I have a math brain, and am pretty good at EXCEL, so decided to do some comparisons. What is better? Critical Focus and Bleeding Critical (for example) or two other feats I might take instead? (Greater Weapon Focus and Shield Focus....for example).
I did an expected value thing first (assuming average damage, etc) and it was interesting, but when you start to take into account actions that have lingering effects (such as bleeding critical) it became tough to do that.
So, I went nutty and started building a combat simulator spreadsheet (generating random numbers for die rolls etc)...after many hours, and several version upgrades, I built an actual combat simulator to where I could pit my 10th level fighter versus himself (for example) and then change some feats on one of them to see how much more damage I did or how often one guy won versus the other. Then, to eliminate "lucky" rolls, I duplicated this test 400 times (filling up a spreadsheet) and then ran that 400 combat test a dozen times to see on average which combination beat the other guy more often, and how much a +1AC (for example) helped. Also, I could do the whole thing again at different AC levels....obviously a very high AC has a different outcome than low AC's where a fighter hits on a 2. I also ran different weapon types though (different crit threat ranges) to see how that played out.
Been a lot of fun - learned a ton of things.
One tidbit to share is that at moderate levels (say, beefy 10th level fighter here...decent magic....decent strength, etc) +1AC is better than +1TH.
Which guy won initiative in a fight was obviously huge (duh - makes sense when I'm pitting a clone fighting himself).
Also, INIT makes even more difference when you are both hasted. Again, no surprise, but what was surprising is how much of a difference winning INIT made. With hasted foes, the guy that won INIT won on average 20% more of the time.
Finally - Greater Weapon spec is better than Shield Focus which is better than Greater Weapon Focus.
And, much to my disapointment, +1TH and +1AC trumped Critical Focus and Bleeding Critical for typical fights. Yes, it's true, that if you were fighting something with a massive amount of HP (and somehow didn't get killed too quickly yourself) over time the Bleeding damage can really add up, but with most fights lasting 3(?) rounds, the bleeding critical damage ON AVERAGE doesn't make up for the +1TH and +1AC. Yes, if you get lucky and get a couple of crits your first round, then that particular fight would be one where you'd love to have bleeding critical, but on average, it doesn't pay for itself. Now, Stagger on the other hand..... ahhhh....shhhh....don't want my DM to see this post lol.
I'm going to do some tests now on how valuable Penetrating Strike is (which, obviously will depend upon how often you face someone with DR)
Sounds like an interesting exercise. Popping the hood and understanding how the numbers really work is always a fun experience. However, be careful - the numbers can lie to you and lead you to conclusions that do not work in an actual game especially if taken to extremes. +1 AC may be > +1 attack bonus. But high defense < high offense in most situations (dead monsters don't hit back).
Also, a mirror match is not a good comparison as monsters follow a different progression than characters do (see the Bestiary for a table that has expected stats for every CR).
I agree that fighting myself wouldn't represent monster combat, but I was trying to do a controlled experiment, having as many things be identical as possible, so I could see the effects of 1 change etc. In my mock battles, I count victories, so to your point Mike J, whichever feat helps the guy win more fights is what I was counting. Now, I do agree that it is situational and there are some situations where AC may not be as important....like....you are both near death and so you want to take the guy down or he'll for sure take you down etc...so just trying to come up with some good rules of thumb here.
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I would think that Greater Weapon focus, in combination with Power Attack, would exactly equal the +2 damage from Greater weapon spec, if you could get the latter without the former.
But yeah, bleed attacks aren't all that awesome unless they occur every hit and stack for massive damage round to round. They are also largely useless against anything with regeneration or fast healing, as the healing effect stops the bleeding.
I did my simulation with bleeding critical and then compared it to Staggering Critical. Yup....no comparision (depending upon the Fort save of whome you are fighting of course). In my case I had the foe have a Fort bonus of 15 and trying to make a 23....so he needed an 8. Still pretty effective with a weapon with a good critical threat range.
yup - reminded me of a fight not too long ago where the party monk fought another monk (who won initiative) and our party monk kept getting stunned EVERY round lol....well...he wasn't laughing :)