Extra Regeneration from Toggling Steamboots

[MacroHard]

Most people are qualitatively aware that toggling Steamboots prior to using regen yields greater results. Here are the quantitative numbers:


General Case Formula


Extra Regen = (Regeneration Amount)*(Health/Mana from +10 Stats)/(Total Pool - Health/Mana from +10 Stats)

Example:
You have 250 out of 800 max health while using Str Steamboots
If you toggle to Agi or Int Steamboots prior to using the potion, you will get 400*190/(800-190) = 124.6 bonus health
Using a Health Potion will give you 400 health (healing you to 650 HP) if you do nothing
Using a Health Potion will give you 524.6 health (healing you to 774.6 HP) if you toggle first

While my graph and table only apply to Bottle and Potions, this general formula can be used for spell healing as well.

Please note that your current health/mana makes no difference! Only your maximum pool factors into the equation!


Graph


http://i56.tinypic.com/2vvvo1x.png
note: unmarked values left of the curves will fully replenish health or mana


Table


http://i53.tinypic.com/25ugryp.png
note: values indicated as "FULL" will fully replenish health or mana


Method


Let

X = current health/mana
H = full health/mana (prior to toggling)
R = regen amount (ie, 135 for Bottle Health, 100 for Mana Potion, etc)
Y = health/mana change from 10 strength/int (190 for strength toggle, 130 for int toggle)

Extra Regen = Regen with Toggling - Regen without Toggling

= [X(H-Y)/H+R]*H/(H-Y) - (X+R)
= [X(H-Y)+RH]/(H-Y) - [(X+R)(H-Y)]/(H-Y)
= [X(H-Y)+RH-(X-R)(H-Y)]/(H-Y)
= (XH-XY+RH-XH+XY-RH+RY)/(H-Y)
= RY/(H-Y)

For Bottle (Health),

R = 135
Y = 190

For Bottle (Mana),

R = 70
Y = 130

For Health Potion,

R = 400
Y = 190

For Mana Potion,

R = 100
Y = 130

[ElementUser]

No assumptions stated MacroHard!

I am disappoint.

[Drasha]

You didn't factor in the loss of health/mana regeneration from having boots on agility.

[Ekamo]

Truly awesome <3

Thanks for helping :)

[MacroHard]

You didn't factor in the loss of health/mana regeneration from having boots on agility.

The 10 strength lost during this duration is 0.3 hp/sec, or about 3 hp total over a 10 second heal with potion or 9 second heal with bottle. Feel free to deduct this from the bonus.

[Frostbiite]

Thank you, that is really helpful. On a semi-related note, if you want to regen more hp just standing still, should you leave steamboots on STR or on agi/int?

[MacroHard]

Leave it on agi to maximize all regen, whether from regular regeneration for from items/spells.

If you feel you are about to be in danger, toggle to Strength.
If you are about to cast spells, toggle to Intelligence.
If you are focusing on last hitting, toggle to your Primary.
If you are just kicking back in between skirmishes, toggle to Agility.

Edit: See post #11 below for a further explanation

[FiskOgHon]

What is the reverse formula?

Say if i have my steamboots on strength and want to clear a creep wave with ss. What is the formula then if i switch to int before casting?

[MacroHard]

What is the reverse formula?

Say if i have my steamboots on strength and want to clear a creep wave with ss. What is the formula then if i switch to int before casting?

Extra Mana = (Usage Amount)*(Mana from +10 Stats)/(Smaller Pool + Mana from +10 Stats)

Example:
You have 250 out of 400 max mana while using Str Steamboots
If you toggle to Int Steamboots prior to using :souls: triple combo, you will be left with 225*130/(400+130) = 55.2 extra mana upon switching back to Strength
Using the combo normally loses 225 mana (leaving you with 25 mana) if you do nothing
Using the combo will cause you to lose 169.8 mana (leaving you with 80.2 mana) if you toggle first

Another great example is Pebbles. Say you have 260 mana while in Strength mode (390 while in Int). By switching to Int right before you cast you will save 80 mana by the time you go back to Str boots. Toggle again and that 80 mana will grow to 120 instantly. With Steamboots you can cast THREE spells with 260 max mana with Pebbles. Cool huh?

[Stokkolm]

You didn't factor in the loss of health/mana regeneration from having boots on agility.

Fun fact: agility steamboots will never regen less health/mana than int or str regardless of hero, items, levels. As percentages of total pool of course.

So to answer Frostbiite, mana will regen at the same rate regardless of attribute (unless you have fixed regen like :glac: aura), while health will always regen slower with steamboots on str.

[MacroHard]

Let

X = current health with Str boots
H = max health with Str boots
R = regen with Str boots

Regen With Strength Boots > Regen With Int Boots

X+R > [X(H-190)/H+(R-.3)]H/(H-190)
X+R > X+H(R-.3)/(H-190)
HR-190R > HR-.3H
.3H > 190R
H/R > 1900/3

Basically, if your health is more than 634 times your regen, you benefit more from leaving your boots on Str.
If your health is less than 633 times your health health, you benefit more from leaving your boots on Agi.

Interestingly enough this 1900:3 is the exact same ratio as health from Strength (19) to Regen from Strength (0.03). Since every hero has built in health regeneration in addition to strength based regen, every hero will fall below this curve. The exception is if you buy two Beast Hearts on a ranged hero prior to buying any regeneration items. This will allow you to overcome the 475 pure health that 0.25 HP/sec regen requires to reach the curve.

In conclusion, assuming you do not buy two Beast Hearts and Steamboots before any regen items, Stokkolm is correct; you will always maximize regen (mana as well, WLOG) by leaving your boots on Agility.

If you feel you are about to be in danger, toggle to Strength.
If you are about to cast spells, toggle to Intelligence.
If you are focusing on last hitting, toggle to your Primary.
If you are just kicking back in between skirmishes, toggle to Agility.

[Radio_Raheem]

super helpful info, as usual, coming from Macro.

[Hubaris]

*Applaud*

Now people won't be so upset when I multiboot steams and try to explain to them regen and scaling.

:nigh:

[IPlayLoL]

Extra Mana = (Usage Amount)*(Mana from +10 Stats)/(Smaller Pool + Mana from +10 Stats)

Example:

You have 250 out of 400 max mana while using Str Steamboots
If you toggle to Int Steamboots prior to using :souls: triple combo, you will be left with 225*130/(400+130) = 55.2 extra mana upon switching back to Strength
Using the combo normally loses 225 mana (leaving you with 25 mana) if you do nothing
Using the combo will cause you to lose 169.8 mana (leaving you with 80.2 mana) if you toggle first


Another great example is Pebbles. Say you have 260 mana while in Strength mode (390 while in Int). By switching to Int right before you cast you will save 80 mana by the time you go back to Str boots. Toggle again and that 80 mana will grow to 120 instantly. With Steamboots you can cast THREE spells with 260 max mana with Pebbles. Cool huh?

The theory is correct, the numbers are not. SS hands are 80 mana each, 240*130/(400+130) = 58.8

Theoretically, if you buy more then one steamboots, and micro effectively, the bonus should scale exponentially with the regen/bottle usage. ;O

[MacroHard]

Hmm. I wonder how long its been that way. Shows how often I party with ss.

[MacroHard]

Theoretically, if you buy more then one steamboots, and micro effectively, the bonus should scale exponentially with the regen/bottle usage. ;O
[/B][/COLOR]

The benefit is hardly exponential. The formula for multiple Steamboots is NRY/(H-NY), where N = number of Steamboots.

Example:
Hero with 60 strength (1290 health). Using bottle for 135 health.

1 Steamboots = 1480 HP -> 19.9 bonus
2 Steamboots = 1670 HP -> 39.8 bonus
3 Steamboots = 1860 HP -> 59.7 bonus

If your health is fixed prior to adding on Steamboots the benefit is linear.

For 1450 gold, having +10 stat and +30 attack speed is still a bargain.

Try this with Hammerstorm (in a low tier match):
Bottle
5x Str Boots
Switch to all int before throwing your stun and using ult. Switch to str for +150 attack speed and +50 str while attacking (you wont even notice any mana missing). Between battles switch to agi and you'll find yourself replenishing to full health and mana with a few bottle sips.

[the_tes]

The benefit is hardly exponential. The formula for multiple Steamboots is NRY/(H-NY), where N = number of Steamboots.

Example:
Hero with 60 strength (1290 health). Using bottle for 135 health.

1 Steamboots = 1480 HP -> 19.9 bonus
2 Steamboots = 1670 HP -> 39.8 bonus
3 Steamboots = 1860 HP -> 59.7 bonus

If your health is fixed prior to adding on Steamboots the benefit is linear.

For 1450 gold, having +10 stat and +30 attack speed is still a bargain.

Try this with Hammerstorm (in a low tier match):
Bottle
5x Str Boots
Switch to all int before throwing your stun and using ult. Switch to str for +150 attack speed and +50 str while attacking (you wont even notice any mana missing). Between battles switch to agi and you'll find yourself replenishing to full health and mana with a few bottle sips.
You'd also need a macro that switches all boots at once to save time.

[MacroHard]

You'd also need a macro that switches all boots at once to save time.

I believe this can be achieved by binding a string of commands to a key using the console. This can also be achieved by creating macros directly on a programmable keyboard/mouse.

[Decency]

Similar question: Where is the breakpoint for where passive health regeneration from the +10 strength is better than having a lower pool, assuming no consumables are used? I assume this also differs from hero to hero, since their base health regeneration rates vary, but I'm just looking for a ballpark figure. Ditto mana regeneration, which I believe should be constant.

Thanks for the thread. =)

[MacroHard]

Similar question: Where is the breakpoint for where passive health regeneration from the +10 strength is better than having a lower pool, assuming no consumables are used? I assume this also differs from hero to hero, since their base health regeneration rates vary, but I'm just looking for a ballpark figure. Ditto mana regeneration, which I believe should be constant.

Thanks for the thread. =)

Never. If regen is your goal, leave boots on Agi. Be sure to switch back to strength prior to the battle though!

See posts 10 and 11 of this thread for a full explanation.

[JazzMan]

so basicly. This means if i want to get more mana from bottle i have to use it on agi or int steamboots. or just int ? Other way ill get normal amount of mp?
How about hp ? If i want to get more hp heal from bottle i have to have my steamboots on agi/int yes ?
It means if lower my HP pool is more hp/ mana ill get from potions, right ?

[MacroHard]

so basicly. This means if i want to get more mana from bottle i have to use it on agi or int steamboots. or just int ? Other way ill get normal amount of mp?
How about hp ? If i want to get more hp heal from bottle i have to have my steamboots on agi/int yes ?
It means if lower my HP pool is more hp/ mana ill get from potions, right ?

Yes. Whenever you get a heal (health or mana heal) you're better off switching boots to agi for the heal duration.

This includes bottle, potions, spells, and even natural regeneration.

[ReD`RubY]

Also if u are carrying a bless orb or similar around and want to regen, u benefit more from dropping it before using the bottle.
So if ur camping somewhere and want to regen faster with ur bottle, Drop any stats item. ;q

[MacroHard]

Also if u are carrying a bless orb or similar around and want to regen, u benefit more from dropping it before using the bottle.
So if ur camping somewhere and want to regen faster with ur bottle, Drop any stats item. ;q

This is also true. Coincidentally, a blessed orb is +10 str so you can use this table to calculate the benefit as it is identical to toggling steamboots.

[Sandyclam]

I understand THAT this works but I fail to understand WHY, can someone please enlighten me?

[MacroHard]

It works because whenever you add or remove stats, your health and mana pool percentage remains the same even though the total changes.

For example, you currently have 900 of 1500 health (60%). Now lets say your courier delivers an Axe of the Malphai (+25 strength, 474 HP). Your new maximum health pool will now instantly increase to 1974. However, you do not gain 474 health instantly! Instead your health pool remains at 60%... so you will have 1184 of 1974 health.

This premise can be manipulated with heals and regeneration. By lowering your max health/mana pool, any heal/regen gives more as a percentage of maximum. Then when you increase your maximum pool, that percentage carries over and gives you more health!

[Nexorian]

Lets say you have 100 base hp and an item that adds 3000 hp.
you have 1 hp out of 3000, with the item
you use a potion and you heal 400.

back to the same scenario, you have 1 hp out of 3000.
you drop the item
you use the potion
you heal to 100.

you pick up the item, your hp percentage remains the same while the max hp goes back to 3000.
so you just healed 3000 hp with a health potion trololol. same happens with steamboots in smaller scales

[ElementUser]

Lets say you have 100 base hp and an item that adds 3000 hp.
you have 1 hp out of 3000 3100, with the item
you use a potion and you heal 400.

back to the same scenario, you have 1 hp out of 3000 3100.
you drop the item
you use the potion
you heal to 100.

you pick up the item, your hp percentage remains the same while the max hp goes back to 3000 3100.

FTFY

[IanDresari]

Can you do this calculation for a very common item: HotBL?
How much additional regeneration would one get from a bottle/health pot by dropping it, factoring in the lost HP/sec reg from HotBL itself?

What about a Behemoth's Heart, would it still be viable to do it with that? What is the threshold max HP you have to be at before dropping for dropping Behemoth's Heart not yielding any additional regen (as Behemöth's Heart regenerates a percentage of max HP, there should be a point of intersection between the two lines generated from extra regen and Heart regen)?

Bonus question: combine dropping HotBL with switching Steamboots!

[MacroHard]

Can you do this calculation for a very common item: HotBL?
How much additional regeneration would one get from a bottle/health pot by dropping it, factoring in the lost HP/sec reg from HotBL itself?

What about a Behemoth's Heart, would it still be viable to do it with that? What is the threshold max HP you have to be at before dropping for dropping Behemoth's Heart not yielding any additional regen (as Behemöth's Heart regenerates a percentage of max HP, there should be a point of intersection between the two lines generated from extra regen and Heart regen)?

Bonus question: combine dropping HotBL with switching Steamboots!

http://forums.heroesofnewerth.com/showthread.php?345025-Hypothetical-and-Ridiculous-HON-Math-Your-Questions-Answered!-For-Entertainment-Only&p=14411647#post14411647
About halfway down, under "How much HP is needed such that holding Behemoth's Heart gives more health than dropping it prior to using bottle?"

[IanDresari]

Oh, ofc you already did it! :)

[J3rk]

Hmm wouldnt this also mean that you could dampen incomming dmg by toggling steamboots between agi and str?
If so what would the math be behind it? Also with more than 1 steamboot.

[Quillenator]

So in between battles while I am low, I should dropp all my items that add stats, use a consumable, and then pick my items up after for max regen because it is percentage based.

[MacroHard]

So in between battles while I am low, I should dropp all my items that add stats, use a consumable, and then pick my items up after for max regen because it is percentage based.

As long as your items are safe from destruction, then this would be beneficial to your regen.

For example, I'm side lane early game and I have safe access to side shop (because I just got a double kill in epic fashion). I already had two +2 stat items and now find myself with a whopping 1300 gold. I have 663 health (27 str) with my items and 587 health (23 str) without them.

Instead of using my 1300 gold to buy my red boots, I drop my items and get a Lifetube and Ring of Regeneration with my 1300 gold. After 14 seconds I sell them back and pick up my items. For zero gold I just gained [(2+5)*14]*(663/587) = 110 health... for free. I can now buy my red boots and whatever else as originally planned.

[D_for_Daddy]

honestly, good job and so on although all you basically say is: switch to agi to get the most out of your bottle. how much free time do you have to do such calculations. no offense but i mean, really?

[ElementUser]

^He simply likes to do the calculations.

[TheDust]

Never. If regen is your goal, leave boots on Agi. (...)

Does it work the same if I want a certain value of MP? I mean a situation when :madm: has ~40 mana and wants to Stalk (60 mana). Is it better to switch on Int (for extra mana and extra mana regen) or to stay Agi and after, let's say 5s, switch it to Int?

[Marach]

generally, whenever you're using spells, you want to switch your steamboots to INT so you waste less mana.

whenever you want to regen mana faster, you keep steamboots on STR or AGI. whenever you want to regen HP faster, you keep steamboots on AGI or INT.

as madman, if you feel safe you would keep steamboots on AGI to regen both mana and HP faster (and increase damage for easier creep last hitting). if you don't feel safe, you would keep steamboots on STR for increased HP pool and to regen only mana faster. when you're about to use a spell or if you don't have enough mana for it, switch steamboots to INT and use the spell (if situation allows), then put steamboots back to AGI or STR (depending on whether you're safe) to increase regen.

---

and one note about steamboots switching and breaking invisibility.

I was about to advise to keep in mind that steamboots switching breaks invis. that is, it would break stalk invis so don't switch steamboots if you intend to be invis as long as possible (untill stalk ends by itself).

BUT then I recalled that switching steamboots would break invis before a certain patch changed that. I remember using this to be able to stack neutrals as nighthound :) (if you didn't switch steamboots constantly while doing it, you would go invis and creeps would stop aggroing you so you wouldn't be able to stack the camps).

now I'm not sure about that anymore. as I said, I remember reading about steamboots not breaking invis in some patch not so long ago.

edit:
found it...


2.6.0 Patch Notes

http://forums.heroesofnewerth.com/showthread.php?420998-2-6-0-Patch-Notes

- The following items were fixed so toggling them will no longer break stealth:
* Abyssal Skull
* Mock of Brilliance
* Nome's Wisdom
* Refreshing Ornament
* Ring of the Teacher
* Steamboots


can anyone verify whether steamboots switching breaks madman's stalk, nighthound's ult, nomad's mirage strike, invis rune, assassin's shroud and other forms of invis now? I'm not home so cannot test it.

[TheDust]

I've tested it and you are right. Toggling Steams does not affect Stalk/Shroud/Mirrage Strike. However...

Toggling Steamboots from STR/AGI form to INT form gives mana. 10 INT = 130 mana. Therefore when you switch AGI -> INT with max mana you gain 130 mana. But if you have 40% of your mana, you gain 40% * 130 = 52 mana. Here lies my problem. I am always wondering, should I switch to INT for more mana or leave on AGI for faster regeneration.

Situation:
I am :madm: with 40 mana on AGI Steams. It takes place after or mid-fight, I want to Stalk but I need 60 mana. I switch Steams to INT form and it adds usually ~10 mana, so I miss only 10 mana more to Stalk. But isn't leaving on AGI for 5 mana and THEN switch so I can have 60 mana. I know it is complicated mixed with my weird English but I find it crucial recently. People kill me when I have 56-59 mana and then I am totally :madm:. 1 second could save me.
Is there any multiplier like 1STR mana point = 1,5INT mana point?

[Marach]

if you quickly need more mana and switching to INT steamboots doesn't provide enough, then optimally you should switch to AGI or STR to increase mana regen rate and every so often try switching back to INT to see if you have enough mana. possible problem in situations when this so so crucial is that it can be kinda hard to switch steamboots so much like that as you're in the same time trying to see what is going on, juking enemies and stuff. as steamboots switching works in a percentage based manner, there is no magic number that I can give you. and even if I could, it'd be hard to check your current mana level and then quickly calculate it out in such hectic situation.

[TheDust]

Yeah, thanks. I thought that there is some magic number that allows me to do quick math like I need 20 mana, so I'll wait for 10 mana in STR mode. Thanks for replies :)

:madm:

[kazzer]

Lets say you have a strength hero like pebbles. he is autoattacking a target standing still. You wanna gain health back from your lifesteal item, is it more effective to have boots on agi and therefore gain from the treadswap or is it more effective to have strength steamboots and lifesteal more?

[TheDust]

If you have basic lifesteal Hungry Spirig (10%) then switching steamboots to STR will give you only 1 HP more lifestealed. The best lifesteal item in game gives you 175% lifesteal, which means STR Steamboots will give you 17,5 HP more lifesteal.

Therefore I think that you should leave Steamboots on AGI/INT because like said before STR improves your HP regeneration. That little lifesteal on STR wont make difference.

Anyone doing some serious math please confirm.

[ElementUser]

If you have basic lifesteal Hungry Spirig (10%) then switching steamboots to STR will give you only 1 HP more lifestealed. The best lifesteal item in game gives you 175% lifesteal, which means STR Steamboots will give you 17,5 HP more lifesteal.

Therefore I think that you should leave Steamboots on AGI/INT because like said before STR improves your HP regeneration. That little lifesteal on STR wont make difference.

Anyone doing some serious math please confirm.

The relative amount of HP gained on autoattack from lifesteal is actually slightly worse because your relative gained HP from lifesteal in this case is overshadowed by the max HP increase of Steamboots (190 HP).

Let's say you have X HP, Y damage and your primary attribute is Strength. If your Steamboots aren't on Str, then your lifesteal from Hungry Spirit will be 0.1*Y (assuming that target has 0 armor). % heal from lifesteal = 0.1*Y/X

If your Steamboots are on Str, then your lifesteal from Hungry Spirit will be 0.1*(Y+10), however the % heal from lifesteal = 0.1*(Y+10)/(X+190). This is worse since you're healing yourself for less % of your total HP.

Let X = 1000 and Y = 100. Without Steamboots set on Str, % HP gained from lifesteal = 0.1*100/1000 = 10/1000 = 1% of your max HP. With Steamboots set on Str, % HP gained from lifesteal = 0.1*(100+10)/(1000+190) = 11/1190 = 0.9244% of your max HP.

===================================

Of course, in any practical situation you'd want to set your Steamboots on Str anyway (as a Strength hero) since the absolute magnitude of the lifesteal increases and you're usually mitigating more damage to your total HP pool (as a %) with the extra +190 HP instead of the armor from Agi anyway. The only case where you might not want to is if you're autoattacking something that doesn't attack back & you don't really need the extra damage from Steamboots and you really want to gain back your HP *slightly* quicker - but that won't happen in any real game, so just keep it on Str.

[kazzer]

Thanks! it's very possible though, if you have a strength hero with lifesteal, most commonly seen Hammerstorm, and you just won a fight and you're taking kongor. You're supposedly not tanking it and you're around half hp. It happened to me and i'd like to know what boots to put on :) it's only logic that you want them on strength when farming