I know that in other d20 games, precision damage is not multiplied to critical hits, but I can't find the answer for 13th Age. Maybe if it doesn't say it, I have to assume that it gets multiplied. Also, what about ability modifiers, do they get multiplied in a critical hit?
The rules don't appear to explicitly say, which seems to be a mild oversight, or perhaps an assumption by the designers. However, the following excerpt from the example of combat (page 175 - 177 in the core rules) shows damage is calculated first, then the crit is applied. The bold is my emphasis:
Mark thinks about the scene and decides that Korin can probably hold out for a little longer. Yani used her shadow walk ability last turn, so this turn she can appear anywhere nearby that she could have moved to normally and she will deal double damage with an attack that hits.
Mark says, “As if from nowhere, Yani suddenly appears behind the savage that is about to rip Ryisha a new one. And she . . . (rolling a d20 and getting a natural 20, a crit, for a total of 29 with her +8 bonus and +1 escalation die bonus) . . . plunges the blade into the creature’s back.” As the table cheers, Rob replies, “You certainly do.
How much damage?” Mark rolls Yani’s weapon damage (2d8) for 4 and adds +5 for Yani’s Dex mod, for a total of 9. Then, since the savage is engaged with Yani’s ally Ryisha, Yani can add her sneak attack damage in and rolls a d8 for 5, giving her a total of 14 damage. But since Yani scored a crit, she gets to deal double damage, which would make it 28 damage. But even better, Yani’s shadow walk allows her to deal double damage on a hit, so she instead gets to deal triple damage. Mark announces to the table that Yani just hit for 42 damage.
Also as shown in the example, the extra doubling from Shadow Walk raises the damage to triple instead. This part of the rule is clearly stated in the core under the Crit rules on page 167.
The rules for critical hits suggest that for speed of play, it's fine to just multiply the damage by two. The section on Damage observes that as character level increases, it's important that ability modifiers to damage scale to stay relevant. Given those two stances, I think that multiplying precision and ability score modifiers to damage on a crit is fine and would be approved by the designers.