include 2020 because scheduling was all messed up so it's hard to compare that year to the others since most teams didn't play a 12-game season.
During the other 9 years, I assumed a hypothetical playoff format of 6 auto-bids and 6 at-large bids since this was prior to the PAC-12 implosion so their champion would get an auto-bid (the only year they wouldn't have was 2020 which I didn't look at for this analysis).
In these 9 years, there were 19 P5 teams total that did NOT win their conference championship but won 11+ games. Every single one of those teams was ranked high enough to warrant an at-large bid. There were 48 P5 teams that didn't win their conference championship and won 10 games (either 10-2 or 10-3). Of those 48 teams, 27 (56.25%) of them were ranked high enough to warrant an at-large bid.
However, when you break it down by conference things change slightly. 18/26 (69.2%) of 10-win SEC/Big Ten teams were ranked high enough to get an at-large bid, but only 9/22 (40.9%) of ACC/Big 12/PAC-12 teams were ranked high enough to get an at-large bid. So while the majority of 10-win teams would have gotten bids, priority would have generally (but not always) been given to teams in the Big Ten and SEC.
If we remove the 10-3 teams and only look at 10-2 teams, then it's 31 total teams, 21 (67.7%) would have gotten an at-large bid. 15/18 (83.3%) of the SEC/Big Ten teams would have gotten an at-large bid, and 6/13 (46.1%) of ACC/Big 12/PAC-12 teams would have gotten an at-large bid.
This may make it sound like a 10-2 Big 12 team would generally have about a 50% chance of getting an at-large bid, but if you only look at the last 3 seasons, the numbers are a bit more skewed:
From 2021-2023, there have been 17 P5 teams that reached 10 wins and NOT won their conference champion. 8 (47.1%) of them would have been ranked high enough to get an at-large bid. By conference, 8/10 (80%) of SEC/Big Teams teams would have gotten an at-large bid, where as 0/7 (0%) of ACC/Big 12/PAC-12 teams would have gotten at large bids.
If you eliminate 10-3 teams as well, then it's 8/12 teams (66.7%) that would have gotten an at-large bid, but 8/8 (100%) of SEC/Big Ten teams would have gotten an auto bid while 0/4 (0%) of ACC/Big 12/PAC-12 teams would have gotten an auto bid.
TLDR, 11-win P5 teams are virtually guaranteed to get into the playoffs with an at-large bid. 10-win teams (especially 10-2 teams) from the SEC and Big Ten are very likely to get an at-large bid as well. 10-win teams from the ACC and Big 12 aren't nearly as likely to get an at-large bid (I'd guess well below 50% at this point).