Every competitive LCS player uses them but I find it hard to justify the 50 gold spent for each pot when it only gives a small fraction of my health bar back and because I usually run out of mana beforehand. So should I invest in health potions or not?
Glowshtick6 votesYes.
Using health potions proficiently is one of the many concepts that it takes to be a better player and climbing the ladder. While they don't seem optimal as they stand, they are actually your best friend in maintaining the ability to farm in lane, cement your lead, and have an optimal start to the match.
Early game, the amount of health gained from 2 health potions alone is 300, which is around 1/3rd of a champions max health. If you're fighting an opponent in lane who doesn't have the sustain from health pots, you can easily end up out-trading them, as you are allowed to regen and keep coming back at them without having to recall and lose gold and experience. These are ESSENTIAL tools for early game and have many times meant the difference in dueling for that first blood gold.
I would always buy health pots if you can to start, and even buy more as the lane phase progresses as to more efficiently outlast your opponent. For the equivalent of 2 warrior minions or so, these items offer a superb boost for setting the early game in your favor. Don't overlook them.
BlackFlux1 votesyeah guess what he said. ^ now looking at my post I didn't even say if there worth it and only said they drop off late game when people have like 2K HP but everyone does like 100-300/that 
ADCs damage
Joxcab2 votesTry not using it and see what it's like after dying.
BlackFlux1 votesI mean,the usefulness of a 
drops off after a bit. if you chose to get something OTHER then like a...lets say 
and have 150 leftover you could,i guess grab a 
cause it refills and only gives 25 less HP a pot. then MAYBE (all honesty going refillable is a bit of a waste but some use it like jungle/top laners) grab yourself a 
,costing 500 gold altogether,healing health and 75 mana,holds an extra charge and as it heals you,you get a burn effect for 15-30 extra damage when you hit a champ. or if your jungle grab a 
,5 charges refills at shop or you can get 1 charge by defeating a large/epic monster. but that's for jg. there is also a mastery that increases the effect of s by turning them into 
....the effects are the same they just give 15 HP and mana on use.
TheHappyReaperz1 votesThe mastery that gives you cookies also increases the duration of all the potions, so if you have it, picking up a refillable or corrupting isn't a bad thing, especially if your not the best at sustain.
Glîtchy1 votesI say what should be done regarding potions is the return of mana potions.
Brutalitops011 votesPotions may not seem worth the 50 gold investment for how little health they restore, but especially before level 6, they are crucial. First off, 150 health over 15 seconds is 10 health per second, which outheals a fair amount of DOTs, especially in the early game. Second, let's put this heal amount into perspective. Alistar is the champion with the highest base health in the game at level 1 (not counting Kled because you can't heal Skaarl's health with pots when dismounted). He has 613 base health (not taking runes/masteries/items into account). This means that each health potion is healing him for a little under 25% of his maximum health in the early game. Anivia's 467 base health level 1 (again, without runes/masteries/items) is the lowest in the game, and health potions heal her for over a third of her max health each. Alistar's base health at level 6 becomes 1,143, meaning that health potions are now ticking him up about 1/7th of his health and they, by this point, become somewhat obsolete for him unless he's in a poke lane or against an ADC that likes to basic attack him and he's staying too close to them. Anivia's is 817, meaning that she's still healing for about 1/5th of her base health at level 6, meaning that health potions would still be pretty relevant to her.
TLDR: they're always useful levels 1-6, but on some champions after that they become obsolete and I would say that they aren't that good on any champion after lane phase ends, and their usefulness diminishes somewhat after 1,000 max health, depending on matchup.
Kled is a unique case because Skaarl's health doesn't heal if he isn't mounted, meaning that their usefulness is limited at level 1 as he only has 340 base health himself +400 from Skaarl, which potions can't heal simultaneously and will prioritize either his or Skaarl's, depending on mount status.
Hallbuster1 votesLooked over the replies, most recommend using them, so I will.