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Due to how the hit chance is calculated the range and tracking do not effect each other and can be considered separately. A nice thing to remember is that against a stationary target the tracking part can be ignored while against a target that is in optimal range the range part can be ignored. | Due to how the hit chance is calculated the range and tracking do not effect each other and can be considered separately. A nice thing to remember is that against a stationary target the tracking part can be ignored while against a target that is in optimal range the range part can be ignored. | ||
== | ==Range== | ||
Every turret has two range parameters called "Optimal Range" and "Accuracy Falloff". | Every turret has two range parameters called "Optimal Range" and "Accuracy Falloff". | ||
A gun's optimal | A gun's optimal range is the range within which distance has no effect on hit chance. In other words in optimal range the distances can be completely ignored and only tracking has any effect on hitting. | ||
Accuracy falloff begins at the end of optimal range. Falloff measures how quickly the chance to hit decreases as the target distance grows ''beyond'' optimal range. At a gun's optimal range ''plus'' its falloff, the chance to hit is reduced to 50%. At a gun's optimal range plus ''twice'' the falloff range, the chance to hit is reduced to only 6.25%. Since other factors can reduce this hit chance even further, at excessive ranges it is often not worth it at all to fire turrets, unless you're trying to draw aggression from a rat (which can be done at maximum targeting range). | Accuracy falloff begins at the end of optimal range. Falloff measures how quickly the chance to hit decreases as the target distance grows ''beyond'' optimal range. At a gun's optimal range ''plus'' its falloff, the chance to hit is reduced to 50%. At a gun's optimal range plus ''twice'' the falloff range, the chance to hit is reduced to only 6.25%. Since other factors can reduce this hit chance even further, at excessive ranges it is often not worth it at all to fire turrets, unless you're trying to draw aggression from a rat (which can be done at maximum targeting range). | ||
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So, for example, you're firing a gun which has 20km optimal range and 6km falloff at a target which is moving steadily straight away from you (zero transversal), starting at only 1km range. You will (if nothing else intervenes) always hit a target that is less than 20km (your optimal range) from you; your chance to hit will gradually decrease as your target moves between 20km and 26km (your optimal + falloff) from you, reaching 50% at 26km. By 32km (optimal + twice your falloff) your chance to hit will be down to 6.25% and decreasing. | So, for example, you're firing a gun which has 20km optimal range and 6km falloff at a target which is moving steadily straight away from you (zero transversal), starting at only 1km range. You will (if nothing else intervenes) always hit a target that is less than 20km (your optimal range) from you; your chance to hit will gradually decrease as your target moves between 20km and 26km (your optimal + falloff) from you, reaching 50% at 26km. By 32km (optimal + twice your falloff) your chance to hit will be down to 6.25% and decreasing. | ||
The penalty for exceeding the optimal range by a small amount is reasonably low; the chance to hit a target at 33% of the falloff range in excess of the optimal range is still above 90%. Minmatar ships especially have | The penalty for exceeding the optimal range by a small amount is reasonably low; the chance to hit a target at 33% of the falloff range in excess of the optimal range is still above 90%. Minmatar ships especially have significant falloff ranges allowing them to fight effectively beyond their optimal range. However, as the distance increases, the chance to hit decreases faster and faster. | ||
When using turrets that fight inside falloff ranges it can be useful to know that being at optimal+(falloff / 2) results in -20% average damage and being at optimal+falloff results in -60% average damage (note: average damage falls faster than hit chance due to how the random damage interval is calculated, see below). | When using turrets that fight inside falloff ranges it can be useful to know that being at optimal+(falloff / 2) results in -20% average damage and being at optimal+falloff results in -60% average damage (note: average damage falls faster than hit chance due to how the random damage interval is calculated, see below). | ||
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The concept of turret tracking value is simple: The smaller a turret is, the faster its tracking speed will be: small autocannon, for example, track faster than medium autocannon. Short-ranged varieties of turret have better tracking than their long-ranged counterparts -- so, for example, medium pulse lasers track faster than medium beam lasers and large blasters track faster than large railguns. There is only one value for tracking unlike the optimal and falloff for range. One way to look at it is to consider the turret to always being in "tracking falloff" witn xero optimal tracking. | The concept of turret tracking value is simple: The smaller a turret is, the faster its tracking speed will be: small autocannon, for example, track faster than medium autocannon. Short-ranged varieties of turret have better tracking than their long-ranged counterparts -- so, for example, medium pulse lasers track faster than medium beam lasers and large blasters track faster than large railguns. There is only one value for tracking unlike the optimal and falloff for range. One way to look at it is to consider the turret to always being in "tracking falloff" witn xero optimal tracking. | ||
[[Image:Angular velocity.png|right|256 px|thumb|The general case of angular velocity. Angular velocity of ship depends on ship velocity, target velocity and distance. The total velocity vector is target velocity vector-your velocity vector and the dashed vectors are parallel and perpendicular components of | [[Image:Angular velocity.png|right|256 px|thumb|The general case of angular velocity. Angular velocity of ship depends on ship velocity, target velocity and distance. The total velocity vector is target velocity vector-your velocity vector and the dashed vectors are parallel and perpendicular components of total velocity vector. Note the 90° angles.]] | ||
[[Image:Orbit angular velcoity.png|right|256 px|thumb|Angular velocity while orbiting is much simpler than the general case. The angular velocity is simply the orbiting velocity multiplied by distance. Many situations where one ship is much faster can be approximated to to be like this.]] | [[Image:Orbit angular velcoity.png|right|256 px|thumb|Angular velocity while orbiting is much simpler than the general case. The angular velocity is simply the orbiting velocity multiplied by distance. Many situations where one ship is much faster can be approximated to to be like this.]] | ||
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The ingame overview can show the angular velocity of a target if you open the settings and tick a box under the tab called columns. Angular velocity is used to determine the penalty to the hit chance based on the turret's tracking ability. Relying on high angular velocities to stay alive is called speed tanking (not to be mixed up with kiting, which is to keep something at range). | The ingame overview can show the angular velocity of a target if you open the settings and tick a box under the tab called columns. Angular velocity is used to determine the penalty to the hit chance based on the turret's tracking ability. Relying on high angular velocities to stay alive is called speed tanking (not to be mixed up with kiting, which is to keep something at range). | ||
Angular velocity is calculated as ω=v<sub>t</sub>/d, where v<sub>t</sub> is | Angular velocity is calculated as ω=v<sub>t</sub>/d, where v<sub>t</sub> is transversal velocity of the target relative to shooter and d is distance to target. Two ships will always have the same angular velocity to each other. | ||
Angular velocity depends on the ratio of transversal velocity and range (it's to do with the geometry of circles and radii) -- but it's easier to think about angular velocity since measurements of it in radians per second relate easily to the figures for gun tracking speed. | Angular velocity depends on the ratio of transversal velocity and range (it's to do with the geometry of circles and radii) -- but it's easier to think about angular velocity since measurements of it in radians per second relate easily to the figures for gun tracking speed. | ||
In chance-to-hit calculations, your guns' tracking speed is compared against your target's angular velocity and signature radius. Angular velocity is a geometric concept to do with radii of circles, but it can be hard to | In chance-to-hit calculations, your guns' tracking speed is compared against your target's angular velocity and signature radius. Angular velocity is a geometric concept to do with radii of circles, but it can be hard to visualize. One way to think about it is to imagine that your screen's point of view in EVE is looking out above the barrels of your turret as it looks at your target -- a turret's-eye-view, so to speak. If your target was moving quickly across your turret's point-of-view, it would have a high angular velocity, and if it was moving slowly across your turret's point-of-view it would have a low angular velocity. Due to symmetry the angular velocity is same for both ships. | ||
The ratio of your target's angular velocity to your guns' tracking speed is what's important. If their angular velocity is high, the ratio will be high, and you're very unlikely to hit them. | The ratio of your target's angular velocity to your guns' tracking speed is what's important. If their angular velocity is high, the ratio will be high, and you're very unlikely to hit them. | ||
The speed at which a target moves across a turret's field of view doesn't depend only on the target's real velocity. The direction the target's moving in relative to the ship firing at it matters too: a ship that burns straight towards you could be quite easy to hit, regardless of its speed, because it's not moving very fast across your turrets' point-of-view. Range also affects angular velocity: a target orbiting you at 400m/s at a range of 7,000m has a much higher angular velocity than a target orbiting you at 400m/s at a range of 30km. | The speed at which a target moves across a turret's field of view doesn't depend only on the target's real velocity. The direction the target's moving in relative to the ship firing at it matters too: a ship that burns straight towards you could be quite easy to hit, regardless of its speed, because it's not moving very fast across your turrets' point-of-view. Range also affects angular velocity: a target orbiting you at 400m/s at a range of 7,000m has a much higher angular velocity than a target orbiting you at 400m/s at a range of 30km. | ||
Lastly the target signature radius. Every ship in EVE has a [[signature radius]] (you can find a figure for yours on the fitting screen). Signature radius represents, roughly speaking, a ship's footprint on everyone else's sensors. This can be | Lastly the target signature radius. Every ship in EVE has a [[signature radius]] (you can find a figure for yours on the fitting screen). Signature radius represents, roughly speaking, a ship's footprint on everyone else's sensors. This can be thought of as multiplier that is applied to the ratio of angular velocity and turret tracking. | ||
Signature radius depends mostly on hull but target painters and many shield modules will increase it. Some examples of ship signature radiuses without modules: | Signature radius depends mostly on hull but target painters and many shield modules will increase it. Some examples of ship signature radiuses without modules: | ||
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Due to how nice ratios are doubling tracking, doubling target signature radius and halving angular velocity all have exactly same effect on hit chance. This makes it very easy to hit large targets at high speeds and also makes webs and manual piloting very effective at manipulating hit chance as seen in sections below. | Due to how nice ratios are doubling tracking, doubling target signature radius and halving angular velocity all have exactly same effect on hit chance. This makes it very easy to hit large targets at high speeds and also makes webs and manual piloting very effective at manipulating hit chance as seen in sections below. | ||
Since the tracking depends on all three: target signature radius, | Since the tracking depends on all three: target signature radius, turret tracking and angular velocity it can be hard to intuitively see when it is possible to hit. For example a medium autocannon with 50 tracking shooting a cruiser with 150 m signature radius and an angular velocity of 0.073 rad/s has 90% chance to hit. In same situation, but when shooting at frigate with 50 m signature, the hit chance is only 39%. | ||
{| class="wikitable" border=0 | {| class="wikitable" border=0 | ||
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|} | |} | ||
It is often best to use [[Third-party tools|a Third-party tools]] to see how well your guns track moving targets. | It is often best to use [[Third-party tools|a Third-party tools]] to see how well your guns track moving targets. Both EFT and PYFA are able to draw damage application figures on moving targets. | ||
Much of this information is most useful when theorycrafting, as there is often little time or need for complex mathematics during combat. However, pilots who are familiar with these concepts can still use them in a general sense to make decisions when in space. | Much of this information is most useful when theorycrafting, as there is often little time or need for complex mathematics during combat. However, pilots who are familiar with these concepts can still use them in a general sense to make decisions when in space. | ||
{{expansion past | Updates to tracking have made it much easier to compare the tracking abilities of different turrets, but they have also made the numbers more abstract and harder to use in combat (not that it was feasible to compare tracking numbers before unless fighting targets of same size). The "Turret Tracking" attribute in the formula used to be split into "Turret Tracking" and "Turret Signature Resolution". Combining them to single | {{expansion past | Updates to tracking have made it much easier to compare the tracking abilities of different turrets, but they have also made the numbers more abstract and harder to use in combat (not that it was feasible to compare tracking numbers before unless fighting targets of same size). The "Turret Tracking" attribute in the formula used to be split into "Turret Tracking" and "Turret Signature Resolution". Combining them to single number simplified the formula without changing any mechanics. If you need to calculate turret hit chance with "Turret Signature Resolution" (for example using old NPC attribute info) just replace 40000 with Turret Signature Resolution. If you encounter nonsensical tracking values anywhere they may be in this old format. | ||
To convert turret tracking speed to rad/s the following formula can be used: | To convert turret tracking speed to rad/s the following formula can be used: | ||
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''fall<sub>turret</sub>'' is falloff range of turret | ''fall<sub>turret</sub>'' is falloff range of turret | ||
The hit chance equation has the form of ''x''<sup>(''a''+''b'')</sup>, which can also be written as ''x<sup>a</sup>x<sup>b</sup>''. In this case, x = 0.5, a = all tracking terms and b = all range terms. In other words, the hit chance equation can be thought of as having two separate parts (tracking and range), which are calculated individually and then multiplied at the end to get the final hit chance. This means that tracking and range don't interfere with one another, they are indeed two | The hit chance equation has the form of ''x''<sup>(''a''+''b'')</sup>, which can also be written as ''x<sup>a</sup>x<sup>b</sup>''. In this case, x = 0.5, a = all tracking terms and b = all range terms. In other words, the hit chance equation can be thought of as having two separate parts (tracking and range), which are calculated individually and then multiplied at the end to get the final hit chance. This means that tracking and range don't interfere with one another, they are indeed two separate things. | ||
The equation also shows that the reduction of hit chance from falloff and tracking respectively follow the same pattern. This is because they both look like ''0.5''<sup>(something / x)<sup>2</sup></sup>, where x is either tracking or falloff. The only | The equation also shows that the reduction of hit chance from falloff and tracking respectively follow the same pattern. This is because they both look like ''0.5''<sup>(something / x)<sup>2</sup></sup>, where x is either tracking or falloff. The only difference between them are the input variables, the output look the same. | ||
The equation is not fully realistic, as it only considers the relative movement between the attacker and the target, and does not take into account any rotation of the attacking ship. From the attacker's point of view, this relative movement appears as a change in the angle to the target. | The equation is not fully realistic, as it only considers the relative movement between the attacker and the target, and does not take into account any rotation of the attacking ship. From the attacker's point of view, this relative movement appears as a change in the angle to the target. | ||
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The damage that a turret deal will be randomly spread around a fixed value called base damage. The base damage is calculated from the turret's Damage Multiplier attribute, the ammo's damage values, hull modifiers and skills. The base damage is the so called "paper damage" that is shown in all info windows. "Paper DPS" is simply "paper damage" divided by rate of fire. | The damage that a turret deal will be randomly spread around a fixed value called base damage. The base damage is calculated from the turret's Damage Multiplier attribute, the ammo's damage values, hull modifiers and skills. The base damage is the so called "paper damage" that is shown in all info windows. "Paper DPS" is simply "paper damage" divided by rate of fire. | ||
But the | But the surprising part of damage mechanic is that the damage calculations are linked to hit chance calculations. At the heart of each turret's damage output is a single randomly generated value between 0 and 1 that is several digits long. This random number is used to determine '''both''' if the turret hits and how much damage it does. Unfortunately, the misses are those random numbers that would have caused the most damage. If the random number is less than 0.01 (1% chance) a special case occurs, a perfect hit, these will always deal exactly 300% of the base damage. A funny result of this is that when the hit chance is 1% or less, only misses and perfect hits can occur. | ||
The damage modifier for a normal hit is calculated with the following formula. In 100% hit chance situation this leads to even distribution from 50% to 150% with extra spike at 300% damage. | The damage modifier for a normal hit is calculated with the following formula. In 100% hit chance situation this leads to even distribution from 50% to 150% with extra spike at 300% damage. | ||
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=Practical applications= | =Practical applications= | ||
[[Image:Eft dps figure.png|right|500 px|thumb|Since the hit chance can be hard to work on intuitively it is often best to use a tool for it. Analyzing these figures allows the pilot to choose best weapon system for the engagement range and the best engagement range for a weapon system. Here is an example dps figure generated with EFT that shows maelstrom with artillery (green) and autocannons (red) shooting at a maelstrom. Here you can easily see that the best range for artillery is at around 40 km and the choice between AC and artillery depends on | [[Image:Eft dps figure.png|right|500 px|thumb|Since the hit chance can be hard to work on intuitively it is often best to use a tool for it. Analyzing these figures allows the pilot to choose best weapon system for the engagement range and the best engagement range for a weapon system. Here is an example dps figure generated with EFT that shows maelstrom with artillery (green) and autocannons (red) shooting at a maelstrom. Here you can easily see that the best range for artillery is at around 40 km and the choice between AC and artillery depends on whether fight happens at below or above 30 km. Both EFT and PYFA can create these figures.]] | ||
The hit chance and its relation to range, tracking, | The hit chance and its relation to range, tracking, velocity and signature radius have many effects on combat with turret ships. Taking advantage of this knowledge allows you to control range, control velocities and choose the right modules for the job. This section gives several useful tricks and maneuvers for ships that either fight with turrets or against a turret ship. | ||
Although you can add angular velocity (or transversal velocity, if you want it) as an extra column to your overview, you'll never have the time in combat to get out a calculator and run through chance-to-hit equations. There are however some tactics which let you use gunnery mechanics to your advantage. | Although you can add angular velocity (or transversal velocity, if you want it) as an extra column to your overview, you'll never have the time in combat to get out a calculator and run through chance-to-hit equations. There are however some tactics which let you use gunnery mechanics to your advantage. | ||
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Although you can use tools like EFT's DPS graphs, this knowledge comes partly with experience. It's much easier to figure out against NPC rats, which always have the same characteristics while kindly heading more or less straight for you until they close into their preferred orbit range, than it is with PvP enemies. | Although you can use tools like EFT's DPS graphs, this knowledge comes partly with experience. It's much easier to figure out against NPC rats, which always have the same characteristics while kindly heading more or less straight for you until they close into their preferred orbit range, than it is with PvP enemies. | ||
But range control is not the end of turret | But range control is not the end of turret management. You must also always remember that range is directly tied to angular velocity. In practice, if you're using long-ranged turrets (artillery, railguns and beam lasers) you will find that once targets get close enough within your optimal range their angular velocity will rise so much that you can't hit them. Some ways to handle small, fast, closely-orbiting targets are discussed below. Besides dealing with them once they do get close, it's worth finding a range which is within your optimal yet far enough away that the enemy are easy to track. | ||
If your ship is faster and more agile, and the opponent is orbiting you, the angular velocity can be minimized (can reach zero) by using Approach. If your ship is slower or less agile, and the opponent is orbiting you, angular velocity can be minimized by using Keep at Range (if set to far away, but be warned: if you reach this range your ship will stop). Alternatively, if your ship has very poor agility, it is better to fly in a straight line to maximize your own speed and let the orbiting ship chase after you. Maximizing the angular velocity is harder but will happen if both ships orbit one another, or if one is using Approach but isn't agile enough to get behind the other. A ships agility is the multiplication of its inertia modifier and mass, a lower value means it can do sharper turns. | If your ship is faster and more agile, and the opponent is orbiting you, the angular velocity can be minimized (can reach zero) by using Approach. If your ship is slower or less agile, and the opponent is orbiting you, angular velocity can be minimized by using Keep at Range (if set to far away, but be warned: if you reach this range your ship will stop). Alternatively, if your ship has very poor agility, it is better to fly in a straight line to maximize your own speed and let the orbiting ship chase after you. Maximizing the angular velocity is harder but will happen if both ships orbit one another, or if one is using Approach but isn't agile enough to get behind the other. A ships agility is the multiplication of its inertia modifier and mass, a lower value means it can do sharper turns. | ||
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* You can try burning away from them -- hopefully encouraging them to follow you in a straight line. | * You can try burning away from them -- hopefully encouraging them to follow you in a straight line. | ||
* If they're not chasing you directly you can try burning on a course parallel to theirs and in the same direction, which should also reduce angular velocity. | * If they're not chasing you directly you can try burning on a course parallel to theirs and in the same direction, which should also reduce angular velocity. | ||
* If they're trying to keep beyond a particular range (web range, for example) from you, you can try burning straight towards them -- they may make the mistake of burning directly away from you along the course you're | * If they're trying to keep beyond a particular range (web range, for example) from you, you can try burning straight towards them -- they may make the mistake of burning directly away from you along the course you're traveling. | ||
* If you're fighting a player who's trying to keep outside of web range, but has to stay within the range of a long point to keep you tackled, you can try burning away to get them to chase you, and then turning around and burning towards them -- at least this will disrupt their orbit, and at best you will trick them into web range (again, remember that overheating increases web range). | * If you're fighting a player who's trying to keep outside of web range, but has to stay within the range of a long point to keep you tackled, you can try burning away to get them to chase you, and then turning around and burning towards them -- at least this will disrupt their orbit, and at best you will trick them into web range (again, remember that overheating increases web range). | ||
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Therefore it's wise to spiral in towards the enemy. To do this: | Therefore it's wise to spiral in towards the enemy. To do this: | ||
# Zoom in reasonably close to your ship and press C to make your camera autofollow the selected enemy (alternatively | # Zoom in reasonably close to your ship and press C to make your camera autofollow the selected enemy (alternatively center the camera on your enemy manually so that it covers up the enemy on your screen.) | ||
# Now double-click in space halfway between your ship and the edge of the screen (in any direction). | # Now double-click in space halfway between your ship and the edge of the screen (in any direction). | ||
# Your ship will begin moving roughly towards the enemy, but not directly at them; it will also move away from its position covering the enemy ship on your screen. | # Your ship will begin moving roughly towards the enemy, but not directly at them; it will also move away from its position covering the enemy ship on your screen. | ||