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According to the rules of familiars the following applies to saving throws

Saving Throws: For each saving throw, use either the familiar's base save bonus (Fortitude +2, Reflex +2, Will +0) or the master's (as calculated from all his classes), whichever is better. The familiar uses its own ability modifiers to saves, and it doesn't share any of the other bonuses that the master might have on saves.

My wizard has Fort 1, Ref 2, Will 3 and my familiar (a Compsognathus) has Fort 4, Ref 0, Will 4. Does that end up with Fort 4, Ref 2, Will 4 for my wizard?

My familiar has Fort +4, Ref +4, Will +0. Does the rule mean that the familiars save bonus changes to Fort 2, Ref 2, Will 0?

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I will assume your wizard is lvl 1 in this answer.

A lvl1 wizard have Fort 0 Ref 0 Will 2 base saves. Let's assume you have CON:12(+1), DEX:14(+2) and WIS:13(+1): it gives you some bonuses to your saves (so you add +1/+2/+3 to your roll saves), but your base saves are still +0/+0/+2.

On the other way the familiar have Fort 2, Ref 2, Will 0 base saves, and +2/+2/+0 bonus because of its statistics. Without the special familiar rule it would make it add +4/+4/+0 to its saves rolls.

Its familiar status makes it able to use the base of the master if it is better than its. In this case the familiar will keep its base in Fort and Ref, and take its master's Will : the total bonus it will add to its save rolls will be +4/+4/+2.

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You must look at the base save bonus for the familiar and for the wizard. For each save which one is better? You take that and then you add the familiar's ability modifiers. So if your wizard (unmodified) base save are Fort 1, Ref 2, Will 3 your familiar take Fort 2, Ref 2, Will 3 and add (fort+2, refl+2) summing Fort 4, Ref 4, Will 3

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