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Let's assume that the character has full BAB. And +5 enhanced weapon. Than he would get total 25 AB at the 20th level. At the same time he would have 11 armor bonus (8 + 3 for mithral full plate) +5 armor enhancement bonus, tower shield with 4 shield bonus and +5 shield enhancement bonus, natural armor bonus +5 and deflection bonus +5, totally +35. So he would hit his own copy only on natural 20 (25 + d20 against 35 + 10).

Well, character could invest in boosting his attack attribute, strength, or dexterity for weapon finesse users. But he could equally boost his defensive attribute, replacing +5 mithral armor with monk's belt and bracers of armor +8. If he could boost his wisdom with buffs at least to 24 (in addition to boosting dexterity), he would get equal armor bonus, but without dexterity cap, so the character could grow his defence attribute at the same rate with offence (and if he is a weapon finesse user, the attributes are the same).

Monk's belt could be used together with shield bonus, just employ persist metamagic on the 1st level spell Shieldbearer from the SpC.

There are feats that increases AB, but there are also feats that allows you to use armor more efficiently, or use TWF for defence. So it is a draw.

So, how a high level character is supposed to hit his own copy?

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  • \$\begingroup\$ RE: "[J]ust employ persist metamagic on the 1st level spell Shieldbearer….": It would likely take a house rule to employ the metamagic feat Persistent Spell on the spell shieldbearer, a spell with a range of touch instead personal or fixed (like, for example, detect magic). Also, the high base attack bonus character probably either has a custom magic item that creates the effect or a cohort who casts it for him, and both rely on the DM. (I know it's a minor point, but the game really does make it difficult to use a shield while not using a shield.) \$\endgroup\$ – Hey I Can Chan Jun 1 '16 at 16:20
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Your hypothetical character, with 20 BAB and +5 sword, must have STR of 10-11, otherwise he'd get a bonus from that as well. Full-BAB characters tend to be strength-focused, so would likely start with high strength, and then raise it further on level-up. Assuming either a min-maxed point buy, or a lucky roll, a starting character could have 18 STR (or more depending on racial modifiers). Levelling up to 20 lets you increase attributes 5 times, bringing you to 23. The bonus for an attribute that high is +6, giving a total attack bonus of 31.

Items can further increase your strength.

  • Belt of Giant Strength: +6 enhancement
  • Manual of Gainful Exercise: +5 inherent

That's +11 to Strength, bringing it to 34. Bonus +12, for a total attack bonus of +37.

Then there are feats that add to your attack bonus. Assuming melee:

  • Weapon Focus: +1
    • Greater: +1
  • Melee Weapon Mastery: +2
  • Crushing Strike: +1 per previous hit this round
  • Weapon Supremacy: +5 (conditional)
  • Overwhelming Assault: +4 (conditional)
  • Mounted Fighting: +1 (conditional)

That's +4 unconditional, with potential for +14 or more if conditions are just right. Total attack bonus between +41 and +51.

Don't forget tactics. There are attack types that increase your attack bonus, or decrease their AC.

  • Charge: +2
  • Flanking: +2
  • Make them flat-footed: -(DEX bonus) to AC
  • Trip them to make them Prone: -4 to AC (vs melee)
  • Stun them: -(DEX bonus) AND -2 to AC

If you have a spellcaster in your party, there are spells that make it easier to hit, too.
(I'm not going to list them)

And, if we're looking at spells, there are so many ways to defeat an enemy that just don't care about AC.
(And most of the ones that do, target Touch AC, which is harder to raise.)

But, you say in a comment on your question, that you're worried about monsters being optimised, and being able to hit them at high levels.

I'd suggest you look at some of the monsters in the MM.
Arguably the most fearsome is the Tarrasque, which has an AC of 35.

It has other features which make it very hard to kill, but actually landing a blow is not that difficult for high-level characters.

And finally... all this needs resources that are limited. If you are trying to max your attack bonus, you can't also max your AC (and vice versa).
If you're a maxed-attack character fighting your mirror image, both of you will be able to hit easily.
If you're a maxed-AC character fighting your mirror image, neither of you will be able to hit easily.

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    \$\begingroup\$ Interesting point about the Tarrasque: its Bite Attack is at +57, so much higher than its AC. \$\endgroup\$ – Matthieu M. May 31 '16 at 6:10
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You have a flawed premise that a high-level character is supposed to be able to hit his own copy even when he has invested everything in not being hit, to the detriment of his own accuracy.

This is not the case. When you put so much into AC that your attack suffers, by definition you will become less able to hit your own clone, since your AC is going up and your attack is going down.

But in practice, this is a terrible strategy; you have too many defenses (armored and touch AC, Fortitude, Reflex, and Will saves, etc.) to worry about to try to maximize them all. You will always have a vulnerability,1 and if you have no offense, then your opponents will eventually determine what it is. The only way to truly eliminate all threats is to be able to eliminate them, and that requires offense of your own.

  1. Not strictly true, actually, but I’m ignoring high-optimization tricks to achieve true invincibility even though they do exist. None of them involve merely pumping ability scores and slapping on a lot of protective gear.
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  • \$\begingroup\$ While I do agree in general with the analysis, I would take the opportunity to note that D&D is normally played by a party of characters, and therefore it would be alright for one amongst the party to concentrate on defense... as long as this means defending the party, and not only itself. A DMM-focused cleric or Persist-focused incantatrix for example, or even a heavily armored Knight, could conceivably aim at protecting the party one way or another, relying on the other team members to provide the offensive power. \$\endgroup\$ – Matthieu M. Jun 1 '16 at 14:42
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    \$\begingroup\$ @MatthieuM. 3.5 provides extremely limited opportunity to protect others effectively. Most are circumstantial (e.g. holding a chokepoint requires there being a chokepoint) and imperfect (e.g. teleportation becomes fairly common at mid levels). Most 3.5 defending relies, basically, on enemies’ tactical failures, rather than anything pro-active you can do to force intelligent enemies to do what you want. For contrast, easily one of the best aspects of 4e, for whatever other flaws it has, is the fact that defenders actually function effectively in that edition. \$\endgroup\$ – KRyan Jun 1 '16 at 14:47
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    \$\begingroup\$ Also, even if you were going to focus on defense, non-touch AC is the least useful defense there is. \$\endgroup\$ – Miniman Jun 1 '16 at 15:06
  • \$\begingroup\$ I think a properly setup defender could work. Already as I mentioned a spellcaster focusing on buffing provides additional defensive power (as well as offensive), debuffers can also be seen as defending, the Shield Other spell offer some production and the Knight's Challenge (despite scaling issues) is a defensive ability... It's few and far between, but I think there are ways to make it work... though it'll be more difficult than optimizing for raw damage (uber-charger, etc...) \$\endgroup\$ – Matthieu M. Jun 1 '16 at 15:08
  • \$\begingroup\$ @MatthieuM. As a practical matter, having tried numerous times, it can kinda-sorta work, but it never works particularly well. For a strong optimizer playing with a low-optimization group, it might be an interesting challenge, but ultimately the effort required never matches up well with the results generated. \$\endgroup\$ – KRyan Jun 1 '16 at 15:10
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D&D is a number games, but there are various approaches to help touching.

First of all, as he mentioned, no heavy hitter will actually have +0 Strength (or Dexterity). Any optimized character will attempt to raise its Attack Bonus as high as necessary to touch often.

For a Strength-focused character this involves:

  • a high starting Strength score: 18 or 20 (depending on racial bonuses)
  • +5 from leveling (remember the +1 you gain every 4 levels)
  • +5 Inherent bonus (Manual of Gainful Exercise or Wish)
  • +6 Enhancement bonus from Belt of Giant Strength (for example)

For a base Strength score of at least 34 (or +12 to Attack Bonus).

There are various feats that may increase your Attack Bonus (such as Weapon Focus) however a feat for a +1 Attack Bonus is actually regarded as weak.

There are some much better feats, of course, Stormguard Warrior (Tome of Battle), is a tactical feat with 3 variants, each of which giving a bonus to Attack Rolls for the next turn.

Also, do not forget that the Power Attack feat is much appreciated and lets you trade away Attack Bonus to get more damage.

Circumstances help a lot:

  • Charging gives a +2 bonus to Attack Rolls
  • Flanking gives a +2 bonus to Attack Rolls

Flanking an opponent is generally, easy, make sure that all melee characters in your group understand how it works and apply it.

There are plenty of other ways to increase your chances to touch your opponent.

  • A staple of Gish builds for example is the Wraithstrike spell (Spell Compendium, p. 243) which transforms your melee attacks in touch attacks (bypassing Natural Armor, Armor and Shield bonus).
  • Tome of Battle has a few Diamond Mind maneuvers such as Ruby Nightmare Blade and Diamond Nightmare Blade allowing you to use a Concentration check to touch; it also has a few Tiger Claw maneuvers such as Soaring Raptor Strike which give you a hefty +4 bonus to Attack Rolls (and some damage) if you succeed on a Jump check.
  • ...

The most important point to understand is that a high-level character seeks some balance:

  • hitting is important, but worthless unless you do some significant damage or cripple the opponent in some way
  • having high damages is important, but worthless unless you can hit reliably
  • AC is not the only thing that may protect your opponents from taking damage, Concealment is another good defense (such as the Blink spell), factor it in
  • having a balance to hit/damage ratio is good, but worthless unless you can close in on the opponent (beware, at higher levels some things fly)

So, you can Fly, negate Concealment (or re-roll) and you have a good balance between hit ratio and damage, all good?

Not quite: what of your survivability? A dead character is pointless, an immobilized one too, a crippled one is not of much use...

... and unfortunately, spellcasters have a wide array of debilitating spells at their disposal. Don't forget the Soulfire enchantment on your shield or armor, nor Fortification (or play a Construct or an Elemental?), ...

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The main thing you are missing is Strength adding to your to hit, as others have said. but there are a couple of other issues with your calc as well.

1) Virtually no-one uses a tower shield. Many posters here argued that no-one ever should use one.

2) Not all characters have access to all of those options. Mages, Rogues etc will have lower AC. You should probably target mages first anyway.

3) Brilliant Energy. Any PCs or NPCs at the power level you are talking about are probably well known. If they stack AC, anyone who is planning to fight them will bring Brilliant Energy

The point of AC at high levels is not to stop people's first attack, but to stop their full attack. Simple high level characters should have 43 AC max. This is:

10 base.

5 natural.

5 deflection.

3 Dex.

13 Armour.

7 shield.

Some characters will be higher than this. Monks can get it very high, I remember seeing some slightly absurd Vow of Poverty Monks with level adjustment races/paragon. But they couldn't really do any damage so the correct way to deal with them was kill the rest of their party first.

By contrast, a simple high level character will have

BaB: 20/15/10/5.

Str Bonus: 14 (or so)

Magic weapon: 5.

Feat: 1.

Haste: 1.

This is already enough to hit yourself on a 3/3/8/13/18. Most characters will have some pluses compared to this - barbarians will rage, fighters may have weapon supremacy, rangers may have you as their favored enemy.

If you go for a +1 brilliant energy weapon instead of a +5, you will instead hit on:

2/2/2/2/2.

AC will not keep you safe from harm. If you don't want to get hit by a sword, don't stand next to a person with a sword.

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  • \$\begingroup\$ Note: your max AC is off. Natural Armor does not cap at 5 (templates and alternative races bring it far higher), Deflection does not cap at 5 either (there are ways to get either Con or Cha modifier as Deflection bonus), the baddest armors are either the BattlePlate (+9 AC, +1 Max Dex) or the Mechanus Gear (+10 AC, +0 Max Dex) and there are feats in Races of Stone (Heavy Armor Optimization and the Greater) which add +2 Armor AC to a Heavy Armor. I've seen very efficient builds based on a Deepstone Sentinel/Fist of the Forest for example (Con to AC twice), so you can take the AC sky high. \$\endgroup\$ – Matthieu M. Jun 1 '16 at 6:42
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    \$\begingroup\$ ... (cont) However (1) monsters do not generally have such high AC and (2) for the same level of optimization AR will also sky-rocket. \$\endgroup\$ – Matthieu M. Jun 1 '16 at 6:44
  • \$\begingroup\$ I never said I was calculating max armour, I said I was calculating typical armour. The amount that most characters can get, whilst sacrificing very little in terms of what their character should actually be good at. The 5 deflection and Natural armour are from the magic items. Similarly, the to hit calculation above is 'typical for a level 20 who put no optimisation into their character' it is FAR from the max. I had forgotten about those alternative armours, because I have actually never played a game in which the DM allowed them. \$\endgroup\$ – Scott Jun 1 '16 at 22:42
  • \$\begingroup\$ And to clarify the sentance 'simple characters should have 43 AC max', the use of max was meant to imply 'wizards will have less', not 'no-one can have more'. As I said, this was just for 'simple' characters taking the default gear and not optimising their character around AC, which very few PCs/NPCs do. However, a lot do optimise around to hit (and/or strength) and then take power attack to trade off that to hit into damage. \$\endgroup\$ – Scott Jun 1 '16 at 23:24
  • \$\begingroup\$ Wizards will usually have more, if polymorph spells are on the board. \$\endgroup\$ – Zachiel Jun 2 '16 at 0:39

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