Card Raid Efficiency

Abstract
This page helps to address issues on how to choose the best cards for your new 12 card raid frontline.

Body

 * Changes to the Raid system:

The raid system has moved from the standard 5 card frontline to a 7 card frontline and 5 card supportline.

The 5 card support line:

The supportline works to boost the over all damage of your front line based on the 5 card's total defence value. I don't know the exact calculations for this but choosing this is too straight forward for me to bother anyway. Just filter your deck for highest def power and choose the top 5 def cards. By def cards I mean cards with higher def than atk. Don't blindly choose as u don't want to end up choosing a 14K+ atk card with 12K+ def for your support just cause it is top 5 def.

The 7 card front line:

This is the line up that does the actual damage to the boss. The power consumption for the 7 cards has switched to a new formula given by:

(PWR sum of your 7 cards +5)/2.7 Rounded off to the nearest whole number.

Because there is a rounding off to the nearest whole number. Sometimes replacing a pwr 14 with a pwr 15 with slightly higher attack may end up loosing effeciency as ur pwr consumption may go up by 1. The reverse is also true. Hence it is important to take note of that.

If u calc the efficiency of a single card based on the new formula, it becomes:

Attack PWR of card/(PWR+5/7)

Because of the new formula, high power cards with atk ratios just slightly lower than low power ones may end up becoming much better. for example:

Xerxes (8890 ATK, PWR 11) with an old efficiency of 808 drops to 759 for raids

Eostre (12775 ATK, PWR 16) with an old efficiency of 798 drops to 764 for raids

And becomes better than xerxes in terms of efficiency.


 * Raid Boss Battle System:

With your 7 cards you will attack the boss together. And the boss will strike back, killing at random any of the 7 of your cards. You will then attack the boss with your 6 remaining cards. The boss strikes back again untill u are left with no cards or the boss dies. You will deal less damage with each subsequent attack as you are left with fewer and fewer cards.


 * Managing PWR consumption:

Using reference to the most recent Starless & Bible Black Bosses, Stealing the boss list and giving credits to the publisher... Cheers: You will realize from the table above that there are a few free frag bosses like the low lvl Lusas, Gany & Welina.

A strong line up with PWR consumption above 40 can easily kill irene in 1 attack. Thats 160K worth of damage. You will not want to waste 40 PWR to kill a 100 HP flutist or 35K Gany. Hence it is good to customize a few line ups to conserve power. I personally saved a low PWR line up specially to deal just enough damage for Welina & Gany, and one more lame 1 single power 2 common card line up just to "poke" my guildie's low HP boss to share repel counts XD.

The important thing to note here is when designing a low PWR line up, one does not simply reduce the number of cards used. Line ups with less than 7 cards are very inefficient due to the boss battle system as mentioned above. With 7 cards you will hit the boss for 7x,6x,5x,4x,3x,2x,1x damage for a total of 28x. A 6 card line up reduces that to 23x and a 5 card line up to 17x and so on, cutting the efficiency significantly. The key is to swap your high power cards out for low power rares/commons, and maintain the 7 card line. A few cards I can recommend are:





There are 2 PWR 5 rares with 700 efficiency for each element, with a total of 6 for you to work with. If you are too lazy for that, just use pwr 2 commons like lost angel like what I do to act as fillers for your 6 or 5 main raid cards.


 * Raid Cards

Raid Cards are cards with skills that deal additional damage to raid bosses, or block raid boss attacks. Their skills are set to activate during 1 of the 7 hits you deal the boss, or 1 of the 7 hits the boss hits your cards.

Block attack cards:

Set to trigger during 1 of the attacks your frontline gets attacked by the boss, preventing the boss from killing 1 of your cards. hence allowing your entire frontline to attack 1 more time, for example, if the skill triggers during the 3rd attack when u have 5 cards left, your attack sequence from 7x,6x,5x,4x,3x,2x,1x becomes 7x,6x,5x,5x,4x,3x,2x,1x, increasing your effiiency from 28x to anywhere from 29x to 35x, depending on the skill level of the card. The special evolution card that comes with the current raid event does just that, greatly boosting your damage output ontop of his already extremely high atk ratio. Block atk cards are however seldom use as the special evolved UR is just too darn expensive for most players and the commons have too low efficiency to justify their use, so I shall not go into too much depth here.

Boss Damage cards:

Boss damage cards are set to have their skill activate anywhere between the 7 attack phases. A skill 10 for example multiplies the attack by 1.7x for that phase. increasing your attack efficiency from 28x to anywhere between 28.7x if triggered on the last attack to 32.9x if triggered on the 1st attack. Obviously you will pray that your raid skill triggers on the 1st few attacks. The average gain in efficiency here is 2.8, from 28 to 30.8, which is just the average of the 2 values above.

There is also however a chance that the raid boss gets killed by the boss before the skill has a chance to trigger.


 * Mission impossible IV:

I shall now attempt to calculate raid effeciency by factoring the raid skill of boss damage cards. This is based on a probility table of assumptions as only god knows when the skill activates and whether it even gets to. My biggest assumptions which I am unable to verify and hence the entire calculation will fall wrong if its false is: The table above attempts to calculate the effeciency gain by obtaining a multiplier to use on the value of the raid boss's skill:
 * 1) The skill of your raid card has equal probility to trigger in any of the 7 phases, provided it is still alive.
 * 2) No 2 raid skills may trigger at the same time if u are using more than 1 raid card. And may hence cannibalize each other.
 * 3) Of cos if your high attack power card gets killed 1st, you will deal less damage subsequently. This is based on an average of many attacks where each card takes turn to get killed at each phase evenly and everything evens out eventually.

Phase: The phase at which the attack is in, phase 1 with 7 cards for 7 efficiency and phase 7 the reverse.

P Chance: The preset probability the boss skill is programmed to activate. My assumption is equal probability for all 7 phases.

A Chance: The Chance your raid card is still alive after each phase. Simple cumulative probability of 6/7, 5/6, 3/4 and so on.

T Chance: The effective chance for the skill to trigger at each attack phase, simple cumulative probability of P and A Chance.

Eff Gain: The increase in raid efficiency if the skill were to trigger at each phase. Simple multiplication of Effeciency and T chance.

So what does the 2.86 mean?

This value is a sum of all 7 Eff gains after all 7 phases of attack. It is used to plug into the forumla below:

2.86 *Raid Skill Multiplier -1

With a Skill 10 raid with 1.7x multiplier, the value becomes:

2.86 *1.7-1 =2

Hence a Raid card with skill 10 is predicted to increase the efficiency of a frontline from 28 to 30. After factoring that the raid card could be killed without using its skill, the gain in efficiency has reduced from 2.8 as shown previously to 2.


 * Raid Card Cannibalization effect:

1 of my assumptions is that no 2 raid skills may trigger at the same time. Hence there is defenitely some cannibalization effect when one uses more than 1 raid card. The gain in effeciency can be estimated by a simple probability of that not happening. The probability of the 2nd raid card clashing with the 1st is a 14% chance. Hence for a 2 raid card line up, there is a 0.86 probability that the 2 raids don't clash. For a 3 raid line up, the 3rd has a 14% chance of clashing with the 1st and another 14% chance with the 2nd, resulting in 0.74 probility of it now clashing with either 1 or 2. Compound with the probablility of 2 not clashing with 1 at 0.86 the effective value is 0.64 for none of the 3 clashing.

When a clash occurs, only 1 of the skills will trigger. Hence 0.14 of the time the raids are only at half effeciency, and 0.86 of the time they are still at full efficiency. Taking this into consideration, 2 raid cards only operate at 0.93 of the original efficiency.

For a 3 raid line up, 0.64 of the time they operate at full effeciency. when all 3 triggers at they same time at 0.02 probilility, they only operate at 1/3 the efficiency. the remainind 0.34 of the time they operate at 1/2 efficiency, for a total of 0.817 of the original efficiency.

Plugging these figures into the chart:

A 1 raid skill 10 line up operates at 30 efficiency

A 2 raid skill 10 line up operates at 28 + 2*1.86 per card = 31.72 efficiency

A 3 raid skill 10 line up operates at 28 + 3*1.63 per card = 32.89 effieiency


 * Not so fast....

We cannot conclude just yet that having 3 or more raids in a line up is better. This is because the efficiency values we have calculated here does not equal overall damage output/PWR consumed, which is what we are trying to calculate in the end. The formula for that is obtained by factoring the raid efficiency value into the original raid equation as belows:

Total ATK of the 7 Cards*Raid efficiency/ROUND[{(Total PWR of the 7 Cards +5)/2.7},0]

ROUND[{(Total PWR of the 7 Cards +5)/2.7},0] just means u need to round off the answer to the nearest whole number.

As we all know Raid cards have significantly lower attack than most other good URs, hence a lower Total ATK multiplied by a higher raid efficiency may be worse off than a higher Total ATK multipled by a lower raid efficiency. Just to quote a simplified example, giving 2 scenarios, one with 3 skill 10 raid cards including Maat, and 1 with 2 raid cards, all things equal but with Maat replaced with a BFCK. The difference in ATK between Maat and BFCK is about 3K. Y I chose Maat and BFCK is because they are both power 14s hence total PWR of the 7 cards do not change and we can cancel out the denominator of both equations, recucing both cases to:

Case 1 with Maat: ATK*32.89

Case 2 with BFCK: (ATK+3K)*31.72

Solve the 2 euqations simutaneously, and u get ATK = around 80K

Hence for good line ups with 13K,14K attack cards where total ATK >80K, it is better to have 2 raids than 3. The reverse is true for line ups with low attack cards. This assumption is made where all 2 or 3 of the raid cards used are skill 10s, for lower skill lvls the efficiency of the raid cards decline and the ATK cut off also drops when choosing between a 3rd raid or a high atk card.


 * Conclusion

I end my topic by providing a chart of skill levels vs raid efficiency for your personalized use to calc ur best raid line up:

Use this Values to add them to the base efficiency value of 28 and apply it into the equation as provided above:

Total ATK of the 7 Cards*Raid efficiency/ROUND[{(Total PWR of the 7 Cards +5)/2.7},0]


 * Future Updates:

The ??? in the chart above is because the multiplier for skill 11 and 12 raids are still currently unknown and I am unable to compute them..... waiting for updates on this.