Captain Cadaver said:
Even though he could still estimate Gohan and Kuririn's strength would be enough for them to win.
I wouldn't use the word "estimate" here. I mean, this is the same Vegeta that thought that could win against final form Freezer while having just a fraction of his power.
I think it's more simple really. Vegeta knew Gohan could increase his power a lot, and he also experienced how troublesome Krilin could be. So his reasoning was simple:
"If I can more or less match Freezer then with the help of those two I can actually win".
Captain Cadaver said:
Only when he's either sure of his chances or is uninformed of the opponent's strength, something he clearly wasn't against Freeza until fighting enough to make a judgement on his power. Vegeta is prideful, but not a complete idiot.
Yeah, he seemed oh so confident like always when Freeza transformed, now didn't he?
Vegeta's confidence only arose AFTER his clash with Freezer, in other words, Vegeta only realised he had a chance to win against Freezer after he seeing how he could "match" him.
That's what he always does, except when he knows for sure that his opponent is stronger (like when the Ginyu forces attacked).
But I don't see how this relates to his strength increasing during the nap. His strength increased with the zenkai after Goku gave him the senzu bean.