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[a smiling bearded cretin]

Combat Speed
It's something that's affected by both movement speed and attack speed.

Movement Speed
Let's say normal movement speed is maintaining a walking speed of 1.000. It's what you start with and is easy enough to use since you won't be too slow, or moving so fast as to become tired or over-exerted (because you did not or could not create your character with Superior Endurance).

If what your character carries/wears, exceeds the limits of your strength and agility and armor skill, walking speed will drop and an opponent will be able to attack many times before your chance to attack arrives. Moving movement speed up to sprint won't offer any benefit, but can eventually make you tired. So for combat, it's best to be relatively unencumbered at a walking speed of 1.000.

Attack Speed
It's initially determined by agility. From a limited testing perspective, assuming you have a walking speed of 1.000 during an encounter, if you and your opponent (who, in this case, is almost twin of yourself, save for the difference in agility) choose the same exact attack (say both of you choose a wild iron short sword stab), whoever has the highest agility will strike first during the exchange. But it's muddier than that, as attack speed, after agility has been counted, is about all about modifying time. Time in Adventure Mode is measured one instant/tick after another. By pressing the comma key "," you will cause one instant/tick to pass.

Standard attacks from most weapons and natural strikes cover a 6 instant span of time which is 3 instants for preparing the attack and delivery, followed by 3 instants for recovery. Aimed/specific attacks (quick, precise, heavy, wild) will act as speed modifiers, either adding or subtracting instant(s) from you or your opponent's prepare and recover. Most weapons and strikes (default:standard) are [ATTACK_PREPARE_AND_RECOVER:3:3] while whips and kicks are [ATTACK_PREPARE_AND_RECOVER:4:4].

PREPARE
Precise Attack 4 instants until delivery
Heavy Attack 3 instants until delivery
Standard Attack 2 instants until delivery
Quick or Wild Attack 1 instant before delivery

DELIVERY 1 instant

RECOVER
Quick Attack 2 instants of recovery, then next instant to Neutral
Standard or Precise Attack 3 instants of recovery, then next instant to Neutral
Heavy Attack 4 instants of recovery, then next instant to Neutral
Wild Attack 5 instants of recovery, then next instant to Neutral

These instants give you a picture of the stages of combat. Full information in combat is stage of attack, attack's prepare/recover speed modifier, attack type, and part of body targeted:

Distant: Attacking you with precise iron short sword stab, aiming for left upper arm.

Stage of attack and prepare/recover speed modifier mean the same thing:

Distant = Precise
Starting = Heavy
Incoming = Standard
IMMINENT = Quick or Wild

But this, like all other combat information, is dependent on your level of Observer Skill. With lower levels of observer, you likely won't know what stage an attack is at, the prepare/recover speed modifier, etc. Mostly you'll see attack type and the body part aimed for, or less as observer level trails downward to Novice Skill. By the time you reach Expert level observer, you'll receive bulk information more often. Being able to benefit from the additional information is a later game boon for peasant/hero.

Usefulness
This fine motor skills approach to combat can save you time. If you know the recovery cost of an opponent's attack in number of instants, you can then choose to safely select slower more precise/powerful strikes that can end the fight faster. Only demigods who start with (around) Talented Observer have the chance to use the fine motor skills approach early in game play. However, the gross motor skills approach is available to the character who begins with Novice Observer (peasant).

Knowing about the minutiae of combat speed is largely academic as this confirms what everyone thought in September 2014. Adventure Mode combat can be reduced to your character having the agility attribute set to high at character creation, maintaining a walking 1.000 movement speed during the encounter, only using a multi-attack variant of quick attack + dodge away (perhaps occasionally blocking to induce an off balance penalty), trying to fight outside when possible, if facing multiples kiting, and lastly a simple target order (hit foot/neck, then move on to damage head/rip open major artery/etc).

All of this can be done only knowing the minimum of combat information, and presuming that your combat speed is always slower than that of your opponent. Of course, your mileage may vary. You may find knowing each instant useful.

[vjmdhzgr]

If the fights not going to last a long time, I'd recommend rather than walking, jogging. While it does make you use more endurance, combat with a single enemy can be ended quite quickly if you have decent skill, and even with standard endurance it takes a long time to get tired from jogging. If you're not very skilled or up against a lot of enemies and don't have a very high endurance, then yeah, just walk.

[a smiling bearded cretin]

Agreed.

I use walking speed just to establish a movement speed with no penalty attached. 

For instance, my dwarf tends o carry a parent bag/backpack with 100 water/ice and say 40-50 plump helmets or 20-50 meat and 25-50 arrows/bolts that really slows him down. Once a fight begins because we've stopped outside a lair, or there's an ambush, my first action is to drop the bag to get back to walking speed 1.000.

If it's an ambush or sorts, often I'll switch to sprint to ensure the enemy meets my character first, instead of my companions. While sprint might make my movement faster so I can get into a specific position faster, in cases like this, it won't affect my attack speed one way or another.

This was just a long-winded way of saying manage what you want to manage so you end up at the right starting point.

But yeah, each of us needs to do what suits our play style best.