Elixirs, what they do, and how they can be improved
In general, I really do like the direction the consumables have taken, mainly because they offer a bunch of unique buffs to your champions, but the overlying theme of them all is that they are for the most part generally not worth the cost as a bunch of their stats make it a very hefty investment for a relatively short duration. Also, I think a bunch of their buffs either are in the wrong elixir or not really living up to the identity of the elixir either.
http://ddragon.leagueoflegends.com/cdn/4.20.1/img/item/2138.png : This item is amazing in a lot of ways. You end up getting tenacity in it, a trailblazer, increased size, and slow resistance. The main thing I love about it is not just the tenacity, but the increased champion size, I mean who doesn't love being extra big when they go stomping on the map? It is like you have a Lulu ult for 400 gold for 3 minutes, they should rename it Alistar's milk elixir because it makes you big and strong. The only thing though is that you would expect that if you had a larger champion, that they would have more HP, but actually they don't! Another thing I have to point out is that the trailblazer is not really that much of a trailblazer, the paths it leaves behind are very short unless your champion is a race car, lasts for a short duration, and it is so narrow that not too many people will even see it, it is almost like having a mini Sona E only if your champions are behind you. The trailblazer would probably be a lot more effective if it lasted longer as well as was a bit wider, its hard enough for your teammates to always follow behind you because a bunch don't even know what the trail does, but it also doesn't really have that much of an AOE to boost other people's speed.
TL;DR, great for tenacity, size increase, needs HP and wider/longer lasting trailblazer
http://ddragon.leagueoflegends.com/cdn/4.20.1/img/item/2137.png : This item paired with dragon buffs makes your champion deal 30-45% increased damage to turrets, wowzers it is an amazing item for split pushing and/or turret sieges, but sadly/fortunately not too many people know it exists! I don't like it how the minions move faster based on this elixir and that was why captains guard was removed for the same thing, but what I do like is that for super fast champions such as Zilean, the minion waves can zoom down the map very very fast since its based on the movement speed of your champion and not a flat % increase. I think the HP you gain from this should be thrown into the Elixir of Iron instead of here and maybe give your champion some attack speed increase or something to make turret sieges more potent, HP doesn't seem like it is the stat that is most needed to destroying towers faster. If all of your teammates buy the elixir of ruin when you are doing turret sieges, you guys can deal up to 225% extra damage to turrets by yourselves and you add in the minions as well, you end up taking down turrets over twice as fast!!!!
TL;DR, great for turret sieges, HP should be moved over to Elixir of Iron and given attack speed instead
http://ddragon.leagueoflegends.com/cdn/4.20.1/img/item/2139.png : This item I haven't even bothered using because I don't see it to be too helpful for most of the game, it has almost no scaling potential or magical properties about it other than being another mana front item. 40 ability power is great and all, but the previous elixir of brilliance gave the same amount at level 18 but also gave 10% cdr and cost 150 gold less. The sorcery buff I don't really think is too viable now, I mean yes true damage is neat, but having a 5 second cool down on activating it is way too long, when I think of magic and sorcery, I think of blowing up the world with raw power, not poking things with sticks until they die. They say it doesn't have a cool down vs turrets, but I honestly think the Elixir of Ruin is way more potent against turrets than dealing 25 true damage per auto attack given that it also buffs minion's damage to turrets as well. Probably this item would be a lot more cooler if the activation cool down was reduced to say one second or two seconds to stack up the true damage and deal a bit more per punch, but right now I don't see it to be too great compared to other elixirs for that high of a cost. It probably would be nice to include some CDR on it as well, I mean spamming spells is what a lot of mages do best!
TL;DR, Not that amazing, probably needs its true damage cool down to be decreased or deal more true damage and it would be great if it had some CDR, it is not that great to turret sieges as the Elixir of Ruin.
http://ddragon.leagueoflegends.com/cdn/4.20.1/img/item/2140.png : This is an interesting item is all I can really say, it reminds me of Master Yi's ultimate passive that kills and assists extend the duration. It grants 25 AD which isn't much, but it also has something that life steal should do in the first place and that is to heal you based on how much physical damage you deal with your champion and not based on auto attacks. The amount seems small of 10%, but I guess coupled with your other life steal items and physical damage abilities it can add up? I am not sure, I haven't tested this out much to get a good feel on it, but it probably would be good if it had attack speed built into it or increase the healing amount or having more AD in it. All I can say is that it really is how life steal should act like because life steal only works with your auto attacks and not your physical damaging abilities, spell vamp works with every other damaging ability except on hit or auto attack augment abilities, including true damaging attacks such as Darius's ult and Cho'Gath's ult, meaning if you wanted to heal from an ability say from Sivir's Q, you would need spell vamp in order to heal from it, so maybe this item is a sign that life steal will be like this in the future.
TL;DR, I don't know how well this works since the stats look so small, but it looks interesting to try out, it really does set an example on how life steal should work in the future though.
Big TL;DR, a bunch of elixirs have their identities all over the place, but they offer new ways to play the game and that is pretty neat, the main problem with them is that they need to either last longer and/or have higher stats offered in them to make them more worth paying the gold for them as well as shift around some of their abilities into other elixirs because they don't really offer the punch they need, my top two favorites are the Elixir of Iron and the Elixir of Ruin, Iron for having big champions and tenacity, Ruin for turret sieges, the other two I don't really see too much usefulness in them.
Thoughts?
Elixir of Sorcery, IMO, needs to be changed. Everything you said about it is true, and to be honest anybody using this elixir isn't going to be AA-ing towers or buildings often or fast enough to benefit from the true damage. They should increase the base AP from +40 to +50, and lower the true damage 5 second CD vs champions to around 2 or 3 seconds, and remove the damage to buildings.
which could add 100 true damage over 4 seconds to any ability. the 40 ap on its own probably isn't much but with a deathcap and dragon buff it gets boosted a bit.