
The OHQ commander performs skill rolls during combat. Operational command is always rolled. Depending on other factors, it also includes offensive tactics, defensive tactics, and other options like Tanks, Guns and infantry tactics. Skill rolls benefit attack and hitpoints and can support withdraw (Escape Artist) and reduction of entrenchment (Demolitions).
The SHQ commander also conducts a high command skill roll during combat.
Per the manual, for units to receive effects of skill bonuses, the unit must be in range of its OHQ. At 100%, a good skill roll always works. It decreases over distance to 0%, where skill rolls never work. The owning SHQ is always in range for the high command skill roll.
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+---------------------+------------------------------------+----------------------------+
| Skill | Offense | Defense |
+---------------------+------------------------------------+----------------------------+
| High Command | Attack and Hitpoint Bonus | Attack and Hitpoint Bonus |
| Operational Command | Attack and Hitpoint Bonus | Attack and Hitpoint Bonus |
| Offensive Tactics | Attack Bonus | None |
| Defensive Tactics | None | Attack and Hitpoint Bonus |
| Tank Tactics | Attack and Hitpoint Bonus | Attack and Hitpoint Bonus |
| Gun Tactics | Attack and Hitpoint Bonus | Attack and Hitpoint Bonus |
| Infantry Tactics | Attack and Hitpoint Bonus | Attack and Hitpoint Bonus |
| Deception | Attack Bonus based on Entrenchment | None |
| Escape Artist | None | Hitpoint Bonus on Withdraw |
| Demolitions | Entrenchment Reduction | None |
+---------------------+------------------------------------+----------------------------+
Attack Bonus: Relevant skill roll for each subordinate's attack. Difficulty is 100.
Adds 1% bonus to attack value for each point above 100 points.
Hitpoint Bonus: Relevant skill roll for each subordinate under fire. Difficulty is 100.
Adds 1% bonus to hitpoint value for each point above 100 points.
Attack Bonus based on Entrenchment: Deception skill roll for each subordinate's attack. Difficulty is 100.
Adds 2% bonus, modified by entrenchment divided by 100, to attack value for each point above 100 points.
Hitpoint Bonus on Withdraw (i.e. Retreat): Escape Artist skill roll for each subordinate's withdraw under fire.
Difficulty is 100. Multiplies hitpoint value by four if roll above 100 points.
Entrenchment Reduction: Demolitions skill roll for each subordinate's attack. Difficulty is 100.
Reduces entrenchment value of the target by 0.5% for each point above 100 points.
It is important to note that the OHQ skill bonuses do NOT apply to its own HQ unit in combat. Per the image above, under Organizational Info, the HQ unit receives 0% HQ Power. Players are cautioned to protect HQ units from combat.
You can have more than one OHQ commander in an engagement, if you mix your formations in an offensive or mix them in a hex during a defensive fight.
Look for morale and experience benefits as well.
Please also note, do not assume the term attack simply means moving to contact as the offensive side. As part of each round of combat, units on the defensive side attack and unit's on offensive side are targets.


Reference discussions:
* https://www.matrixgames.com/forums/tm.asp?m=4834576
* https://www.matrixgames.com/forums/tm.asp?m=4834681
* Discover the Formation Type Overview