Multikill is related to the cumulative 10% monster stat increase after the first monster you battle in any Fight except Incursions and Dungeons, where they are fought one by one or without any multikill penalty or bonus. With the Pack Hunter and Carnage Skills maxed, players can fight up to 15 monsters in an action, 20 with the hellfire injection, which gives +5 monsters. As hellfire injections can only be acquired very expensively on market or from T7 incursions, we will assume that the max kill of the player is 15.
Every monster you fight after the first gets their stats increased by 10%, so the 2nd monster is 110% strong, the 3rd monster 120% strong, etc… until you reach 15th monster, which is 240% strong, or 20th monster, which is 290% strong. For example, if a monster's base armor is 100, then the 15th monster will have 240 armor. This bonus applies to every stat of the monster, including damage reduction.
Player Compendium Bonus
The multikill bonus of -1% is acquired when the player kills 1M of any monster and gets the 3rd and final reward in that monster's Compendium. The bonus means that we reduce the 2nd monster's 110% base stats to 109%, 3rd monster's base stats to 119% and so on.
If we achieve -11% multikill bonus, this means that the 2nd monster is the same as the first one (not 99%!), the 3rd monster is 109% strong and so on. The multikill bonus cannot reduce the monster's base stats lower than 100%.
One of the Corporation buffs is called Compendium Multikill and at max level, it gives 20% bonus to multikill bonuses we have.
So, what does this bonus mean to us? How strong is it? To find out, we need some math:
Let's assume we kill 15 monsters. We have 1% multikill. Multiply base numbers by 10 for simplicity. 10 is base rating.
15 monsters is 10 (base) + 11 + 12 + … + 24 = (24*25/2) - (9 *10/2) = 300 - 45 = 255 total monster rating. 1% multikill means we substract 0.1 from everything above the base monster, which is 14 * 0.1 = 1.4. That's our reduction. 255-1.4=253.6 (255/253.6)*100 - 100 = 0.552%
If we add in the 20% Compendium Multikill corp buff bonus, we get 0.552% * 1.2 = 0.662%. For simplicity, lets assume 0.666%, which means at 3% multikill bonus, we get 2% reduction in overall difficulty of killing 15 monsters.
To put it in fractions, with max corp buff, every multikill bonus gives us 2/300 reduction in difficulty.
Is it worth it?
When you look at the reduction, you would think less than 1% reduction in the difficulty sucks and isn't worth it. However, think about the 1% stat increase that comes with every Empowerment after 9*. That 1% stat increase does not cover IDC, min damage, max damage, and damage modifiers we have. Since many players stacks IDR and damage modifiers, a part of the 1% stat increase is wasted. Monsters, however, do not suffer such waste and have their IDR increased (they don't have damage modifier like players do).
With that small detail in mind, I argue that a -1% compendium bonus is as powerful as an all stat increase empower. Even if we get 11 multikill bonuses and the 11th one has just a bit reduced effect, it's still as important as when we had 10 multikill bonuses, as the last monster will always be the hardest to kill; reducing that monster's stats is always worthwhile. Of the 15 monsters that have a total of 255 base rating, the 15th monster has 24 of that, which is 9.4% of the whole thing. The last few monsters will deal you the most damage, and thus, you always have to keep the last monster in mind when calculating your build. The multikill bonus always does effect the last few monsters.
To put the reduction in perspective, take the steamdrake, an essential monster that is required to be killed in vast quantities for many mainline and daily quests. A 1% multikill reduction would mean reducing the enemy stats by 1% for 14 times. With base armor of 400, that means we have effectively reduced a total of 400/100*15=60 armor from the 15 steamdrakes we face, and that's only 1 stat. The 1% multikill bonus doesn't grant us direct stats like the compendium bonuses do, but it reduces enemy stats by a noticeable margin in the long run.