Base Speed, Armor, and Order of Operations

[TheFlyingPhoton]

If you have a speed reduction due to armor and an enhancement bonus to speed, which do you add first to calculate your total speed?

If you have a small character in medium or heavy armor and Boots of Striding and Springing, if you add the enhancement first, his speed is 20 ft, but if you subtract the penalty first, his speed is 25 ft.
If you have a medium barbarian in medium armor and the Boots of Striding and Springing, if you add the enhancement first, his speed is 35 ft, but if you subtract the penalty first, his speed is 40 ft.
If one were to take the approach of "the armor penalty and the boots should negate each other," it would require different orders of operations in the above two examples in order for the character to reach his "original" speed.

Also, would you consider the order of operations on this issue be different if the enhancement bonus were permanent (Boots of Striding and Springing) vs if the enhancement had a duration (Longstrider, Expeditious Retreat)?

[DM_Blake]

You will notice that size and encumbrance do not add or subtract to base speeds. They simply change them to a new number. In other words, being small is not a -10 penalty to base speed, it just changes your base speed to 20. Likewise, being encumbered (medium armor or medium load) does not apply a -10 penalty to your base speed, it changes it to 20, or 15 if you're small). So do those first because they are changes, not adjustments.

That should clear up most of the conflicts.

If you still have a remaining conflict, I usually apply permanent adjustments before temporary ones, and I usually prefer the mathematical order of operations (multiply before adding, etc.). But some of that is up to each GM to figure out on his or her own.

If there are any conflicts left, please provide an example.

[TheFlyingPhoton]

Ah, okay. I missed that nuance when looking over the base speed/speed adjustment tables.

[Gauss]

Just a note, being small does not change your base speed. A character's size has nothing to do with his movement speed.

Size and speed are unrelated qualities (ARG p218).

[kinevon]

Usual order I see it done:

Base speed (20/30)
Add enhancements/adjustments to it (e.g. +10 = 30/40)
Adjust for encumbrance/armor (e.g. 30 becomes 20, 40 becomes 30)

Permanency doesn't have a real bearing, other than tracking durations.
Type of bonus or penalty is much more important, remember that bonuses of the same type (other than dodge and untyped) don't stack, and penalties form the same source (encumbrance/armor, for example) don't stack.

Also remember that some penalties may be bypassed. A dwarf with boots of striding and springing always moves at 30', as long as he is not so encumbered that he cannot move at all.