Arduino AVR Boards 1.6.20 is bundled with Arduino IDE 1.8.5.
Arduino AVR Boards 1.6.22 is bundled with Arduino IDE 1.8.6.
Arduino AVR Boards 1.6.23 is bundled with Arduino IDE 1.8.6.
But ever since the introduction of Boards Manager, it doesn't make sense to associate Arduino AVR Boards versions with a specific Arduino IDE version. You could have any Arduino AVR Boards version installed with any Arduino IDE version.
I would say it's just as likely that someone using Arduino IDE 1.8.5 would have Arduino AVR Boards 1.6.23 installed, since by default the IDE nags you to update when there is a newer version available.
Arduino AVR Boards 1.6.22 and newer uses an AVR-GCC version that has some serious problems and the solution is to roll back to the last good version. So quite a few people running Arduino IDE 1.8.7 will be using Arduino AVR Boards 1.6.21.
Then there was the issue of the Nano bootloader change in Arduino AVR Boards 1.6.21. Even though the solution was simply to select the correct thing in the Tools > Processor menu, that was too difficult for some people and so instead they chose the (much more difficult) solution of rolling back to Arduino AVR Boards 1.6.20.