As Flenyar quoted in his answer:
Each time he gains a new level, he chooses two classes, takes the best
aspects of each and applies them to his characteristic.
This implies that if one class would gain a BAB at it's respective level, you do as well. Note that unlike normal multiclass characters, your stats do depend on what order you take the classes in.
Notice how Flenyar's progression (6 levels of Fighter/Rogue, then 4 levels of Wizard/Rogue) gives a BAB of +9, but the following progression gives you a full BAB of +10, even though the character is still a Fighter 6/Wizard 4//Rogue 10:
- Fighter 1 / Rogue 1 (+1 [Fighters gain +1 every level])
- Fighter 2 / Rogue 2 (+1 [Fighters gain +1 every level])
- Fighter 3 / Rogue 3 (+1 [Fighters gain +1 every level])
- Fighter 4 / Rogue 4 (+1 [Fighters gain +1 every level])
- Fighter 5 / Rogue 5 (+1 [Fighters gain +1 every level])
- Wizard 1 / Rogue 6 (+1 [Rogues gain +1 at 6th level])
- Wizard 2 / Rogue 7 (+1 [Both Wizards and Rogues BAB improves])
- Wizard 3 / Rogue 8 (+1 [Rogues gain +1 at 8th level])
- Fighter 6 / Rogue 9 (+1 [Fighters gain +1 every level])
- Wizard 4 / Rogue 10 (+1 [Both Wizards and Rogues BAB improves])
Total BAB at level 10 is +10.
This means that even a Wizard//Sorcerer gestalt (or any other two low BAB classes) can have a perfect BAB if you take just one level of another perfect BAB class:
- Wizard 1 / Fighter 1 (+1 [Fighters gain +1 every level])
- Wizard 2 / Sorcerer 1 (+1 [Wizards gain +1 at 2nd level])
- Wizard 3 / Sorcerer 2 (+1 [Sorcerer gain +1 at 2nd level])
- Wizard 4 / Sorcerer 3 (+1 [Wizards gain +1 at 4th level])
- Wizard 5 / Sorcerer 4 (+1 [Sorcerer gain +1 at 4th level])
- Wizard 6 / Sorcerer 5 (+1 [Wizards gain +1 at 6th level])
- Wizard 7 / Sorcerer 6 (+1 [Sorcerer gain +1 at 6th level])
- Wizard 8 / Sorcerer 7 (+1 [Wizards gain +1 at 8th level])
- Wizard 9 / Sorcerer 8 (+1 [Sorcerer gain +1 at 8th level])
- Wizard 10 / Sorcerer 9 (+1 [Wizards gain +1 at 10th level])
Total BAB at level 10 for this Wizard 10//Fighter 1/Sorcerer 9 is +10 (perfect.) This cannot be determined without the order of the levels taken.
However...
...the DM may overrule this, based on the wording of this rule:
Base Attack Bonus: Choose the better progression from the two classes. (Emphasis mine.)
It is conceivable, then, that the Wizard 10//Fighter 1/Sorcerer 9 is a character with 1 level of perfect BAB progression (+1) and 9 levels of low BAB progression (+4), leaving him with only a BAB of +5.
I'm not sure of any official errata on the matter, but it makes a big difference in some cases. Ask your DM, or make sure your players know your ruling if you are the DM. Personally, I would stick with the latter "better progression" rule over the "better increase" rule, since it seems to be the intent of gestalt.
There is also the "Fractional Base Bonuses" house rule, presented on Unearthed Arcana p.73, which is designed to allow smooth leveling of gestalt multiclass characters without any of these exploitable loopholes.
Saves
Since you mentioned saves in your comment, I'll touch on it briefly:
Saves would indeed work the same was as BAB, but beware that they are even easier to inflate artificially if you use the first presented "better increase" rule. This is because at first level of every class with good saves, that save "increases" from +0 to +2. Therefore it's even easier to end up with ridiculously high saves through multiclassing gestalt, if you don't simple lump all progression levels together before calculating character stats.
As a side note, consider two classes which gain 1d6 sneak attack every other level. Staggering them as I suggest staggering BAB increases still cannot double your sneak attack damage, since the book explicitly states:
Class features that two classes share accrue at the rate of the faster class.
No, but you can fake it
On the surface, there's no way I know of to do this. That said, you can achieve something similar as a Cleric:
Divine Favor
The spell Divine Power makes your BAB your character level, which is pretty similar:
Calling upon the divine power of your patron, you imbue yourself with
strength and skill in combat. Your base attack bonus becomes equal to
your character level (which may give you additional attacks), you gain
a +6 enhancement bonus to Strength, and you gain 1 temporary hit point
per caster level.
You'll note that it's not permanent. This is where you have to fake it. The Metamagic feat Persistent Spell (Complete Arcane) makes the duration 24 hours. The cost is very steep, but you can use the feat Divine Metamagic (Complete Divine) to pay for it with turn undead attempts. Do that every day, and it's quasi-permanent.
(Arcane casters have the spell Transformation that does something similar, but can't make it permanent so easily because they can't use Divine Metamagic and it costs them spellcasting while it's active.)
Other then that, there's no real way to do it. The best you can do is take Prestige Classes like Abjurant Champion that grant both full BAB and full caster progression. That won't help your levels already taken, but it gets you a higher than normal BAB without giving much up.
Best Answer
It depends on the rules your DM wants to use. The Player’s Handbook is ambiguous, but most tables seem to do the simplest thing and just read the values from the two tables and add them together. Since those values are obtained by rounding down, this method has been known as the “round before adding” method, though a lot of people will just claim it is the default method or the PHB method.
That’s because it is contrasted with a variant proposed by Unearthed Arcana, the “fractional” (or “round after adding”) method. Since this is a variant, this is claimed as evidence that the default is the “round before adding” method. Personally, I agree with you that the Player’s Handbook is ambiguous, and I know a lot of people who have, without ever seeing UA, used “round after adding” just assuming it was what the PHB meant. Either way, this approach handles multiclassing between good (½ level + 2) and poor (⅓ level) save progressions, and medium (¾ level) and poor (½ level) BAB progressions, so your cleric 1/rogue 1 has a BAB of ¾×1 + ¾×1 = 1½ which rounds down to 1, while a cleric 1/wizard 1 would have a BAB of ¾×1 + ½×1 = 1¼ which also rounds down to 1 (but as more levels are gained, falls behind).
Ultimately, I strongly recommend the “fractional”/“round after adding” variant, or as I like to call it, the sane way of doing things. While the round-before approach is simpler, it’s not much simpler, and it produces very wonky numbers that are inappropriate. I typically combine this with a houserule saying that you do not get repeated +2’s for having multiple classes with the same good saves (e.g. a barbarian 1/fighter 2 should not have +5 base Fortitude any more than he should have +0 base Reflex—under my rules, he would have +3 base Fortitude and +1 base Reflex).
This produces the best numbers (as in, most similar to single-classed characters of the same level). It also allows you to simply just add together all your levels of a given progression, and just use that number off the table. For example, a cleric/rogue has the same BAB as a cleric or a rogue would have at the same (combined) level, and a cleric/wizard would have the same base Will as a cleric or wizard would. You do have to do a little bit of math to handle cases of mixed progressions, but it’s a small price to pay for avoiding the weird numbers that you get otherwise, which can cause awkwardness and annoyances in play.
The choice, however, has to be agreed upon by the group, so that everyone (PCs and NPCs) are doing the same thing. A player cannot unilaterally decide which method to use for his or her character without ensuring it matches how the rest of the game is being played.
An example of each. The \$\lfloor\ \rfloor\$ symbols mean “round down” whatever is between them.
\begin{array}{l|r|r} \text{Example} & \text{Round-Before} & \text{Round-After} \\ \hline \text{Cleric 1/Rogue 1 BAB} & \lfloor \frac{3}{4} \left(1\right) \rfloor + \lfloor \frac{3}{4} \left(1\right) \rfloor = & \lfloor \frac{3}{4} \left(1\right) + \frac{3}{4} \left(1\right) \rfloor = \\ & \lfloor 0.75 \rfloor + \lfloor 0.75 \rfloor = & \lfloor 0.75 + 0.75 \rfloor = \\ & 0 + 0 = & \lfloor 1.5 \rfloor = \\ & 0 & 1 \end{array}