the way chance to hit is calculated (and the fact turret "tracking" isn't actual tracking at all, but something else entirely), Kazuo Ishiguro is absolutely, 100% correct. The faster you go, the lower the hit chance. Drops slowly at low speeds, starts dropping faster and faster as you get closer to the 50% chance to hit speed mentioned above, then starts dropping slower and slower again.
EDIT : Just to make it a bit clearer.
Quote: So, with my skills, the Blasters have an optimal of D = 6750m and R = 0.03518 rad/s. Therefore V = D*R = 6750*0.03518 = 237.5 m/s
The example in the OP, the "perfect orbit speed" you get there is not the orbit speed for 100% chance to hit nor 100% DPS. It's actually the "orbit speed for 50% chance to hit", and roughly 40% DPS output.
Originally by: Marine HK4861 There is however a maximum speed you can orbit at optimal distance, where you'll have the best chance of hitting.
Hate to repeat myself, and Kazuo Ishiguro too. That maximum speed is exactly zero. Anything other than zero, and you have less than 100% chance to hit.
______
Now, to RE-PHRASE the question of the OP, so he can better understand the underlying issues:
"How fast should I be going so that the ratio of (damage inflicted by me to the target - damage the target can repair) / (damage inflicted by my target to me - damage I can repair) is maximized, while making sure I can survive longer than my target will ?"
If you want to do any math, do it on this:
z is the "To-Hit Chance", a number between 0 (0%) and 1 (100%) x = random number between 0 and 1 z = ((1/2)^((((Transv/(Range*Tracking))*(Sig_Res/Sig_Rad))^2) +((max(0,Range-Optimal))/Falloff)^2))
If {x<0.01} Then {quality = 3} else {quality = x + 0.49} If {x<z} Then {damage = quality x expected base damage}
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Marine HK4861
Caldari Radical Technologies
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Posted - 2008.03.09 14:00:00 -
[12]
Originally by: Akita T
Originally by: Marine HK4861 There is however a maximum speed you can orbit at optimal distance, where you'll have the best chance of hitting.
Hate to repeat myself, and Kazuo Ishiguro too. That maximum speed is exactly zero. Anything other than zero, and you have less than 100% chance to hit.
Hmmm, I don't think I explained myself clearly enough.
Yes, the perfect chance to hit is when you're both stationary, but as stated elsewhere in the thread, the chance to hit under optimal range is a gaussian curve.
There is a point on the curve at which the chance of hitting drops at a linear rate - this is the point I meant where you'll have the best chance of hitting while still moving.
Crunching some numbers, this point is approximately about 0.5 on the Transversal/(Range*Tracking) function, so at optimal distance, you can be moving at half the value calculated by Complex Potential's equation and still have an 85-ish% chance of hitting, on tracking alone.
Of course once you start taking into account Signature Resolution/Signature Radius and the other factors, it's not so perfect anymore, but that's not the point of the thread.
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Akita T
Caldari Navy Volunteer Task Force
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Posted - 2008.03.09 15:58:00 -
[13]
Edited by: Akita T on 09/03/2008 15:58:46
Well, the word you're looking for is not "best" then, but rather "good enough". And, as with everything human, the exact definition of "good enough" is pretty volatile.
You know, stuff like "still have a 90% chance to hit" or "still deal around 90% DPS" would make a lot more sense.
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Gabriel Karade
Nulli-Secundus
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Posted - 2008.03.09 16:10:00 -
[14]
It's a real shame tracking is modelled using two point-like objects, and makes no account of the angle of arc the target subtends at different ranges; it would add a lot tactics wise if ship rotation actually affected the relative angular velocity between the target and shooter, and missing a Km long Battleship blotting out the sun didn't occur...
Anyway as has been pointed out it's basically a 50% hit chance at turret 'tracking speed', which incidentally has nothing to do with the turret not being able to 'keep up' - all turrets in Eve visibly transverse through 360 degrees in a couple of seconds.
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Video - 'War-Machine' |
Akita T
Caldari Navy Volunteer Task Force
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Posted - 2008.03.11 14:03:00 -
[15]
To be honest, it would make a lot more sense to have turret tracking actually be "tracking" (can keep up, can't keep up, and OWN ship rotation would matter too), and accuracy actually be "accuracy" (gaussian "splatter pattern" distribution assumed in a certain volumetric angle centered on the target)... then we wouldn't need the "signature resolution" at all.
The side-effects however would be that: * sniping fits would have a lot of trouble hitting a stationary small target right besides a stationary huge target that gets easily hit * a fast ship orbiting an identical ship that just sits there gets results as if the target is holding still, but the standing-around-not-moving ship would have problems hitting the orbiter
Pretty much everything else would remain almost the same... but you'd have to include optimal/falloff in the damage multiplier category, not the chance to hit formula.
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Marine HK4861
Caldari Radical Technologies
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Posted - 2008.03.11 18:24:00 -
[16]
Originally by: Akita T
* a fast ship orbiting an identical ship that just sits there gets results as if the target is holding still, but the standing-around-not-moving ship would have problems hitting the orbiter
This would also have the side effect of making nano-turret ships able to deal damage as they no longer have a tracking issue.
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Dismus
Gallente The Scope
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Posted - 2008.03.11 21:09:00 -
[17]
Akita, another cause of the current tracking system might likely be that, due to the increased amount of calculations your method would require (maybe I'm wrong and it's just the way it looks at first glance), there would - in the end - be more server load, since most calculations happen on the server to prevent anyone gaining the ability to alter the game's values as they're sitting on the client-side (ie. the PC running the game, not the server orchestrating it).
I really wish they'd institute a tracking system like you've suggested as well, but given all these optimizations that have been thrown at Tranquility over the last year, it might be easier said than done.
Maybe we're all lucky, though, and this is coming after they get some breathing room for the processors.
Originally by: Draeca Domi isn't ugly, it actually looks quite symphatic. I mean, a crossbreed of a whale and a potato.. Now how cute is that?
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Akita T
Caldari Navy Volunteer Task Force
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Posted - 2008.03.11 21:17:00 -
[18]
Yes, it would be a bit more "computationally expensive" to do it that way (since you'd have to also compute ship and gun orientation in 3D), but then again they could just double all damages and halve all rates of fire to go back to about the same overall load, for instance. However, it can be further optimized, since the "can track" part would be a boolean value that could be used as a condition to calculate the actual shot in case you can track (all the damage calculations), otherwise don't shoot and throw a "turret can't keep up with target" message.
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