Gunnery 201

From UniWiki

Contents 1 Class Information 1.1 General Information 1.2 Notes for the Teacher 2 Class Contents 2.1 Introduction 2.2 Introduction to the "To Hit Equation" 2.3 Myth: EVE combat is "spreadsheets in space" 2.4 Coupling of "To Hit" and "Damage" 2.5 Separation Into Distinct Terms 2.6 Signature Term 2.7 Tracking Term 2.8 Range Term 2.9 To-Hit Equation Summary 2.10 Optional Exercise 2.11 Class Wrap-up

Class Information

This chapter contains the standard information of this class pertaining to scheduling and class contents. The General Information should be sufficient to create a proper class topic for scheduling on the Eve University forum. Additional information relevant to the teacher is listed under Notes for the Teacher.

General Information

Illustration link for class description on the Eve University forum: http://util.eveuniversity.org/media/img/Charlie_Gunnery.gif

This is an Advanced Class and thus a basic level of gunnery knowledge is assumed. It is recommended (but not strictly required) that the student have attended or listened to a recording of the "Gunnery 101" class. Those who have not may still attend, but the instructor try to avoid reviewing the basic material to stay within the scheduled class time.

• Duration: 1.5 hours
• Location: Docked up safely in a station

Class contents:

• High level class topics
• Key sections of content
• Outlined in sequence
• Q&A

Student requirements:

• Mumble registration and access - make sure you have Mumble sorted out and operational well before the class begins. Use this guide for set-up: http://wiki.eveuniversity.org/Mumble
• Access to the Class.E-UNI in-game chat channel
• Optional: Understanding of basic gunnery concepts as taught in the Gunnery 101 class

Additional information: This class is primarily lecture delivered in the Class.E-UNI channel in Mumble, followed by Q&A.

Notes for the Teacher

Required materials:

• Class.E-UNI chat channel, to receive questions and post relevant links
• List any relevant links to teacher's references on the wiki or other resources, if needed
• Describe any ships, fittings, modules, or tools required to have on hand, if needed

Any particular notes or tips about how to deliver the class go here.

Class Contents

Introduction

Welcome to this class on Advanced Gunnery!

This course is designed primarily for students familiar with the basic concepts covered in the Gunnery 101 (Beginning Gunnery) class.

In this first of the Advanced Gunnery classes we will discuss the "To Hit Equation" in detail, its effects, implications, and both theoretical and practical applications. We will investigate both the effects and magnitudes of combat variables and how they apply to Turret Mechanics in a dynamic combat environment. And perhaps most importantly, we will attempt to understand how to manipulate these values to maximize your combat effectiveness, in both offensive and defensive capacities.

(Instructor should then introduce himself or herself - covering relevant experience level and background.)

We have a few ground rules for this class:

• Please put your Mumble settings on "Push to Talk" if you have not already done so.
• Feel free to type any questions in the Class.E-UNI chat channel as we proceed - I will try to answer your questions as they come during the class. [At the end of my lecture, we'll open Mumble for any further questions or general discussion.]
• This class is entirely lecture. There are no live exercises.
• It will seem like there is a lot of math. That's because... there is. But we'll try to explain the math so that anybody can understand it.

Everyone ready? OK, then - let's begin....

Introduction to the "To Hit Equation"

• It was determined by players through observation and analysis
• CCP...
  • did not hand the equation over to the players
  • hasn't even officially confirmed the equation (accuracy, or even existence)
• It may not be entirely correct or accurate
  • example: Aperture Harmonics, Magnetars, and tracking
  • still lots of empirical evidence that it is correct
    • like a theory, it has not been disproven
• CCP can change at any time, without verification
  • probably won't unless they change core game mechanics

Myth: EVE combat is "spreadsheets in space"

• you don't need to be good at math to be deadly in EVE
• nobody (in their right mind) uses this for realtime calculations during combat
• why technical analysis?
  • understand how it behaves
  • understand how behavior changes in different situations

Coupling of "To Hit" and "Damage"

• It's called the "To Hit" equation, but...
  • "To Hit" and "Damage" are strongly coupled in EVE Online
    • compare to classic RPG/MMO
      • separate rolls for "to hit" and for "damage"
    • EVE has...
      • fewer random "unlucky streaks"
      • banded damage potential
• Players generally consider only "to hit"
  • "to hit" is directly determined by controllable factors
  • it is the determinant for "damage"

Separation Into Distinct Terms

• 0.5 ^ combined_term
  • combined_term = ( (tracking_term * signature_term)^2 + (range_term)^2 )
    • Tracking Term
      • transversal / ( range * tracking )
    • Signature Term
      • sig resolution / sig radius
    • Range Term
      • (range - optimal) / falloff
  • result is chance to hit expressed as a decimal, e.g. 0.1 = 10% chance, 0.25 = 25% chance, etc.
  • analyze by looking at limits and sample values
    • all terms are 1: 0.5 ^ ((1*1)^2 + 1^2) = 0.5^(1+1) = 0.5^2 = 0.25 (25% chance to hit)
      • as the combined_term grows beyond 1, chance to hit approaches zero
        • 0.5 ^ 2 = 0.25 (25%), 0.5 ^ 5 = 0.03 (3%), 0.5 ^ 10 = 0.0009 (effectively zero)
    • all terms are 0.5: 0.5 ^ ((0.5 * 0.5)^2 + 0.5^2) = 0.5 ^ (0.25^2 + 0.25) = 0.805 (81% chance to hit)
    • all terms are zero: 0.5 ^ ((0*0)^2 + 0^2) = 0.5^0 = 1 (100% chance to hit)
      • as the combined_term approaches 0, chance to hit approaches 100%
    • combined_term can never be < 0 because we are adding squares

• 0.5 ^ ( (tracking_term * signature_term)^2 + (range_term)^2 )
  • things we want to figure out (analyze)
    • the limits of each term by themselves
    • how the terms affect one another
    • how all the terms taken together affect the entire To-Hit Equation

Signature Term

• sig resolution / sig radius
• always remember: this is multiplied by the tracking term!

• typically static per target
  • gun size matches target size, then it about equals 1
    • x=1, y=0.5
• when guns don't match target size
  • guns too large for target, x>1 so y<0.5
    • example: battleship gun sigres=400, destroyer hull sigrad=62
    • considering only the signature term: 0.5^((400/62)^2) = 0.5^(6.45^2) = 0.5^41.6 = 0.000 000 000 000 33 (0.000 000 000 033% or 1 in 33 billion chance to hit)
  • guns too small for target, x<1 so y>0.5
    • example: cruiser gun sigres=125, battleship hull sigrad=550
    • considering only the signature term: 0.5^((125/550)^2) = 0.5^(0.227^2) = 0.5^0.051 = 0.965 (96.5% chance to hit)
• mostly determined before the fight even begins
  • increased by microwarpdrive signature bloom
    • increases by 500%!
    • example: battleship gun vs destroyer above but with MWD
    • modified: 0.5^((400/310)^2) = 0.5^(1.29^2) = 0.5^1.66 = 0.316 (31.6% chance to hit)
  • increased by target painters
  • decreased by ship bonuses, boosters, etc.
• Limits: none, really
  • Signature Term will always be a positive number
  • never result in an error, sig radius is never zero
  • never negative, no guns have negative sigres, no ships have negative sigrad

Tracking Term

• transversal / (range * tracking)
• always remember: this is multiplied by the signature term!
• (same graph as the Signature Term)
• dynamic value during combat, changes with movement and with changes in movement

• "Tracking Unity Limit", TUL (pronounced "tool"), AITMU (acronym I totally made up)
  • values where the Tracking Term = 1
  • target's range * tracking speed of your guns = target's transversal
    • example: 12,000 meters range * 0.03438 rad/s tracking = 412.56 m/s transversal
    • (INSTRUCTOR: Instead, ask students for example values using a long-range turret, e.g. beam laser/artillery/railgun, pref. taken directly from a personal ship or fitting.)
  • Tracking Unity Limit can be a fair upper bound or soft limit
    • if at all possible, get it lower, THE LOWER THE BETTER!
    • TUL example: 5500 meters range * 0.132 rad/s tracking = 726 m/s transversal, TUL: 726/726 = 1
    • TUL example considering only the Tracking Term: 0.5^(1^2) = 0.5^1 = 0.5 (50% chance to hit)
    • easy hit example: target is only at 300 m/s at same range, so Tracking Term is 300/726 = 0.413
    • easy hit example considering only the Tracking Term: 0.5^(0.413^2) = 0.5^0.171 = 0.888 (88.8% chance to hit)
    • difficult hit example: target is at 2000 m/s at same range, so Tracking Term is 2000/726 = 2.755
    • difficult hit example considering only the Tracking Term: 0.5^(2.755^2) = 0.5^7.59 = 0.0052 (0.52% chance to hit)
    • (INSTRUCTOR: Instead, ask students for example values using a short-range turret, e.g. pulse laser/autocannon/blaster, pref. taken directly from a personal ship or fitting. Calculate at TUL, ~1/3rd speed, and very fast speed.)
• Limits
  • transversal can go to zero, resulting in a zero Tracking Term AND A ZERO SIGNATURE TERM (remember, they are multiplied)
    • target ship and yourself are in zero transverse motion to one another (neither of you are necessarily standing still)
    • examples: matched speed and course, direct opposite motion, kiting
    • REMEMBER: your targets transversal EXACTLY EQUALS your transversal to him, which also means your target's angular velocity EXACTLY EQUALS your angular velocity to him
  • range can be zero, resulting in DIVIDE BY ZERO ERROR
    • game interpretation: always hits as if transversal is zero (as far as anybody can tell)
  • never practically negative
    • negative transversal or range is transversal or range in the opposite direction
    • no guns have negative tracking
      • (INSTRUCTOR: Can insert mention of Aperture Harmonics and Magnetars here.)

Range Term

• (range - optimal) / falloff, if < 0 then 0
• always remember: this is added to the signature*tracking terms!

• In this graph...
  • 0 to 1: inside optimal range
  • 2: optimal + falloff
  • 3: optimal + 2x falloff
• example within optimal range: 12,000 range - 12,000 optimal / 21,000 falloff = 0/21,000 = 0
  • to hit at optimal range, zero transversal: 0.5^(0^2) = 0.5^0 = 1 (100% chance)
• example at optimal + falloff: 33,000 range - 12,000 optimal / 21,000 falloff = 21,000/21,000 = 1
  • to hit at optimal + falloff, zero transversal: 0.5^(1^2) = 0.5^1 = 0.5 (50% chance)
• example at optimal + 2x falloff: 54,0000 range - 12,000 optimal / 21,000 falloff = 42,000/21,000 = 2
  • to hit at optimal + 2x falloff, zero transversal: 0.5^(2^2) = 0.5^4 = 0.0625 (6.25% chance)
• (INSTRUCTOR: Instead, ask students for example values within optimal, near optimal+falloff, and at or beyond optimal+2*falloff, pref. taken directly from a personal ship or fitting.)
• Limits
  • term goes to zero within optimal range, thus adding nothing to the tracking*signature term
  • never result in an error (no guns have zero falloff)

To-Hit Equation Summary

• 0.5 raised to the power of 3 different terms, two of which are multiplied and one is added
  • Tracking Term and Signature Term are multiplied by one another
    • if the Tracking Term can get extremely small or zero, then it can negate most or all of the Signature Term
      • otherwise, the Signature Term can make hitting with oversized guns REALLY difficult
    • if the Signature Term is small (undersized guns, overblown sigrad from MWD or TP), can make up for poor tracking
  • Range Term is added
    • Range Term is a non-issue when within Optimal Range
  • the lower the Combined Term, the greater chance to hit, at 0.5^0 = 100% chance to hit
    • only happens if the Tracking Term is zero (zero transversal) AND the Range Term is zero (within optimal range)

Optional Exercise

• INSTRUCTOR: Have the class talk through the situation through Class.E-UNI (or other) chat channel. Ask them what is the BEST immediate course of action.
  • Guide them and explain both good and bad ideas, and if necessary provide hints on things they may be missing or not considering.
  • If necessary, give them the following choices:
    • A) Keep orbiting, do not slow down your motion for any reason.
    • B) Turn toward the stargate and hit your MWD to GTFO as fast as possible.
    • C) Turn toward the stargate but slowboat to it, and jump out when you can.
    • D) Turn in any direction that is perpendicular to the enemy sniper and then continue in a straight line to keep your transversal up.
    • E) Turn directly away from the enemy ship and hit your MWD to increase your distance as fast as possible.
    • F) Turn away from the sun and move in a straight line without MWD.
    • G) Align to a random celestial and GTFO ASAP.
    • H) Nothing, wait for your FC to tell you what to do.
  • Best choice is F but poses a long-term risk if no further action is taken. A close second is G, which is also the best solution in the long term but introduces a large risk in the short term (initial few seconds to align and warp). A good alternate is D, and solution F is simply the best directional selection in D's subset, but also suffers from F's long-term risk.

Class Wrap-up

• Thanks for attending this class!
  • I would appreciate any feedback from people on how to improve the class
• Questions ?