Level division

[Balor01]

Lvl 18 wizard has very good chances of defeating lvl 20 wizard. With each level drop, this chance diminishes and at certain level difference, weaker member of the conflict becomes completely irrelevant at all.

I'd ask Playground to help me separate PC lvls into parts within which weaker opponents still have the chance of defeating stronger opponents. Something like this:
1.) lvl 1 - 3
2.) lvl 2 - 4
3.) lvl 3 - 6
4.) lvl 4 - 7
5.) lvl 5 - 8

... meaning that lvl 1 wizard has a chance of defeating lvl 3 wizard, but is pretty surely unable to beat lvl 4 wizard. Lvl 2 wizard has a chance of defeating lvl 4 wizard, but is pretty surely unable to beat lvl 5 wizard etc ...

There are class differences ofc and this is all "make it by the gut feeling" approach, but I'd appreciate it anyway.

tnx

[nedz]

Wizards are Quadratic so 18th level wizard against 20th level is 20x20/18x18 = 23% power increase. You should be able to work out the rest your self.

[Chronos]

Wizards are Quadratic so 18th level wizard against 20th level is 20x20/18x18 = 23% power increase.Somewhere between quadratic and cubic, actually, since you also gain more uses per day of your lower-level spells. And there are indications in the rules that all of the classes were intended to be exponential in power, since doubling the size of an encounter adds a fixed amount (+2, IIRC) to the CR.

[Godskook]

Wizards are Quadratic so 18th level wizard against 20th level is 20x20/18x18 = 23% power increase. You should be able to work out the rest your self.

1.That term is not mathematical in this context. The exact growth rate isn't actually known. The point of the saying* is to explain the dramatically growing difference between casters and non-casters over increasing levels.

2.The difference between a level 17 and 20 wizard is almost non-existent unless prestige classes are brought to bear.

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@OP, the only significant difference between casters are centered around spell levels and prestige classes. Assuming a single-classed wizard, this means the divisions are:

1)1-2
2)3-4
3)5-6
4)7-8
5)9-10
6)11-12
7)13-14
8)15-16
9)17-20

[gkathellar]

2.The difference between a level 17 and 20 wizard is almost non-existent unless prestige classes are brought to bear.

Spells/day don't count for anything? Or the feat at 18th? Or the bonus feat at 20th?

In general, though, this is on the mark. New spell levels are the big divider.

[Godskook]

Spells/day don't count for anything? Or the feat at 18th? Or the bonus feat at 20th?

Not enough of one to really matter. Sure, the lvl 20 probably wins more often than not due to CL, feats, and higher HD(in case of an Enervation war). Specifically, spells/day don't typically count for anything in duels cause you almost never run out of spells; as for the feats, I can't think of any you'd wait till level 18 to get that'd change the game significantly.

[Rubik]

I'd say WBL has a significant impact on things, though overall the latter points still hold.

[Zeta Kai]

WBL & the capacity to boost one's caster level to great degrees make a difference. But overall, yes, the divisions are between the spell levels. It's a good rule of thumb for the casters, & it has a granularity that most likely rings true for the non-casters.

Of course, since Wizards & Sorcerers have different progressions, they would have irreconcilable divisions. It can't be helped.

[Balor01]

@OP, the only significant difference between casters are centered around spell levels and prestige classes. Assuming a single-classed wizard, this means the divisions are:

1)1-2
2)3-4
3)5-6
4)7-8
5)9-10
6)11-12
7)13-14
8)15-16
9)17-20

These levels are MUCH closer then I expected. I am surprised that, say, lvl 5 wiz woudl have such bac chances vs. lvl 8 wiz. or lvl 12 vs lvl 17. Of course, WBL is very relevant here.

[Tyndmyr]

Wizards are Quadratic so 18th level wizard against 20th level is 20x20/18x18 = 23% power increase. You should be able to work out the rest your self.

See...that's not entirely true.

Honestly, the biggest difference between an 18th level wizard and a 20th level wizard is WBL. Take that away, and it's almost an even fight. Init still matters a crapload more than a couple extra spell slots.

That said, optimization differences can matter a great deal. For instance, a first level Wizard with Abrupt Jaunt and Power Word: Pain is pretty much going to kill any opposing wizard with <50 hp unless he's immune to mind affecting.