Mathcraft Regarding Tanky Items

[quote=Jebus McAzn]There's a certain amount of armor you have at any given time. Let's call that amount A. So at any moment, the amount of damage reduction you'll have with A armor is equal to (A)/(A+100). Example: If you have 50 armor, you take 50/150 or 1/3 reduced damage. The amount of health you'll have at any time will be denoted by H. So your effective health is therefore (H) / (1- (A)/(A+100) ) or (HA+100H)/100. Example: If you have 2000 health and 100 armor, you have 4000 effective health with the above formula. Anyway, I did a lot of other calculations today, which will not be posted on this thread, but the gist of it is that certain items give you a lot more effective health than other items. The following calculations assume 2000 health and 100 armor at level 18, which are generous assumptions for most squishies. Armor Item=Additional Effective HP (EHP) + Extra Bonuses Thornmail=2000 EHP + Damage reflection Sunfire Cape=2002.5 EHP + AoE damage Frozen Heart=1980 EHP + CDR + Mana + AS debuff Randuin's Omen=1917 EHP + CDR + HP5 + AS debuff + MS debuff + active Warmog's Armor=1840 EHP + HP5 To put things into perspective, pre-nerf Randuin's gave approximately 2700 EHP for its cost, while also providing 15% CDR and an amazing active. Post-nerf is comparatively balanced. What defensive item do you plan on purchasing as a tank for armor now? I'm leaning strongly toward SFC in my opinion, as it slightly outshines Randuin's now for me.[/quote]

[quote=JunSupport][icon=Sunfire Cape size=36] [icon=Thornmail size=36] Can you do the math to show me how Sunfire Cape can give equal Effective health to Thornmail? Armor should be more effective then Health Points when below the 200 mark if I recall and Sunfire possesses less then half the armor of Thornmail, and not even 500 HP. It should barely give 1000 for the 2000 initial HP, and 200~300 for the Cape's HP, if my estimates are accurate. o_o[/quote]

[quote=Searz]Aaawww, you beat me to doing these :( But everything isn't right here.. PHP=Physical HP MHP=Magical HP EHP=Effective HP EHP=MHP+PHP/2. You're using EHP when you're supposed to use PHP. [quote=Jebus McAzn] (HA+100H)/100.[/quote] This one is just wrong. Some typo? [quote](H)/(1-(A)/(A+100))[/quote] This one works, but is more complicated than it needs to. This one is simpler: H/(100/100+A) But that is also more complicated than it needs to be. Each point of armor increases the damage required to kill you with physical damage by 1%. How you should go about calculating EHP: Item bonus EHP=EHP with item-EHP without it[/quote]

[quote=Searz][quote=JunSupport] Armor should be more effective then Health Points when below the 200 mark if I recall and Sunfire possesses less then half the armor of Thornmail, and not even 500 HP. It should barely give 1000 for the 2000 initial HP, and 200~300 for the Cape's HP, if my estimates are accurate. o_o[/quote] Armor does not have diminishing returns from an effective health perspective. Each point of armor increases the amount of physical damage required to kill the champion by 1% of the champion's HP.[/quote]

[quote=Searz]Ok, so calculating EHP gains from an item is apparently complicated as apeshit, but I think I've gotten the formula down. I said the whole "Item bonus EHP=EHP with item-EHP without it" thing before and now I've got the complete formula for it: Item bonus EHP = (((HP+itemHP)*(100+Armor+itemArmor)/100)+((HP+itemHP)*(100+MR+itemMR)/100))/2 - (HP*(100+baseArmor)/100+HP*(100+baseMR)/100)/2 Yup, apeshit indeed. Here are my results on a few items: Base stats are 1900HP, 70armor and 30MR. ((1900+0)*(1.7+0.0)+(1900+0)*(1.3+0.0))/2-2850 [[Thornmail]]: +950EHP and 25%damage reflection [[Sunfire Cape]]: +1203.75EHP and AOE damage [[Frozen Heart]]: +940.5EHP, +500Mana, +20%CDR and an aura [[Randuin's Omen]]: +1033EHP, +25HP5, a passive and an active [[Warmog's Armor]]: +1380EHP, +30HP5 and grows stronger (+2055EHP and +45HP5 when fully stacked) [[Guardian Angel]]: +1007EHP and a revival with 750HP and 350mana every 6min [[Force of Nature]]: +722EHP, +8%MS and 1.75% of total HP+40 in HP5(basically; a shitload of regen) [[Banshee's Veil]]: +1131.25EHP, +375Mana and a spell block every 45sec Keep the item costs in mind when looking at these! These comparisons are with only base stats, we will have to make comparisons that include full builds to be fair. These comparisons only work as references as to which item to get as your first item.[/quote]

[quote=HeAt][quote=Jebus McAzn] There's a certain amount of armor you have at any given time. Let's call that amount A. So at any moment, the amount of damage reduction you'll have with A armor is equal to (A)/(A+100). Example: If you have 50 armor, you take 50/150 or 1/3 reduced damage. The amount of health you'll have at any time will be denoted by H. So your effective health is therefore (H) / (1- (A)/(A+100) ) or (HA+100H)/100. Example: If you have 2000 health and 100 armor, you have 4000 effective health with the above formula. Anyway, I did a lot of other calculations today, which will not be posted on this thread, but the gist of it is that certain items give you a lot more effective health than other items. The following calculations assume 2000 health and 100 armor at level 18, which are generous assumptions for most squishies. Armor Item=Additional Effective HP (EHP) + Extra Bonuses Thornmail=2000 EHP + Damage reflection Sunfire Cape=2002.5 EHP + AoE damage Frozen Heart=1980 EHP + CDR + Mana + AS debuff Randuin's Omen=1917 EHP + CDR + HP5 + AS debuff + MS debuff + active Warmog's Armor=1840 EHP + HP5 To put things into perspective, pre-nerf Randuin's gave approximately 2700 EHP for its cost, while also providing 15% CDR and an amazing active. Post-nerf is comparatively balanced. What defensive item do you plan on purchasing as a tank for armor now? I'm leaning strongly toward SFC in my opinion, as it slightly outshines Randuin's now for me. [/quote] I explained the whole armor formula as well as how the items work in my game mechanics btw.[/quote]

[quote=Jebus McAzn]Searz: I simplified it quite a bit. EHP regarding armor was only concerning physical damage and EHP regarding MR was only concerning magic damage. Those calculations do accurately lead to the conclusion that buying a Thornmail with those stats will make you about as tanky vs physical damage as if you bought a Sunfire Cape. Your formula accounts for both types of damage, but this thread is meant primarily to discuss viable armor items, not viable all around tanky items.[/quote]

[quote=Searz][quote=Jebus McAzn] EHP regarding armor was only concerning physical damage and EHP regarding MR was only concerning magic damage.[/quote] Yea, but I did mention that you should have used PHP instead of EHP because you used physical HP in your comparisons. [quote]Those calculations do accurately lead to the conclusion that buying a Thornmail with those stats will make you about as tanky vs physical damage as if you bought a Sunfire Cape. Your formula accounts for both types of damage, but this thread is meant primarily to discuss viable armor items, not viable all around tanky items.[/quote] Ok. I'm gonna try to confirm your calculations by using the somewhat simple method of: total PHP=PHP with item-PHP without That should leave no room for error, right? I believe your calculations are wrong on the HP items because you need a whole different method to include HP stats in only PHP and not EHP.[/quote]

[quote=Searz][quote=Jebus McAzn] Thornmail=2000 EHP + Damage reflection Sunfire Cape=2002.5 EHP + AoE damage Frozen Heart=1980 EHP + CDR + Mana + AS debuff Randuin's Omen=1917 EHP + CDR + HP5 + AS debuff + MS debuff + active Warmog's Armor=1840 EHP + HP5[/quote] Thornmail: +2000PHP Sunfire Cape: +2002.5PHP Frozen Heart: +1980PHP Randuin's Omen: +1819PHP (some typo on your end?) Warmog's Armor: +1840PHP I guess you did manage to do right. Good boy! ^_^ I guess you used the "total PHP=PHP with item-PHP without" way of calculating too. Silly me >.>[/quote]

[quote=Trojan995]Since Warmog's provides both high PHP and high MHP, does that mean it's a good item now? 0.o Or is it so easily countered with a MBR/DFG that it's not worth it? Or should high health just be gained from other items (SFC)?[/quote]