Dragon Ball, DB Z, DB GT/Are the base Saiyajins above Freeza?
QUESTION: To be honest its real easy to provide evidence for base Saiyajins to be > Freeza.
1. Vegeta was willing to fight #18 and Piccolo at the tournament.
2. Vegeta destroying Pui-Pui easily.
3. The Daiz stated the kids were rivaling #18 in power.
Q1. My first question is how did the saiyajins increase so much in the hyperbolic time chamber?
Q2. Is there any real solid evidence to suggest Freeza > base Saiyajins? Besides BoG? Like within the manga?
ANSWER: 1) Well, Vegeta's statement could be taken as typical Vegeta arrogance. It's well within his character to claim that he's stronger and able to do more than he actually is able to. It would be different if someone other than him confirmed or supported that statement, but given that he's the only one stating it, I have a feeling that it was more one of his usual boasts rather than a valid claim.
2) There's nothing assuming that Pui Pui is strong at all, apart from East Kaioushin's inflated opinion of Babi-di's fighters. Given that Pui Pui acted and believed that 10x gravity was a spectacular feat, his actual abilities are rather lacking. He could be actually fairly low, like in the hundreds of thousands.
3) That Daizenshuu entry is a bit...off, since #18 was only fighting evenly with them prior to learning they were actually anything but strong humans. It wasn't until after they transformed that she realized who they were, so she probably wasn't going all out on them at all. Given that #18 wasn't really giving it her all, then the Daizenshuu's entry is a bit inaccurate. However, it's clear that, as Super Saiya-jin, they were stronger than #18 was.
Q1. As for your questions, as you can see, I personally don't believe the base Saiya-jin to be above Freeza, so as such, I don't think their increases in the Room of Spirit and Time are that high. Given my own estimates, I have Gohan's base strength, upon leaving the Room, at about 70 million, with Goku's being in the upper 60 millions. By the time they get into the Battle of Gods era, I've got Goku at maybe just shy of 90 million or so, having spent most of those seven years in the Afterlife working on obtaining Ssj2 and 3.
Q2. There's nothing really outside of Battle of Gods to really say whether or not base Saiya-jin are weaker than Freeza, but, at the same time, there's nothing really suggesting they're stronger. Vegeta's claim can be explained away, Pui Pui's strength isn't really established to be all that high or anything (outside of Kaioushin's inflated fear), and it's clear that #18 was holding back against the boys while they were in base (not knowing who they were), so there's nothing saying which was stronger or weaker at any point, until the end of the manga entirely.
Once you reach the ten year time jump after Buu's defeat, it's a safe assumption that out of Goku, Goten, Trunks, and Vegeta, that Goku is at least stronger than Freeza in his base, seeing as how he was able to handle Uub fairly well even after riling up his full strength. Given that this strength should by all rights be equal to Pure Buu, that would put Goku's base at the time at roughly Buu levels, which means he'd easily be able to take out Freeza.
---------- FOLLOW-UP ----------
QUESTION: 1) Wasn't Gohan also confident in winning the tournament since he knows Piccolo and Android 18 will be competing?
He never made any kind of comment, at least as far as the manga is concerned, about his capacity to win the Budoukai. Most of his concerns regarding the Budoukai were centered around keeping himself and his family/friends as far under the radar as possible.