Bounded Accuracy as described in the Next playtest doesn't really exist in 5e — it requires that there's no expectation for bonuses based on level or magic items. It requires very large damage bonuses per level to happen and the player base freaked out when they started showing big numbers for classes. So they mostly threw it out and used 4e's math and divided all values by 2.
You should, if you're playing the game from level 1-20, expect to find the equivalent of a +3 weapon by 20th level if you play the typical campaign(
I ran the math, I've been called out as being correct on the
official WotC podcast #328 at approximately the 10 minute point, they then put the actual numbers in Xanathar). You should find approximately 5 good magic items that change your power level. You just aren't certain you'll get exactly a +3 weapon. You might get a +2. You might get a belt of giant strength. Or poorly for the game, you might get a +1 weapon only or a +3 weapon
and a belt of giant strength.
So at that point, a level 20 PC likely has an additional +4 from proficiency(+2 to +6), +2 from stat(16 or 17 to 20), and +3 from magic = +9. An equivalent 4e level 20 PC would have an additional +10 from level, +2.5 from stat(likely +2), +4 from magic, and +2 from expertise for a total of +18. Or important skills — +4 from proficiency, +2 from stat = +6. In 4e, +10 from level, +2 from stat = +12. Even proficiency's starting point, +2, is half of Skill Training's +5 from 4e.