axe ultimate maxed out is 625 flat dmg goes through anything no armor or magical just pure hp ...so that becomes uncounterable by anything other then raw hp then you dont have armor or magic reduction to save you from counter helix or the rest of the team which will be based on physical dmg or either nukes ... anyways axe's ultimate goes through abadon when he is using his ultimate that was the question not how axe should take abadon out 1v1 (which he can provided abadon comes with creeps
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to put into perspective why percentage gain is not a good thing for axe is because we already have a similar spell called reapers scyth of necrolyte which takes out based on your missing hp in other words you can kill someone if there on half hp (provided no magical dmg reduction items such as hood or pipe is present)
an example to show the actual power of axe's ultimate will be comparing it to lina or lions nukes which do inherently 25% less damage due to inherent hero magic reduciton ...not counting viper's skin, pudge, phantom lancer and many others hell bristal back completely makes there ulti into a joke with 40% reduction outright ...do the math 1025 for lion and 1250 for lina with scepter upgrades ..now reduce those amounts by 40% ... now reduce the amount further by atleast more then 25% since someone will get a pipe or bristle will have hood which is 30% diminishing ... now thats a very small amount of damage is it not ?
now compare it to flat 625 damage no bullshit involved ...wont matter if your in bkb, repel or abadon ultimate your going to kill him at 625 hp or anything less then that ... an abadon at lvl 25 has 2,198 hp ...lets make it aprox 2500 if he has some bracers thats your tank class which you can kill at his one third aprox hp ... an average drow, sniper or even troll has roughly 1600 - 1800 hp since they go for damage items ...thats a very good and easy kill for axe ...and to top it off after aghanim you gain 6 sec cooldown ...thats a joke
(oh you get 25% movement speed for all your nearby allies too)
in short dont go after axe just never go near him, kite him and etc but not near his ult range when your near his culling dmg