Three years ago I called 5th edition Dungeons & Dragons the least balanced of all D&D editions. While I am a lot less exasperated by the rules now, I still believe this is true. However at least for my own campaign I now also know how to better balance the system, and that without having to change the rules.

A level 1 fighter and a level 1 wizard are going adventuring together. Who is going to do better? The fighter has a 16 Strength and a greataxe, which gives him a +5 to hit modifier, dealing 1d12+3 points of damage on a hit. The wizard has a burning hands spell, dealing 3d6 damage on multiple opponents, no to hit roll required, but the monsters can roll a saving throw for half damage. He has a sleep spell that affects 5d8 worth of monster hit points. His other level 1 spells are similar in power, So in the first fight the wizard is very likely to make a much stronger appearance than the fighter. While the fighter kills 1 kobold every round, the wizard knocks out several in each of the first two rounds. However the wizard gets only 2 spell slots at level 1, plus a third once per day with arcane recovery.

A marathon runner and a sprinter are racing each other. Who is going to do better? The answer obviously depends on the length of the race. In a short race the sprinter has a clear advantage, but the longer the race is, the more likely the marathon runner is to catch up. The marathon runner in 5E is the fighter, or similar classes, while the sprinter is the wizard, or other classes with lots of burst damage. While fights in 5E are generally short, the rules are designed around an adventuring day of 6 to 8 encounters. That is 20+ combat rounds. Yes, the wizard is going to dominate 3 of them. But for the rest he is going to sit there and cast the fire bolt cantrip for straight 1d10 damage, while the fighter is still doing his 1d12+3 with the same attack bonus. If you plot the cumulative damage the fighter and the wizard deal over the adventuring day, at some point the fighter will catch up or surpass the wizard.

So is the system balanced? Unfortunately that depends now very much on the DM. Because it is the DM who ultimately decides the length of the race, how many rounds of combat each adventuring day has. Most people still think that the wizard is the far stronger class than the fighter. The 6 to 8 encounters per day rule isn't widely applied, and most people have less encounters before a long rest, which favors the wizard sprinter over the fighter marathon runner. And of course there is the psychology of people simply not remembering boring combat rounds in which everybody just did his base attack; the wizard dropping a bunch of monsters with one fell swoop is a lot more memorable and exciting.