Extra Regeneration from Toggling Steamboots

[[S2]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

note: unmarked values left of the curves will fully replenish health or mana

Table

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

[[S2]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.

[[eR]Ekamo]

Truly awesome <3

Thanks for helping

[[S2]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?

[[S2]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

[[iRBa]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?

[[S2]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 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 aura), while health will always regen slower with steamboots on str.

[[S2]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.

[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 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

[[S2]MacroHard]

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

[[S2]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.

[[H]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.

[[S2]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.

[[Flag]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. =)

[[S2]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.