Note that this is not based on name brand of teams, otherwise victories over Texas, USC, Tennessee etc teams would be higher, even when those teams were bad. This is based on the most impressive on-field results based on opponent quality

1. 2021 #21 Utah: Only #21 at the time, but Utah finished #12 in the AP Poll and #11 Sagarin, making this the best EOS victory for BYU in the independence era and the only victory over a P5 that finished the season ranked.
2. 2018 #6 Wisconsin: The highest rated (as of gametime) victory, though Wisconsin would go on to have a somewhat disappointing season, finishing 8-5 and unranked in the poll (though Sagarin did have them #25, so they were still a pretty good team)
3. 2022 #9 Baylor: this one was amazing at the time...but suffers a bit in retrospect since Baylor ended up with a losing record (albeit a respectable #27 in end of season Sagarin)
4. 2019 #14 Boise St: One of the only 2 times in Independence (along with #1 on this list) that we beat a team that was both ranked at the time (#14) and at the end of the season (#23) though Sagarin has them down at #32
5. 2019 #24 USC: Finished 8-5 and unranked, but at least they were close (#26 Sagarin).
6. 2021 #19 Arizona St: This is the budget version of the 2022 Baylor victory, not quite as good as it seemed at the time, with Arizona St finishing #36 in end of season Sagarin, but 8-5 at least
7. 2020 #21 Boise St: The lone ranked victory in 2020. Ultimately Boise St did not have an impressive season though, finishing unranked and #41 by Sagarin
8. 2021 Utah St: Not a huge deal at the time...but one of only 4 times (along with #1, #4, and #5) that BYU beat a team that finished the season AP Ranked, with USU ending up #24. Only #55 by Sagarin though and not ranked at the time, so other games rank ahead, but that final AP rank keeps this one from falling too far.
9. 2019 Tennessee: Not ranked at the time, not ranked later, but still a good SEC team and #35 by Sagarin. The lack of the opponent ever being ranked holds this one down some, but it's the best of that group
10. 2020 UCF: Rates as the best EOS victory in a magical 2020 season, with UCF coming in as the #37 team by Sagarin
11. 2023 Texas Tech: TTU comes in as a 6-6 team and #40 by Sagarin. Depending how their bowl games goes they likely move up or down one spot.
12. 2021 Washington St: Could easily be flipped with Tech above. Wazzu finished 7-6, but #45 by Sagarin
13. 2016 Mississippi St: This team was actually pretty mediocre, despite the name. Not as bad as 2021 USC, or 2016 Michigan St though so they still make the list, despite being 6-7 and #47 by Sagarin. Really, these previous few are all interchangeable.
14. 2022 Boise St: Finished an impressive 10-4 and #52 by Sagarin
15. 2016 Toledo: A suprising entry here, but they were #52 in Sagari that season and finished 9-4. An underappreciated solid victory
16. 2013 Houston: 8-5 with a #50 Sagarin rank. Not anything incredible, but gets them onto the list
17. 2014 Virginia: Rinse and repeat. Another P5 opponent with a poor record (5-7) and middling Sagarin rank (#51)
18. 2014 Texas: Finished 6-7 and #53 by Sagarin, right behind UVA (above) and Utah St (who was #52 and beat us that year). Not a good team or as big a victory as the name indicates... 
19. 2023 Arkansas: Finished 4-8 and #54 by Sagarin, so another case of a big name not having a big year, but the best win over a losing team
20. 2020 San Diego St: Only 4-4, but #59 by Sagarin means that they barely miss the cut here, ekeing out 2014 Cal by virtue of not having a losing record

Notable ommissions

• 2021 Virginia: 6-6 and #64 Sagarin. Not terrible, but not quite enough to make the list
• 2018 Arizona: 5-7 and #65 by Sagarin. Not a gimme win... but also not that impressive
• 2021 USC: People will wonder where this game is...but USC finished 4-8, #73 by Sagarin and fired their head coach. This game shouldn't even get HM and is only here because people will ask about it. Note that the 2019 victory is way up there though 
• 2016 Michigan St: Another big name; another terrible team. They finished 3-9 and #84 by Sagarin
• 2023 Cincinnati: Not really a notable ommission, but here to highlight why the Michigan St game is left out. 2023 Cincy was 3-9 and #81 by Sagarin

So let's hear it. What games am I missing? I'm sure there's at least one that should be in there that slipped my mind