Stats

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STR or Strength affects the damage that physical attacks deal.

DEF or Defense affects the damage you take from enemy attacks.

SPR or Spirit affects the effectiveness of your Yo-kai's Technique move.

SPD or Speed affects the turn order and the number of turns the Yo-kai get each battle.

Other Stats

HP reaches 0 and the Yo-kai is KO'd.

Soul Meter is full then players can activate the Yo-kai's Soultimate.

Rank ranges from E, D, C, B, A, S. Higher the rank equals more powerful Yo-kai.

EXP or experience points filled up when your defeat Yo-kai and complete quests. When a full bar is filled up, the Yo-kai gains a level.

Hidden Stat Ranks

At the moment they are befriended, evolved, or fused, each Yo-kai has hidden "stat ranks" assigned to it that can never be changed unless you recruit/evolve/fuse a new one. Each stat has its own rank that influences how it will develop while leveling up. For example, a Frostail with a low SPR rank might have ~145 SPR at Lvl 50, while one with a high SPR rank might have ~155 (Attitudes not taken into account). The exact highs and lows are very specific for each Yo-kai. Here are some facts related to hidden stat ranks:

• There is a separate one for each stat.
• The ranks are generally rigid. Unlike Pokemon where the stat increase could be anywhere from 0 to 31 at Lvl 99, there is generally a set group of numbers the stat could end up at, e.g. 175, 188, 200, 212, or 225 (not accounting for Attitude).
• The higher the Yo-kai's natural stat, the more influential the ranks are. If your Yo-kai has very poor STR, low or high ranks won't be very influential, but if it has a very high STR, the ranks will make a big difference. Therefore, the goal of "soft-resetting" a Yo-kai's stats is to have high ranks in the high stats for overall superior stats.
• There appears to be some natural balancing - if a Yo-kai has a very highly-ranked stat, there will be less ranks to go around overall. Unlike Pokemon, there is no "31 in all IVs" equivalent, it's all a give and take.
• The balancing may not be 100% perfect - it is possible to occasionally find a Yo-kai with an overall exceptional allocation, although my tests only took them to Lvl 50, so it's possible it'll balance out by Lvl99.
• Very high or very low ranks are very rare. The game prioritizes more average allocations.

TL;DR If you're a min-maxing soft-resetter, aim for highs of the high stats and lows of the low stats.