1 simple answer, it will deal tons of damage. Just think of that nice juicy tender ultimate shooting from afar and hitting that ad ****py in the back of the team for half health.
Doesn't take a bill nye to figure that ap kog is the best kog.

Pros:
Leet Skeet Void Monster
Tons of Damage
Can beat chuck norris in a 1v1
Can use 9 quints

"but Phreak, where are the cons" - captain pisscan
Well, Kog'Maw has no flaws.

Kog'Maw's Spit ability (Q) is not really that useful but it deals an okay amount of damage i guess, but the range is too short. Get a point early, and max it last.
Kog'Maw's leet skeet spit ability (W) adds tons of damage to his auto attacks and increases the range of them. (also makes kogmaw look more leet skeet) Grab a point early, and max it by level 13.
Kog'Maw's Puke ability (E) is the 2nd best thing about ap Kog'Maw It slows, deals tons of damage, and has a decent range, Grab a point at level 1, and max it First.
Kog'Maws Piss in a spit bottle yultimate (R) is the best yultimate in the game, with your staff of gems this also slows, but at long range (even longer than my *****). Deals tons of Damage.
Get it at level 6 as with all yultimates and at 11, 16.

These choices will give you the ap needed to succeed as a pro as heck void monster.

"but phreak i need more mana because im always oom" - Captain Pisscan
Well Captain Pisscan, The simple answer to that is Chalice of Harmony, We added it into the game for Kog'Maw because it allows you to spam your yultimate and be able to get mana back.
"but why ap per level? my early game will be weak" - Captain Pisscan
Well Kog'maw doesn't need early game because hes not too strong early game, thats how we balance the people out.
AP PER LEVEL WILL DEAL TONS OF DAMAGE LATE GAME.

Starting with boots of sped due to the sheer fact of getting away from those nasty ganks fail champions make on you, the best champion, Kog'Maw. Getting a Dolan's ring to help early damage, health, and mana regen. Getting a cup of bear grylls piss will allow you to spam your yultimate if you have it. And also make you tankier against those pesky non kog'maws.
Building into an athene's is perfect, because hes the best gamer in the world and this item just is all around a great item, more tons of damage, more tanky, more mana regen, what more could you want. After that get the rabadoodle, it's the coolest looking hat in the game, the other hats aren't as cool. Leet skeet wizards have a staff with their hat, so grab a staff of gems while you're at it. Since Kog'Maw is the coolest champion in the world, get another staff. No other wizards have 2 staffs. Finish off the build with a trinity force to deal tons of damage because trinity force is the best item in the world on everybody because it deals tons of damage because it's just that good of an item.

Flash because you need to flash to get into range for your yultimate
Ignite so you can flash up to ignite a mordehuehue so he doesn't heal up

"but phreak, theres nothing here." - Captain Pisscan
Well Pisscan, it's because Kog'Maw will lose most lane matchups until level 6, And then it will become EZ MODE and then you will win everything with your tons of damage.

you shoot your yultimate at them from far away.