User:Evon R'al/Draft

Frequency Crystals (used by laser turrets), and Mining Crystals, used by modulated mining modules in EVE Online may receive "damage" and eventually be consumed (or in common terms, shatter). These crystals have a Hit Point value much like any other destructible object, and shattering occurs when enough damage is taken by the crystal to lower its hit points to zero. The life expectancy of a given crystal, i.e. the average amount of time it may be used before it shatters, may be calculated from its attributes.

As with most transportable objects in EVE Online, one may right-click a combat or mining crystal and choose Show Info. The information in which we are interested are within the Attributes tab of the Show Info window.

Attributes

There are four attributes that affect the life expectancy of a crystal. These attributes function identically for both combat and mining crystals.

Structure Hitpoints

This is the total Hit Points of the crystal. All crystals in the game have exactly 1 HP.

Volatility

This attribute is the chance of the crystal taking damage upon every activation cycle. For example, a Volatility of 10% would mean that each activation cycle the crystal has a 10% (1 in 10) chance of receiving damage. The actual amount of damage is fixed, and is given by the Volatility Damage attribute.

Some combat crystals have a 100% chance of damage per shot. It also means that the life expectancy of these combat crystals may be calculated exactly, because every shot will always damage the crystal. (Faction combat crystals have a 100% Volatility, i.e. a 100% chance of crystal damage inflicted per shot.)

Volatility Damage

This is the actual amount of damage the crystal may receive during an activation cycle based upon its Volatility.

Crystals Take Damage

This attribute is always either True or False. If it is True, then the crystal actually takes damage based upon the other attributes above, and it will eventually shatter.

The only crystals in the game whose Crystals Take Damage value is False are the Tech 1 combat crystals. These will never take damage and thus they may be used indefinitely. Note that if the value of this attribute is False, then it will not even be listed in the Attributes tab of the Show Info window.

Activation Cycles

In terms of Volatility, an Activation Cycle is a single cycled use of a crystal by the turret within which it is loaded. With combat crystals, each time the energy weapon is fired is considered one cycle.

With mining crystals, a cycle may begin with the activation of the mining laser and may end with either the deactivation of the laser or the acquisition of materials (ore or ice). This means that a cycle is completed even if a mining laser is turned off early. Repeatedly turning a mining laser on and off will risk damaging the crystal whether or not any actual materials were mined.

Formula

The formula for determining average life expectancy of a crystal is simple:

[math]\text{Life Expectancy (in cycles)} = \text{Structure Hitpoints} / \text{Volatility} / \text{Volatility Damage}[/math]

For mining crystals, one may then multiply the expected cycles by the cycle time to calculate a crystal's life expectancy over time. Remember that Volatility is a percentage, so for example, a crystal with a Volatility of 10% must use the value 0.10 in the equation.

Examples

As the volatility damage is chance based the following numbers are only an indication.

The Simple Asteroid Mining Crystal Type A I has a Volatility of 10%, which means that for every cycle there is a 10% chance that it will receive damage. The amount of damage it receives will be the Volatility Damage value of 0.05 HP. It will shatter when its total damage reaches the Structure Hitpoints value of 1 HP.

This means that, on the average, the crystal has a life expectancy of [math]1 / 0.10 / 0.05 = 200[/math] cycles. With a standard (unbonused) strip mining cycle time of 180 seconds, one may estimate that a crystal will endure approximately 36,000 seconds, or 10 hours, of constant mining before shattering.

The Simple Asteroid Mining Crystal Type A II has a Volatility of 12%. It has the same 0.05 HP Volatility Damage, and 1 HP Structure Hitpoints as the tech I variant. As a result, the crystal has a life expectancy of [math]1 / 0.12 / 0.05 = 166[/math] cycles, about 8 hours.

However, a ship using these crystals will likely not be operating unbonused; it will likely be flying with significant improvements to its mining cycle time. So, while an unbonused strip miner cycle takes 180 seconds and a tech II A type crystal would last around 8 hours, strip miners fitted to a max-skilled Hulk , enhanced by a Mining Laser Optimization Charge from a Rorqual , can cycle in as little as ~73 seconds, thus reducing the crystals lifespan to a mere 141 minutes.

The math for strip miner duration reduction

Only using a Hulk with all relevant skills to level V. Role bonus for the Hulk - 15% strip miner duration reduction. Skill bonus for  Exhumers - 3% strip miner duration reduction per level. [math]\text{duration} = \text{base duration} \times ( 1- \text{Hulk Role bonus}) \times (1-(\text{Exhumers skill bonus} \times \text{level}) )[/math] [math]180 \times (1-0.15) \times (1-(0.03 \times 5) )[/math] [math]180 \times (1-0.15) \times (1-0.15)[/math] [math]180 \times 0.85 \times 0.85 = 130.05 \text{ seconds}[/math] Using the Hulk above and a boosting Rorqual using a Tech 2 Mining Foreman Boost and Mining Foreman Mindlink with all relevant skills to level V. Mining Foreman Burst with Mining Laser Optimization Charge - 15% strip miner duration reduction. The Mining Laser Optimization Charge(MLOC) bonus has its own bonuses: Using a Mining Foreman Boost II(MFB II) - 25% bonus to the effect strength of charges launched Using a Mining Foreman Mindlink(MFM) - 25% bonus to Mining Foreman Burst strength and duration Skill bonus for  Mining Director(MD) - 10% bonus to the strength of Mining Foreman Burst effects per level. Skill bonus for  Capital Industrial Ships(CIS) - 5% Mining Foreman Burst effect increase per level. (Ship bonus) [math]\text{MLOC bonus} = \text{base MLOC bonus} \times (1+ \text{MFB II bonus}) \times (1+ \text{MFM bonus}) \times (1 + (\text{MD skill bonus} \times \text{level}) ) \times (1 + (\text{CIS skill bonus} \times \text{level})[/math] [math]15 \times (1+0.25) \times (1+0.25) \times (1+ (0.1 \times 5) \times (1+ (0.05 \times 5)[/math] [math]15 \times (1+0.25) \times (1+0.25) \times (1+ 0.5) \times (1+ 0.25)[/math] [math]15 \times 1.25 \times 1.25 \times 1.5 \times 1.25 = 43.9453125\%[/math] The bonus can be even further increased by using an Industrial Core [math]\text{duration} = \text{base duration} \times (1- \text{Hulk Role bonus}) \times (1-(\text{Exhumers skill bonus} \times \text{level}) \times (1- \text{Mining Laser Optimization Charge bonus} )[/math] [math]180 \times (1-0.15) \times (1-(0.03 \times 5) \times (1-0.439453125)[/math] [math]180 \times 0.85 \times 0.85 \times 0.560546875 = 72.89912109375 \text{ seconds}[/math]

However, to compensate, if further enhanced by a Mining Equipment Preservation Charge, the crystals volatility can be reduced by up to ~44%, resulting in a new life expectancy of [math]1 / 0.067 / 0.05 = 298[/math] cycles, which at ~73 seconds per cycle comes out to ~21,754 seconds, or ~6 hours of constant mining before shattering.

The math for crystal volatility reduction

Using a Tech 2 Mining Foreman Boost and all relevant skills to V. Mining Foreman Burst with Mining Equipment Preservation Charge - 15% volatility reduction. The Mining Equipment Preservation Charge{MEPC) bonus has its own bonuses: Using a Mining Foreman Boost II(MFB II) - 25% bonus to the effect strength of charges launched Using a Mining Foreman Mindlink(MFM) - 25% bonus to Mining Foreman Burst strength and duration Skill bonus for  Mining Director(MD) - 10% bonus to the strength of Mining Foreman Burst effects per level. Skill bonus for  Capital Industrial Ships(CIS) - 5% Mining Foreman Burst effect increase per level. (Ship bonus) [math]\text{MEPC bonus} = \text{base MEPC bonus} \times (1+ \text{MFB II bonus}) \times (1+ \text{MFM bonus}) \times (1 + (\text{MD skill bonus} \times \text{level}) ) \times (1 + (\text{CIS skill bonus} \times \text{level})[/math] [math]15 \times (1+0.25) \times (1+0.25) \times (1+ (0.1 \times 5) \times (1+ (0.05 \times 5)[/math] [math]15 \times (1+0.25) \times (1+0.25) \times (1+ 0.5) \times (1+ 0.25)[/math] [math]15 \times 1.25 \times 1.25 \times 1.5 \times 1.25 = 43.9453125\%[/math] The bonus can be even further increased by using an Industrial Core For a Simple Asteroid Mining Crystal Type A II [math]\text{base volatility} \times (1- \text{Mining Equipment Preservation Charge bonus} )[/math] [math]12 \times (1- 0.439453125)[/math] [math]12 \times 0.560546875 = 6.7265625\%[/math]

Note:

Keep in mind that the damage is chance based. So in a (theoretical) worst case scenario a crystal could take damage at each use. Effectively making the Volatility 100%, taking it out of the calculation. Resulting in 20 cycles for a mining crystal ([math]1 / 0.05 = 20[/math]).

Quick reference

Crystal Type	Volatility	Volatility Damage	Expected Cycles
Frequency Crystals (Tech I)	N/A	N/A	(Infinite)
Frequency Crystals (Faction)	100%	0.00025HP	4000
Frequency Crystals (Tech II)	10%	0.01HP	~1000
Mining Crystals Type A (Tech I)	10%	0.05HP	~200
Mining Crystals Type A (Tech II)	12%	0.05HP	~166
Mining Crystals Type B (Tech I)	15%	0.05HP	~133
Mining Crystals Type B (Tech II)	19.6%	0.05HP	~102
Mining Crystals Type C (Tech I)	24%	0.05HP	~83
Mining Crystals Type C (Tech II)	30%	0.05HP	~66