What Advantage Actually Gives You (It's Not +5)
Advantage is worth about +3.3 on average, but it's worth the most when you need to roll an 11.
The common rule of thumb that "advantage equals +5" is wrong. Advantage mathematically gives you between +0.95 (when you need a natural 20) and +5.0 (when you need exactly an 11), with the average falling around +3.3. The important intuition: advantage helps most when the task is moderate difficulty (need to roll 8-14) and helps least when the task is already very easy or very hard. If you need a natural 20, advantage gives you a 9.75% chance instead of 5% — better, but still unlikely.
The practical takeaway: don't spend resources (spell slots, inspiration, class features) to get advantage on rolls where you already succeed on a 5 or lower, or where you still need a 16 or higher. Save advantage for the middle range where it has the biggest impact. And for DMs: a monster with advantage is much deadlier if its attacks are in the "hits on 8-14" range — that's where advantage adds the most effective damage.
What a +1 Actually Means (More Than You Think)
A +1 bonus increases your success chance by exactly 5 percentage points — but the relative value depends on where you start.
A +1 bonus always adds 5% to your absolute success chance on a d20 roll. But the relative value varies dramatically. Going from needing a 20 (5% chance) to needing a 19 (10% chance) doubles your success rate. Going from needing a 10 (55% chance) to needing a 9 (60% chance) is a ~9% relative improvement. Going from needing a 3 (90% chance) to needing a 2 (95% chance) is a ~5.5% improvement. This is why "+1 weapons are boring but mathematically significant" — over a campaign, a +1 weapon will turn ~5% of your misses into hits.
The practical takeaway for character building: stacking multiple small bonuses is more reliable than fishing for big bonuses. A +2 from Archery fighting style, +1 from a magic weapon, and +1d4 from Bless gives you +3.5+1d4 worth of effective bonus, and every point stacks additively. The community's consensus from probability analysis: you want your primary attack bonus high enough that you hit on an 8 or better against typical AC for your level. Above that threshold, invest in damage, not accuracy.
Bounded Accuracy: Why 5e Numbers Stay Small
5e's math keeps AC and attack bonuses in a narrow range so low-CR monsters stay threatening in numbers.
5e's "bounded accuracy" design means AC rarely exceeds 22 and attack bonuses rarely exceed +11 (without magic items). This is deliberate: a CR 1/2 hobgoblin (+3 to hit) can still hit a level 20 character in plate armor (AC 18) on a 15 or higher — a 30% chance. In previous editions, the hobgoblin would need a natural 20. The design goal: low-level threats remain relevant in numbers, and the d20 roll always matters more than the modifier.
What this means for DMs: encounters with many low-CR enemies are more dangerous than one high-CR enemy because bounded accuracy gives them a baseline chance to hit. Twenty goblins with shortbows (each +4 to hit, 1d6+2 damage) will land about 7 shots per round against AC 18, dealing ~38 damage — enough to threaten a mid-level party. The community's advice: don't underestimate horde encounters, and don't overvalue AC increases — going from 18 AC to 20 AC prevents 10% of attacks, not 50%.