It's laughable when people say this item is a poor purchase when it's actually one of the best items in the game. Getting Mejai's when you're already carrying the game usually results in an instant win when you realize it's the highest cost efficient item in the game. At 25 x 5 AP + Flat 20 AP = 145 AP FOR ONLY 1400 gold!
TonsOfGains5 votesMejai's explicit cost efficiency has never been in dispute as far as I know, in the 8 years that LoL has existed. Its implicit value is what is often disputed. Let's look at the math. The function for Mejai's AP relative to its gold value is as follows:
G = (193.1 + 193.1K + 96.55A - 482.75D)/1400, G <= 1 Where: G is a coefficient measuring its actual efficiency relative to its maximum efficiency K is kills A is assists D is deaths All are measured after the last time Mejai's had 0 stacks.
Now we can also measure each individual factor relative to the maximum efficiency: Kills = 13.79% Assists = 6.9% Deaths = -34.48% Base: 13.79%
First off, we note that Mejai's has a starting efficiency of just under 14%. At its maximum (100%) efficiency, Mejai's offers AP at 9.66 gold. Therefore, at purchase Mejai's offers AP at 70.05 gold which is 3.24 times more expensive than ability power's theoretical value. The implicit cost here is that the 1400 gold could've been spent on other items with an immediate efficiency or gold/AP ratio that is 3.24 times better than Mejai's. Extrapolating, a player could potentially capitalize on these immediate benefits in way which exceeds the future benefits of Mejai's.
Secondly, at maximum efficiency, Mejai's is 2.25 more cost effective than other items. We note here that Mejai's efficiency at its peak does not balance out its expensive starting cost. This would suggest that, given the time required to gain factors of efficiency and the initial power gimp from Mejai's purchase, it might not be difficult for other purchases to exceed Mejai's implicit value through earlier capitalization.
Lastly, we analyze the factors and their relationships. The average contributing factor grants 10.35% efficiency while the average negating factor reduces efficiency by 34.48%. This means that, over the scope of many games, a player must maintain a (K+A)/D coefficient above 3.33 in order to get Mejai's efficiency closer to its maximum. At a glance, this isn't difficult especially if a player is competing against less competent players. However, this also means that in the event of any extenuating circumstances, it is multitudes less likely for Mejai's to gain any efficiency at all - much less reach maximum efficiency.
Hallbuster1 votesMejai's explicit cost efficiency has never been in dispute as far as I know, in the 8 years that LoL has existed. Its implicit value is what is often disputed. Let's look at the math. The function for Mejai's AP relative to its gold value is as follows:
G = (193.1 + 193.1K + 96.55A - 482.75D)/1400, G <= 1 Where: G is a coefficient measuring its actual efficiency relative to its maximum efficiency K is kills A is assists D is deaths All are measured after the last time Mejai's had 0 stacks.
Now we can also measure each individual factor relative to the maximum efficiency: Kills = 13.79% Assists = 6.9% Deaths = -34.48% Base: 13.79%
First off, we note that Mejai's has a starting efficiency of just under 14%. At its maximum (100%) efficiency, Mejai's offers AP at 9.66 gold. Therefore, at purchase Mejai's offers AP at 70.05 gold which is 3.24 times more expensive than ability power's theoretical value. The implicit cost here is that the 1400 gold could've been spent on other items with an immediate efficiency or gold/AP ratio that is 3.24 times better than Mejai's. Extrapolating, a player could potentially capitalize on these immediate benefits in way which exceeds the future benefits of Mejai's.
Secondly, at maximum efficiency, Mejai's is 2.25 more cost effective than other items. We note here that Mejai's efficiency at its peak does not balance out its expensive starting cost. This would suggest that, given the time required to gain factors of efficiency and the initial power gimp from Mejai's purchase, it might not be difficult for other purchases to exceed Mejai's implicit value through earlier capitalization.
Lastly, we analyze the factors and their relationships. The average contributing factor grants 10.35% efficiency while the average negating factor reduces efficiency by 34.48%. This means that, over the scope of many games, a player must maintain a (K+A)/D coefficient above 3.33 in order to get Mejai's efficiency closer to its maximum. At a glance, this isn't difficult especially if a player is competing against less competent players. However, this also means that in the event of any extenuating circumstances, it is multitudes less likely for Mejai's to gain any efficiency at all - much less reach maximum efficiency.
This was difficult to understand, like my Economics class, but I think I know most of what you mean.
King of Demons1 votesThe base stats are really bad and of course the item is really strong once fully stacked but getting there is pretty tough. You can't do it every game, you will miss out on cooldown reduction from a Morellonomicon or another core item and even if you do manage to get all the stacks up dying once can ruin you.
It's not that the item is bad, just that it is too risky to be built regularly unless you are severely outskilling your opponents every game and manage to never die.
Hallbuster1 votes[{quoted}](name=Taku of Rivia,realm=EUW,application-id=3ErqAdtq,discussion-id=dJP092L4,comment-id=0000,timestamp=2017-06-02T15:54:10.199+0000)
The base stats are really bad and of course the item is really strong once fully stacked but getting there is pretty tough. You can't do it every game, you will miss out on cooldown reduction from a Morellonomicon or another core item and even if you do manage to get all the stacks up dying once can ruin you.
It's not that the item is bad, just that it is too risky to be built regularly unless you are severely outskilling your opponents every game and manage to never die.
Champions with mobility/escapes should definitely look forward to getting this item, but not every champion like you said. You want this on: 
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King of Demons1 votesBasically: Buy Dark Seal and never upgrade it until you can sell it to get something better if you feel like you should get Mejai's.