Health v DPS: Health wins

test is thrown off immensely due to impact of Ooze, which specifically debuffs the stat that the damage stacking beast is stacking. 

i admire your dedication but these results seem to prove little other than the fact that Ooze severely impacts the auto-attack stat, which we already knew from reading the tooltip. 

Furious blade is going to be active WAY WAY WAY more than 15% of the time in a sustained conflict.  This whole thing is fatally flawed by you only having it active 15% of the time.  Lets say that you were attacking once per second (which is slow).  Even then chances are better than 50% that it would proc at least once in a 5 second span, and the effect lasts 5 seconds.  This would lead to it being active substantially more than half the time I would think.

Your items are a bit screwy.  The HP UB requires about 22k gold while the DPS UB requires only 17k gold.  An extra 5k gold is a big advantage.  I think that the items that you give the damage UB are EXTREMELY questionable also.  I'm not sure which items a UB would want if it does pure DPS stacking (in part because nobody does pure DPS stacking - they always have SOME cost effective armor/health items so this whole comparison is a bit flawed in any case), but I really dont think that this is what I'd do as far as your items.

And yeah, having a UB build that depends on attack speed going at a UB build that debuffs attack speed is kind of lame.

In any case, just because something is superior in a 1v1 situation does not mean that its superior overall.  There are many situations where you would want increased damage over increased survivability even if thats now a winning strategy for controlled 1v1 duelling.  For example, a lot of situations boil down to whether or not you can kill somebody before they are able to run back to a flag or their teammates arrive.

I personally think that on reasonably sized teams that you want a combination of damage dealers and HP stackers.

Want to see the same numbers ran with a non-Ooze build?  Link to a guide and I'll re-run it according to the ability progression indicated.

The numbers you see do include the reduction in attack speed from Ooze.

I chose the DPS items because they give the best DPS per gold.  If you've got a list you prefer, I'd love to discuss.

As TB, I love when people stack health. I'm rarely in a position to get attacked, and it just means if I am, they do that much less. 

If they have more HPs, it just takes longer to attrition them back. Unless they have the HoL. I hate that item and I'm so glad it's being moved.

Well, with things that expensive you need to mix things in that are just providing the best DPS without looking at cost that much.

You just demonstrated that a build with 22k of equipment beats a build with 17k of equipment.  That probably doesnt say a whole lot about the builds, dont you think?

If I'm reading the table correcty, at level 15 the DPS build purchases magslayer while the HP build has purchased nothing of equal power, and yet the HP build is STILL coming out on top by a slither. The total spend for the final figure is off by a 5k piece of equipment buffing damage, but before that its a 3k split the other way and yet HP is still coming out a long way ahead.

My suggestion: try this with an auto attack reg build using AF/Mines/MotB. That way the ooze debuffs arent going to come into play, alternatively change to a spit build, this will further skew things towards the HP stacker since he will have HP regen.

Whether or not the testing is slightly off, I think you're making a good point. The benefit from purchasing +HP items early far outweighs the benefit of buying + damage items. If this is the case, what is the point of the cheap gloves for example, why would ANY class want these items over the early armor or boots?

I think the HoL change will see +damage items become more effective in real situations since harassment will atually work as a strategy.

A character with lots of HP has more life expectancy than a character with no HP, who'd of thought?

You should of used the time you spent writing this to learn how lag and ping works in the game.

To model a furious blade, you can work on the basis of whether previous attacks triggered the effect or not. If the effect lasts 5 seconds then what you need to know is if any attack in the last 5 seconds triggered the effect. That becomes complicated because the effect itself increases speed. I don't have time to solve it, but you can approximate it. You can even do multiple iterations to converge on the answer.

(chance of not activating)^(number of attack in the last 5 seconds) gives you the probability that any individual attack is not affected by the furious blade. If the attack speed is one, then it's 0.85^5 = ~0.44 so a 54% chance of any attack being affected by furious blade and thus a 54% uptime and .54*0.3 = 16.2% average attack speed increase. Of course, you get more attacks in 5 seconds with this, so it's only an approximation. With a 16.2% increase we get 1.162 attacks per second and thus 5.8 attacks per 5 seconds. Doing the calculation over again with 5.8 we get 61% uptime instead of 54%. Average speed increase of 18.3%.

And so we keep getting closer to the real answer by smaller and smaller amounts the more times we do this. A typical numerical method. Maybe someone wants to solve it for an exact solution?

Edit: note, this is for an attack speed of 1, don't forget.

Damage and health stacking can only be directly equated in a 1v1. The more players there are in the game, the more a team can benefit from DPS+. People stacking damage know to stay in the back of the fight out of harm's way (regulus) or otherwise protect themselves. Furthermore, such theorycrafting does not take into account a player's ability to move around the field, and thus is rendered more theory than craft.

Maybe you should have used the time you spent writing that post to figure out that life expectancy is how long they survive against the other UB. It's damage gear vs dps gear. Whoever has the highest life expectancy is the winner.

I think the real trouble with this comparison is that you only want just as much HP as you need to survive, but you always benefit from more damage. There's no real reason to go all HP or all damage in a game, unless your team is specializing to some huge degree.

Trying to figure out whether the HP items actually are better than the damage items is a laudable goal, just not sure if this is a workable way to do it.

You dont even have to calculate anything to realize that health wins over DPS. You can easily triple your health but you need like Ashkandor to triple your damage. In reality you also have to get atleast 1-2 health items, because otherwise you will be running around with very low hp and trust me you dont want to have 2000-2500 hp at level 10+ or you will be the primary target all the time. The regulus might be able to pull this off with sniper scope or massive slowing, but otherwise you are toast.

You can use demigoddb.com to see the fine tuning between +speed attack and +dmg. But you are correct, ntropy, it is easier to stack health than stack damage/attack speed due to more items having +health.

DPS is kind of gimped in a game where both sides stack health. It is easier to pull off skills/potions when you have a lot of health to buffer you up for those critical moments. Factor in priests that heal % of your health and it becomes very hard to kill you via DPS. In this case, focus fire and burst damage are your best friends. This gives assassins the bigger edge.

Don't also forget a huge detriment to stacking dps - armor, which comes pretty naturaly with stacking hp and hugely diminishes the effectivnes of dps bulds that rely on autoattack for most damage.

There are a whole bunch of hp/armor items, low to mid cost, and their bonus percentage is higher on average!

- Banded Armor, 400 hp and 5 hps for 550g

- Unbreakable Boots, 600 hp and 5 hps for 1500g (also has +800 mana)

- Nimoth Chest Armor, 500 hp and 750 armor for 1500g (best cost/effect armor piece!)

- Hauberk of Life, 600 hp and 10 hps for 1750g

- (Bloodstone Ring), 400 hp for 1750 (also has 3% health steal)

- Namoth's Ring, 750 hp and 20 hps for 4000g (also has 8% health steal)

... and these are only the low-to-mid price items, not including primarily armor focused items!

There are very few cost effective dps items! Dps build work best with Regulus and Oak, because they both have skills to additionaly boost their auto-attack! However you trade health for this, which is very dangerous, because it makes you squishy!

- Gautlets of Brutality, +25 damage for 400g

- Nature's Reckoning, +37.5 damage for 1500g (also has +600 mana and the damage is AoE)

- (Warlord's Punisher), +30 damage for 2250g (also has AoE trigger with mana steal)

- Slayer's Wraps, +30 damage and +10% crit2x for 3300g (also has 10 hps)

These are about the only 3 reasonable low-to-mid price dps items!

Conclusion

Let's say you start with about an average of 1600 health, and you get around +1000 health on the way to level 10. You easily get another 2000-2500 health with items (over 3000 with favor) ending at 5500-6000 health.

Now, your damage starts out at around 150 (which is about 100 dps with 0.66 attack rate). You will get about +90 damage on the way to level 10 and your attack rate increases to 0.75 (which is like 142 dps). Let's say you got the items above, then you have +85 damage and some crit and also +37.5 damage added on top of that. You will be at 300 dps. However this will ruin your survivability because you are running around with 2500-3000 health and facing spells that hit with ~1000 damage on average, so you have to play extremly defensive.

Alot of players will get 1 health item + blood of the fallen, which will get you to around 3500-4000 health. That's more reasonable and you can maintain a high dps build.

Actually, if both UBs have the same percentage of autoattack damage/second reduced by ooze, it won't change who wins(both life expectancies should go up by the same percent).  This is because the life expectancy is determined by (health/(1-decimal form of percent mitigation))/(dps taken).  For example, if dps is 80% of normal for both of them, the life expectancy will increase by 25% for both of them.  My impression is that ooze I will basically mean your attack "reload" period is multiplied by 1.1(based on my observations of attack bonuses going the other direction, a +30% for 1.39s was 0.97s meaning the original value was multiplied by 0.7 or 1-0.3, I assume ooze just changes it to something like 1+0.1).  Damage that was formally dealt in one second, will take 1.1s so dps will change by a factor of 1/1.1 for both beasts(which means it's the same percentage reduction therefore the life expectancies increase by the same percent).  The ooze attack speed debuff should have no effect on the test if I'm correctly understanding how the debuff works.

The ooze damage is a different matter.  The actual damages are even, so if the armor's were the same, it would have the same effect on life expectancy for both test subjects.  However, the armor values are significantly higher for the health stacker so ooze is actually lowering his life expectancy more.  The health stacker's health is literally worth more because of the assumed mitigation of most damage.  A point of health at 50% mitigation is worth 2 points of health vs auto-attack damage, a point of helath at 75% mitigation is worth 4 points of health vs auto-attack damage.

In conclusion, ooze should favor the dps build over the health stacker.

Same percentage, vesuvius, but different raw amounts. The actual total DPS lowered by Ooze is greater on the DPS build, which is why it was unfair.

You're forgetting another thing that further amplifies your conclusion - they also have some additional armor at level 10 (more so for the hp build), so while the HP build will have always more than doubled the healthpoints, the DPS build will have the dps reduced by 30-40%.

Example - TB level 10, Banded Armor, Blood of the Fallen, Nimoth Chest Armor, Scalemail, Unbreakable Boots, Vlemish Faceguard:
4700 hp, 1860 armor (42,7% damage mitigation), 18,5 hp/s - up from
1400 hp, 240 armor (8,8% damage mitigation), 2,2 hp/s (level 1 base no items)

That is 3,3x the base hp and almost 35% more damage mitigation with additional 26,4 dps (18,5 + 42,7%) mitigated by regen.

Meanwhile, for example Oak starts with 110 dps base at level 1 (160 average damage).  Actual direct damage at base against above TB will be 207 * 0,912 - 2,4 = 98 dps.
At level 10 his base damage will grow to 187 dps (234 average damage).  He will gain as per your example ~100 damage + 100 damage from soul power and spirits.  430 average damage, lets say ~340 dps. Against above TB, 340 * 0,573 - 26,4 = 168 dps, or only
1,72x more dps. 

Off course, not all damage on the hp build will be mitigated by armor, but still you'd be hard pressed to match it in pure 1v1 with a dps build.

If anyone's curious, here are the life expectancies if you remove the ooze attack speed debuff:

HP Build

18.424833893036
18.7086396850086
15.5309808129847
15.6199298637656
15.7862726919594
15.9403363271948
18.2509186610441
15.6713342085885
15.341356651815
13.8055086690204
13.1528953006298
13.1903260480513
12.9825082610458
13.0112606591372
10.4893623344175
10.4243276610035
13.2917409392681
13.203997799315
13.1126447895942
13.0182262807354

DPS Build

10.6950444387675
11.2042485798719
11.4432697696798
9.4216172662969
9.79813003342115
10.1540772518213
8.80163357393646
9.10607085019384
9.20988976705958
8.24831115275606
8.25709684317447
8.48768124083064
8.59404186084006
8.80268612272403
9.28687282452083
9.36059808302781
8.87165725031639
9.14127020619081
9.38726937479043
9.61123834529548

So things get close when the DPS build gets a mageslayer and the HP build doesn't have an artifact yet, but the HP build still wins.  (Sorry for the lazy copy/paste job, I didn't feel like formatting that stuff from the spreadsheet).

Yeah damage is a very poor stat to improve unless you are Reg or TB, even then it can be beneficial to prefer Health and Armour over damage.

One thing to consider in this question is relative benefits.

The HP build increases the health of UB by 77% and increases damage reduction from 15% to 30%

The damage build increases the damage by 15% and the rate by 30% (which, if you multiply it out actually is about a 50% dps increase). 

So, just looking at those ratios, the HP build would win, all else being equal. 

The auto-attack based lifespans each increase by the same amount as a result of the percentage being the same.  I showed the equation for this in my post but I suppose I should also show the development of that equation.

The lifespan is total_health/health_lost_per_second.  If you have trouble seeing why, think of the time it takes to run around a race track, if you've got speed and distance, you can calculate the time it took by distance/speed.  Since there is also mitigation your formula ends up being total_health/(opponent's_dps * fraction_of_damage_that_goes_through).  If you rearrange this a little(because the fraction of the attack damage is really 1 - the decimal form of your percent mitigation), you get what I pointed out in my first post.  If you take the final equation, and lower the opponent's dps by a certain percent, the lifespan will increase by a percent that is constant that depends only on the percent by which dps was lowered(initial damage and health values do not matter).

TB is probably the worst DG in the autoattack department.  Only his fire build has any dps buffs, but it's totally broken and wrong to use it in that mode.  Ice is pure ranged control...

TB has no autoattack synergy whatsoever while being the squishiest DG of them all.  I don't see any TB dps build even remotely viable.

Well, DPS is combined of two different types of Damage, that which does get effected by armor, and that which doesn't. So your numbers are not completely correct, especially given that damage is being done by both of these sources. Ooze at rank 4 is doing a significant 135 damage, that is not being negated by armor, but is negating a % of the auto attack damage(Multiplicatively with armor mitigation).

So, your actual equation should be:

base health /(ability dps + AutoAttackDps * (1 - ArmorMit%) )

The ability DPS is the same between the two builds, base health, auto attack DPS and armor Mit are not. Because the TOTAL dps for the oen build is made up MORE by auto attacks, then a greater percentage of that DPS is eaten away by the ooze debuff.  Example:

Total DPS for Health build = 135 + 150 = 285, before Ooze (let's assume armor is already figured in). .6 of 150 is 90, so 60dps is lost. For the DPS build, they'll have more like 135 + 250 = 385. .6 of 250 = 150, meaning it loses 100 dps.

The dps change is greater on one than the other, and further more it is not the same percentage f the total. 60/285 = 21% and 100/385 = 25%.

These are all ficitional starting numbers, but the point I am proving is that the numbers are different, and favor the health build.

Hmm yeah you're right, I shouldn't have tried to separate those effects in my initial analysis.  Usually spell damage is too unpredictable to account for :/.  However, I will say that if we're accounting for effects that ignore mitigation, the ooze self damage and health regen need to be taken into account as well.  I'm not sure what the self damage will do to the numbers but the regen will significantly favor the health stacker again.

Regardless, I think it's worth pointing out that this thread has the wrong idea.  Health stacking as a strategy may be better than dps stacking as a strategy, but that does not make either of them ideal.  A more interesting analysis would be to take all the items in specific price ranges and compare their situational effectiveness.  I think the result will be that many of the health items often just give you the most raw power for your gold.