Initiative System:

Initiative Rating is as much a mental trait associated with aggression and mental quickness as a physical one associated with reflexes.

Example of a way to calculate Initiative for integration into the HERO games system.  
In Hero this replaces the normal timing system based around phases and SPD attribute.

Initiative:  3  +  (INT + DEX)/5 (cost 3 pts per additional initiative pt)

 An actions "time cost" is in terms of initiative and varies considerably from action to action. Ranging atleast from 1 to 6 pts. 

  [ Most actions also have costs in terms of fatigue (and some few in terms of actual damage.) ]

Passing the initiative: a theoretical action whereby one reduces ones initiative less than the next highest initiative. There is no intrinsic advantage to this... and it usually represents a character performing a passive/inobvious action such as resting, scanning for openings to attack/escape or similar actions.

The standard combat attack as handled in HERO includes scanning for an opening to attack and is a 2 initiative cost action.

Attacking without looking for an opening is done at a penalty but targets any location not necessarily the one left open it is generally at about a - 4 but costs only 1 initiative. (If you like heros optional hit location system use the appropriate penalty based on hit location)

 Converting An Actions Timing:

Actions which presently take a full turn are about 6 initiative pts

1/2 phase actions are 1 defenses or 2 pt attacks [ occasionally either may be a point lower or higher] for instance desperate defenses are 0 initiative actions(but at a definite penalty).

A 3 initiative cost action is approximately = a full phase action.