Upgrade your account to a Community Supporter account and remove most of the site ads.

Reply to thread

Message: <blockquote data-quote="Mike Sullivan" data-source="post: 933305" data-attributes="member: 9824">The above is somewhat incorrect on a purely mathematical level.A -1 penalty to hit does not correspond to a 5% reduction in expected damage.  For example:Suppose that after all adjustments, you hit on a D20 roll of 11 (50% of the time), and do 2d6 damage, against a target not susceptible to crits (average damage = 7).  Thus, your per-attack expected damage is 3.5 (7 * 50%).Now, suppose you take an additional -1 to hit, meaning that you now hit on a 12.  You still do 2d6 damage, no crits, but you hit only 45% of the time (a 5% reduction in chance to hit).  Your per-attack expected damage is now 7 * 45%, or 3.15.However, 3.15 is not 95% of 3.5.  In fact, it's 90% of 3.5.Why is this?  Because it's not your damage which suffers a 5% reduction in chances, it's your chance to hit.  Your chance to hit was already only 50% and you're reducing it to 45%.  45% is 90% of 50% -- and that's what matters.What's the practical upshot of the above?  That it's very difficult to calculate the tradeoff between attack and damage bonuses.  For example, suppose you hit on a 19, normally.  Is a -1 to hit worth it to you, if your average damage is, say, 10?  No, because that -1 to hit actually halves your odds of hitting!  You go from having a 10% chance of hitting to a 5% -- and that means that you only get 50% as many hits in.  So it's only worth it to you if you're going to get a 50%+ increase in damage as well.On the other extreme, if you hit on a 2+ normally, taking a -1 to hit means you hit on a 3+ afterwards.  In this case, you're going from a 95% chance to hit to a 90% chance to hit, which is a total of a 6.3% decrease in potential damage -- so if the corresponding +1 to damage increases your total by more than 6.3%, it's a good deal for you.Now, I said that Andy Collins' quote is "somewhat wrong," because though the details are incorrect, the basic sentiment is (sort of) correct.Let's examine two different fighters under 3.0.We've got Greatsword Fighter Bob, and Double-Shortsword Fighter Joe.  Both are fourth level, and are human.Bob has Str 18, Dex 13, and the feats Weapon Focus (greatsword), Weapon Specailization (greatsword), Power Attack, and some other ones.Joe has Str 13, Dex 18, and the feats Weapon Focus (short sword), ambidexterity, TWF, Weapon Specialization (short sword), Weapon Finesse (short sword), and Power Attack.Bob attacks with his greatsword at +4 (base) + 4 (strength) + 1 (Weapon focus) = +9.  He does 2d6 + 6 (str) + 2 (specialization) damage, or a total of 2d6 + 8 = 15 damage base, with a 19-20/x2 crit, for a total of 16.5 expected damage per hit, after crits.Joe attacks with two shortswords at +4 (base) + 4 (dexterity) + 1 (Weapon focus) - 2 (TWF) = +7/+7.  His "on" short sword does 1d6 + 1 (str) +2 (specialization) damage, or 1d6 + 3 = 6.5 before crits, 7.15 damage after.  His "off" short sword does 1d6 + 2 (specialization) damage, or 5.5 before crits, 6.05 after.Okay, let's examine their performance against various opponents.  I'm going to stick with relatively low-AC opponents, because the purpose of this exercise is to examine PA, and PA is never worthwhile against high AC opponents.AC 20 OpponentBob needs an 11 to hit (50% hit ratio).  His damage is 16.5, on average, leading to a total expected damage of 8.25.Is it worthwhile for Bob to PA?  Well, let's look at the -1 to hit.  That means he needs a 12 to hit, so his chances drop to 45% chance to hit, but his average damage increases to 17.6.  That means his per-round expected damage is 7.92 -- it's not worth it for Bob to PA.Joe needs 13's (40%) to hit with each sword.  His expected damage per round with his "on" sword is 7.15 * .40 = 2.86, and his damage per round with his "off" sword is 6.05 * .40 = 2.42.  Thus, his per-round average damage is 2.86 + 2.42 = 5.28.Is it worthwhile for Joe to PA?  If he takes a -1 to hit, his odds of hitting with each sword drops to 35%.  His average damage with his "on" sword goes up to 8.25, and the damage on his off sowrd goes to 7.15.  That means his per-round damage goes to 5.39.  Thus, it's marginally worthwhile for Joe to PA for 1 point.  It won't be worth it again.So we see that against an AC 20 opponent, Power Attack is more worthwhile for the two-shortsword guy than for the greatsword guy....  BUT, it's still better to be the greatsword guy overall.AC 15 OpponentBob attacking at +9 hits on a 6+, 75% of the time.  His average damage is 16.5, so his per-round expected damage is 12.375.If Bob PA's for 1, his chance of hitting drops to 70%, but his average damage increases to 17.6.  That means his per-round expected damage is 12.32 -- it's STILL not worthwhile for Bob to PA.Joe, on the other hand, is hitting 65% of the time (8+) with each sword.  His on sword does 7.15 * .65 = 4.65 damage, and his off sword does 6.05 * .65 = 3.93 damage, for a total of 8.59 expected damage per round.If Joe PA's for 1, his chances of hitting drop to 60% for each short sword, and his average damages increase to 8.25 and 7.15.  That means that his per-round expected damage is 9.24!If Joe PA's for 2, his chances of hitting drop to 55% for each sword, but his average damages increase to 9.35 and 8.25.  Per-round expected damage is 9.68!If Joe PA's for 3, his chances of hitting drop to 50%, and average damage increase to 10.45 and 9.35.  Per round expected damage is 9.9!If Joe PA's for 4, his chances of hitting drop to 45%, and average damages increase to 11.55 and 10.45.  Per round expected damage is 9.9 again -- and after that, it's downhill.So Joe, by strong use of PA, sees an increase in damage from 8.59 damage per round to 9.9...  A much better bonus than Bob gets from PA, but still not enough to increase Joe's damage to be comparable to Bob's.An AC 10 opponent would be even more favorable to Joe and less to Bob -- TWF is a style which is advantaged when fighting low-AC people, and PA excaberates this.Another interesting point:  If your pre-critical-hit average per-hit damage is above 20, it's only worthwhile to PA when it doesn't affect your chances of hitting at all.  (ie, if you're attacking at +20 and your opponent has AC 15, you can PA for 6, and still only miss on a natural 1).What about things not in this analysis?  It's hard to say.  Joe does less damage than Bob, that's clear, even with the relative utility of PA for him.  However, Joe also has an 18 Dex, which gives him a +4 to reflex saves, initiative, and AC, over Bob's 13 Dex, giving him only a +1.  Also, we're looking at isolated points in their careers.  Later on, magic weapons enter the picture (and generally advantage Joe, though at a monetary cost), as do iterative attacks (which advantage Bob).  And, of course, Bob has more feats to throw around...Now, expanding out to 3.5e, contrary to what's above in this thread, it's not simple to say which style is more advantaged.  Some points:Power Attack:  This is pretty obviously a buff for the two-handers and a nerf for the two-weapon fighters.  BUT, see below...Higher Monster AC's:  TWF is better, the lower the AC's, so having generally higher-AC opponents is a nerf to TWF.  But PA is also better, the lower the AC's, so this nerfs PA as well, mitigating the differential above.Lower Feat Costs, Lower Feat Requirements(?):  This is obviously a buff for TWF, in no uncertain terms.Greater Weapon Specialization:  Assuming that this feat gives a larger damage bonus than the standard +2 for normal weapon spec, it's a buff for TWF (our iconic double-shortsword wielder gets twice as many attempts to put the damage bonus into play).  It's also a bit of a nerf to PA, because PA doesn't play well with other damage bonuses (ie, it will be sooner before PA is obviated, even with the *2 bonus).So, at the end of the day, Andy Collins is right in generalities if not specifics: as written, PA is better for TWF than for two-handed fighters.  For purely flavour reasons, he may have thought that was inappropriate regardless of whether either style was to be "nerfed" or "buffed."  I don't think that it's really possible to back up a claim that either TWF or two-handed fighting are objectively weaker or stronger in 3.5 than in 3.0e.</blockquote>

Verification