The effect of leadership during combat

[Gray Fox]

(With apologies, this thread has parts that unfortunately deal with the four letter word...math.)

One of the factors in calculating the "to hit chance" for fire or assault combat is called the Total Command Modifier (TCM). It is the difference between the stack and unit leader values of the offender and defender and looks something like this:

[(stack commander offense value x 0.05) + (unit leader offense value x 0.03)] = A
[(stack commander defense value x 0.05) + (unit leader defense value x 0.03)] = B
TCM = 1 + A - B

Now if everyone is a 3-1-1 (or a 6-6-6), then A equals B and the factor has no effect, since the calculated "to hit chance" is then multiplied by 1. However, taken to extremes, a military genius stack commander with straight 6's and a unit commander protege with the same:

[(6 x 0.05 = 0.30) + (6 x 0.03 = 0.18)] = 0.48

versus an unfortunate pair of 3-1-1's

[(1 x 0.05 = 0.05 + (1 x 0.03 = 0.03)] = 0.08

gives a TCM (1 + 0.48 - 0.08) of 1.4 for the offense and a TCM (1 + 0.08 - 0.48) of 0.6 for the defense.

What do the numbers really mean? Even your best leadership against their worst only has a modest overall effect. For a hypothetical "to hit chance" of say 40%, the best leadership differential you can hope for would change the chance by 16%:

40% x 1.4 = 56% for your attacking unit or 40% x 0.6 = 24% for a unit attacking you.

Note that a Division alone would gain a greater "to hit chance" by just having a more senior "stack commander", even if he is a 3-1-1 and not a designated Corps commander for an extra + or - 0.05 to the TCM.

"If you find yourself in a fair fight, then you've done something terribly wrong."

Bearing this military axiom in mind, if you attack their best leaders with your best then you will need to use superior numbers or something else to win, because the leaders will simply negate each other. Good luck!

[ArmChairGeneral]

+1, very insightful.

The example you give actually provides a HUGE swing in fighting ability, though: the better leader's troops would score hits more than twice as often, assuming all else equal.

Now of course, we would never see that large of a differential between the two sides, and the base hit chance for anything other than artillery would be more like 20% even in favorable conditions, so the above example is a rough theoretical max to the effect of leadership. In most battles the two sides' leadership will be much closer, leading to the modest effects that you are trying to point out. In practice, we would be lucky to see a 1.1 TCM.

I have sometimes wondered whether an independent division gets the .05 modifier because the division commander is counted as the stack leader, or just .03 because he only counts as the unit leader. This is easy enough to check I suppose, the calculation is shown in the battle log, so if no one else chimes in I will take a peek some time. Either way, the very useful trick of giving the stack a more senior leader gets the .08 number which is superior in both cases.

(I love these kinds of threads! For what it's worth, the calculations the battle engine does are pretty straightforward, and lend themselves well to this kind of useful analysis.)

[Gray Fox]

Thanks!
I was interested in Jagger2013's comment in the Corps/Division design thread that stack artillery lose out on a "substantial" Division commander leadership factor. Turns out this would at most be 0.18 to the TCM and more likely only make it to 0.03. I posted that I use a general with the artillery officer trait in those stacks. It turns out that this gives the stack artillery a 0.2 modifier, which indeed more than compensates.

The artificial "stack commander" idea just struck me as something that might work. I always send an extra general to lone garrison Divisions to get the CP count up to four anyway.

P.S. I'm sure this is just another "gamey" crime against humanity that I have committed.

[Taillebois]

Which file can I change to my advantage in combat - presumably it is one that is altered when you change the AI difficulty setting?

[Gray Fox]

I suppose you mean this?

http://www.ageod-forum.com/showthread.php?5358-Official-Files-for-modding

[ArmChairGeneral]

AFAIK the combat engine is only indirectly affected by the various difficulty settings. The higher speed from the Rank setting means they arrive at battle with less cohesion lost to marching, for example. Bonus to Activation appears to give higher strat ratings to AI generals (rather than just giving them a bonus on the activation roll, which is what the tooltip implies) which makes them better at engaging/disengaging in addition to the activity considerations. I don't think there is a place in any of the files where you can give one side or the other a direct bonus to combat, but I would be interested in knowing for sure.

[ArmChairGeneral]

I suppose that you could change the stats of one side's models, although that sounds tedious. I don't have a lot of experience with the model files beyond just altering leader stats.

[Ace]

Gray, you failed to take into account frontage bonus generals gives in woods/plains. Also I think generals stats give only bonus to hit, there is no bonus to evade hits.

[Gray Fox]

True, I was only explaining the exact number's for the effect on combat. I explained frontage in another thread somewhere. If you have enough troops in the right terrain, a good commander can put more into the fight than an average commander. However, this would only be open terrain in good weather.