Let's start with Dragon Ball Z. Sure, Goku and pals train in the hyperbolic time chamber when they get the chance, but the real power spikes happen when the chips are down and the big bad villain is seconds away from blowing up the planet if there isn’t anyone strong enough to stop them. In fact, the most iconic power-up moment in the series comes when Goku finally achieves Super Saiyan after Freeza kills Krillin. Even though he’s been beaten within an inch of his life, Goku summons up all of his righteous anger at the death of his friends and channels it into his very first Super Saiyan transformation! The story actually does justify this moment by essentially saying that the power of determination is built into Saiyan biology, but we hardly care about the specifics – it’s time for Freeza to pay for the evil he’s wrought upon the galaxy!

Now who needs strategy and realistic expectations when you can just believe in the Heart of the Cards? Yugi Muto is one of the best Duel Monsters players in the world, but something tells us that it has more to do with the fact that he can manipulate probability as the plot demands it rather than any of his training or deck-building tactics. In the very first episode of Yu-Gi-Oh!, he soundly defeats Kaiba by summoning Exodia —a play that requires randomly drawing five specific cards from a 40-card deck— which would be nigh impossible in the short time that it takes Yugi to accomplish the move. But by trusting in the power of the cards, he did it... somehow.

Do you want more examples? Then let's take a look at another huge anime series. For being a show about musclebound men punching each other with ghostly familiars named after classic rock songs, the powerups in JoJo's Bizarre Adventure tend to be pretty well justified. But, particularly in Golden Wind, characters are able to survive what should be fatal injuries because of their rock solid resolve. The most egregious instance of this happens during the White Album fight, when Mista musters up the power of his resolve to stay standing even after being riddled with so many of his own reflected bullets that he rivals Fugo’s suit in his resemblance to Swiss cheese. Then Giorno steps in to save him, and together the two Gangstars kill White Album’s very loud user and leave the battle no worse for wear.