Linking or unlinking poison combos
A commonly repeated bit of advice is that you should match hearts separately but always link poisons together. Let’s say you have this board:
Why is it better to link the poisons, but unlink the hearts?
Poison math:
Matching 3 reduces your HP by 20%. Additional orbs add 5% per orb.
Matching 6 connected, then, is 20% + 5%*3 which is 35%. Matching 2 combos of 3 would be 40%. So clearly when you have 6 or more poisons, you should just link them all together, right?
RCV math (ignoring heart OE*):
Matching 3 hearts gives you hp equal to your team RCV. Each additional heart orb increases this by 25%. If you have 6 heart orbs, making 2 heart combos will get you 2x your RCV value, where matching 6 linked will only get you 1.75x.
However, the key difference here is that healing benefits from combo bonus while poison damage is fixed. Each additional combo increases this recovery by 25%. So when you match two heart combos, the effective recovered health is in fact (2*RCV)*1.25 which is 2.5xRCV.
So… which is it?
This is where it gets interesting. Given that poison damage is relative to your max HP and RCV gets a bonus from combos, there is a HP/RCV ratio where it is actually better to unlink poisons to get the combo boost to RCV, even though that means poisons do more damage. Here’s the base math to find the ratio:
We want RCV/HP where .25(RCV) > .05(HP), so the 25% bonus to recovery outweighs the additional 5% max hp damage you will incur. Solving for RCV/HP, we get the break-even ratio of 1/5. This means if your RCV is 20% of your HP or more, you should unlink poisons.
How do I find this ratio?
There’s a lot that goes into this – latents, stat boosts from leads, etc. The easiest way is to enter endless and take note of your max HP. Match 3 hearts and note the green recovery number on your HP bar that shows your base RCV. Divide RCV by HP to find your team’s ratio.
*Heart OEs change a lot of these calculations (How many enhanced hearts? How many heart OE awakenings? What distribution per combo?) and is left out for simplicity.
*Article submitted by Discord user Bloom
Nice analysis! Two things to point out (one obvious, one less obvious):
1. The analysis only applies for situations where you have both poison and heart orbs on board. If you only have poison orbs on board, it’s always better to link them (or, even more obviously, don’t match them at all), unless you need the damage boost from an additional combo to one-shot the floor or break a combo shield.
2. The breakeven also depends on how many heart combos you can make. That is, if you can make 2 heart combos, you’re better off unlinking poisons if your RCV is at least 1/10 your HP. In general, divide the 1/5 breakeven by the number of heart combos (so 1/15 for three, 1/20 for four, etc.).