Hi all . I am going to give you an extremely close value for the hp threshold , at which garen kills you if he casts r at lvl 6 ( vs lvl 6 ) Every melee gets 32.1 mr lvl 1 , at lvl 6 has 39.7 mr -> 29% magic damage reduction . Every single melee ( gaining just a dorans' item for hp until lvl 6 ) will have on average 1150 hp . Assuming that garen is mostly about ad damage most people will not take an mr rune ( +8 mr ) or two mr runes ( +16 mr ) against him , but i will calculate that scenario too ( at 47.7 mr dmg reduction close to 33% ) .

WHEN YOU GOT NO MR RUNE (MELEE)

Garens' ultimate does 175 + 28.6% of enemy missing health in magic damage . So he must bring you down to 297 hp to execute you ( at 1150 average hp , higher than you die at very slightly higher health , lower than that at very slightly less current hp ) Mathematical explanation : 1150 (average health) – 852 ( damage done already ) = 298 ( current hp ) . 298 – 175 x 0.71 ( -> raw ultimate dmg post resistancies ) = 173,75 . 173.75 – 0.286 ( ultimate percentage multiplier ) x 852 ( 852 is the result of 1150 – x = 298 or in other words , opponents' missing hp) x 0.71 ( dmg multiplier due to 29% resistance ) = 0,74 hp . So target lives for roughly 1 hp .

WITH 1 MR RUNE(MELEE)

If the target has 1 mr rune his resistance is very slightly less than 33 % -> multiplier from 0.71 to 0.675 . In other words , you must have 4 % lower current hp (to certainly ) be executed than 297 , meaning 12 hp less -> 285 ( result gives – 0,11 hp )

WITH 2 MR RUNES(MELEE)

If the target has 2 mr runes ( + 16 mr ) then he has roughly 55,6 mr , equaling very close 36 % -> multiplier x 0.643 ( last digit close to precise value) . This means that the target must have around 7% less hp than the initial mrless character . -> 276 current hp ( gives 2,75 hp left at 7% )

WHEN YOU GOT NO MR RUNE (RANGED)

Ranged matchups ( Apart from graves , orianna -> more and less resistancies than normal respectively ) have on average (with a dorans' item at lvl 6 ) 1100 hp with 33 mr -> close to 25 % resistance , multiplier 0.756 ( last digit very close to real value ) . This means that youneed to have 305 current hp to survive ( result gives less than 1 hp left)

WITH 1 MR RUNE (RANGED)

With 1 mr rune , you gain 8 mr , meaning you have 41 mr -> 29.5 % reduction , multiplier 0,715 . So you need to have a bit less than 5% less current hp than those without mr rune -> 305 – 5×305/100 = 290 hp ( result gives -1 hp )

WITH 2 MR RUNES (RANGED)

With 2 mr runes , you gain 16 mr , meaning you now have 49 mr -> a bit less than 33% reduction , multiplier 0,673 ( last digit close to real value ). So you need around 9% less current hp to die -> 305 – 9 x 305 / 100 = 275.4 , let's call it 275 .( result gives – 1,56 hp)

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IMPORTANT NOTES :

1. Always make sure to have nullifying orb or tonic in your runes . First gives shield against magic damage , second gives instant 75 hp back if you drink regular potion – corrupting potion / 63 if you drink refillable potion , meaning that even with ignite on you , you will most likely survive
2. I say on average because although resistancies are the exact same , health differs slightly.
3. Kayle has roughly the same mr value as malee at lvl 6 ( 37 base mr instead of 39 of most malees ) . Jayce gets melee/ranged value respectively based on the form he is into currently . Nidalee is not a top lane matchup so it is undefined , i suspect sth similar . Garen ( mirror matchup ) is undefined because his w , based on farming , gives him a different bonus each time .
4. Calculate around +1 current hp bcs garens' ultimate takes a while to land and hp regen kicks in during its animation , + 10 if you have some short of lifesteal , because almost every attack lands faster than the ultimate of garen
5. Even matchups not presented ( talon , sylas , -> initial mr 39 / 36 , poppy bcs of the extra value she gains from w , olaf bcs of extra armor-mr from r , nasus bcs of ultimate effect but he dies more easily at low hp , bcs of elevated max hp ) are really close to those values up to max 6% hp required for each class

TLDR : Through some maths , to be executed , the average melee laner at lvl 6 with just a dorans' item for hp needs to be at : 297/286/274 hp , based on if you have 0/1/2 mr runes giving you 0/8/16 mr respectively . If target has +150 hp thanks to an extra ruby crystal , he dies at extra ( + 0.286 x resistance value x 150 = 30/28,5/27,5 hp ) than 297/286/274 . To be executed as the average ranged laner with a dorans' item for health , you need to be at : 305/290/275hp based on if you have 0/1/2 mr runes , giving you 0/8/16 mr respectively. If you have an extra ruby crystal , you die at extra ( 0.286 x resistance value x 150 = 30/28,5/27,5 hp ) than 305/290/275hp.

Every hp you have higher than 1150 (for melee) or 1100 (for ranged) at lvl 6 is bringing you closer to death for this exact amount ( 0.286 x resistance value x added hp value ) when at the same current hp as the presented values above . Cheers.

MAIN EDIT : i am aware this is really difficult to read , part because of my formatting and part because of its complexity . If you have any ideas on how to format this in a more acceptable way pm me . I do not know what else to do tbh , but i am open to ideas .