I apologize for not having a more specific set of information (I'm pretty new to modding TW) ... but there is a set of traits associated with Battle-scarred that for each of the four levels is set at 1, 2, 3, and 4.

I went ahead and changed the last two levels to be 6 and 9, and I now have yet to have another "Scarface" appear after many many battles with my general.

Basically, by changing the 3, and 4 #s, I think that I have altered the number of HPs that my general needs to lose, or perhaps the number of battles he needs to fight in or something along those lines... but in any event, it certainly has drastically reduced the number of level 3 and level 4 scarred individuals in my family, which means that I end up with less influence inhibited and "Scarface" named generals running around!

Again -- apologies for the lack of true detail as to which parameter specifically to change. However, if you look in the section where the 4 scarred levels are, I think that it will be fairly clear what I am talking about. Hope so, anyhow!

Cheers.