Oohhh, I am going to make a biiig calculation with this one.
Let's start with the data:
What useful stats for Yorick are there on Trinity Force?
* 30 attack damage
* 250 health
* 200 mana
* 8% movement speed
* 25% chance of slowing 30% (single target)
* 150% bonus base damage after using a spell (single target)
What useful stats for Yorick are there on Iceborn Gauntlet?
* 500 mana
* 60 armor
* 15% CDR
* 125% bonus base damage after using a spell (aoe)
* 35% slow after using a spell (aoe)
What is the difference?
Let us subtract all the Trinity Force stats from Iceborn Gauntlet creating:
* 300 mana
* -30 attack damage
* 60 armor
* -250 health
* -8% movement speed
Yorick always takes Manamune which grants 2% of your mana as attack damage.
So: 300 * 2% = 300 * 0,02 = 6 attack damage.
So we have now this:
* -24 attack damage
* 60 armor
* -250 health
* -8% movement speed
Does the armor, mana and slow effect compensate for the attack damage, health and movement speed?
* The less armor you have, the more armor is worth, since the amount of % that raises per armor, is lower each point of armor. The health is more worth when the armor is already above 150 or so.
* The good slow compensates for the movement speed, once you get in range of the enemy.
* When activating the Muramana, you will have just -6 attack damage, which is not a lot, but this is only when you activate the item, and are full mana all the time.
Conclusion
Though you will do less damage with Iceborn Gauntlet, I believe it is better for Yorick due to the amount of defense and slows it brings.
I agree with Nighthawk. Yorick does indeed need some form of mana item unless you're getting blue buff due to being a mid laner, or your mid laner having no need for it. I also think that Frozen Fist is very strong on Yorick. Most of the time when I play Yorick I end up building a Glacial Shroud anyways.
Yorick needs a mana item, whether it be Tear, Chalice, or lots of regen runes. I believe lots of pro players still build mune because it solves Yoricks early and mid game problems, or at the least take tear.
Mind you I'm pretty sure Triforce is really to expensive and I think Gauntlet would be alright, but not sure.
Though, I always take manamune, and some of the top guides do aswell, so I assumed everyone takes manamune as yorick, which of course is not the case :P
Situational. Triforce is more luxury that you'll get if you are ahead and can afford to buy a frozen heart after. Frozen Fist is a cheap alternative that gives you all the necessary stats. Both items are good, there's no optimal it's whatever the situation calls for.
Let's start with the data:
What useful stats for Yorick are there on Trinity Force?
* 30 attack damage
* 250 health
* 200 mana
* 8% movement speed
* 25% chance of slowing 30% (single target)
* 150% bonus base damage after using a spell (single target)
What useful stats for Yorick are there on Iceborn Gauntlet?
* 500 mana
* 60 armor
* 15% CDR
* 125% bonus base damage after using a spell (aoe)
* 35% slow after using a spell (aoe)
What is the difference?
Let us subtract all the Trinity Force stats from Iceborn Gauntlet creating:
* 300 mana
* -30 attack damage
* 60 armor
* -250 health
* -8% movement speed
Yorick always takes Manamune which grants 2% of your mana as attack damage.
So: 300 * 2% = 300 * 0,02 = 6 attack damage.
So we have now this:
* -24 attack damage
* 60 armor
* -250 health
* -8% movement speed
The slow of Iceborn Gauntlet is way better than the one of Trinity Force due to the 5% more slow, and a 100% chance of applying the slow after using a spell. Iceborn Gauntlet even has an aoe effect!
The Sheen effect is pretty equal, since the 125% of Iceborn Gauntlet is aoe, and Trinity Forces 150% is single target.
The 300 more mana gain from Iceborn Gauntlet also helps the active of Muramana, which increases damage output by 18.
Does the armor, mana and slow effect compensate for the attack damage, health and movement speed?
* The less armor you have, the more armor is worth, since the amount of % that raises per armor, is lower each point of armor. The health is more worth when the armor is already above 150 or so.
* The good slow compensates for the movement speed, once you get in range of the enemy.
* When activating the Muramana, you will have just -6 attack damage, which is not a lot, but this is only when you activate the item, and are full mana all the time.
Conclusion
Though you will do less damage with Iceborn Gauntlet, I believe it is better for Yorick due to the amount of defense and slows it brings.
Trinity Force is also very good for Yorick, but is more offensive.
I hoped this helped! :D
-Meiyjhe
Mind you I'm pretty sure Triforce is really to expensive and I think Gauntlet would be alright, but not sure.
So I only looked at what is really really important :P
But yeah, I kept AS, crit and AP out
False. Manamune isn't necessary in the slightest. Plenty of Yorick players don't build it at all.
Also you ignored AS, crit and AP. They are useful stats, even if they aren't optimal.
With the Yorick rework, Trinity force buffs your ghouls, maiden of the mist, and Yorick himself. So 9 times out of 10 you should get it.
:)