There are 6 statistics that enhance the player character. Statistics have a value between 0 and 9. The primary way of increasing stats is collecting Stat Up consumables, like Luck Up, that permanently increase a stat by one, or praying at corresponding Blessing altars. Other ways to increase stats include:
The game doesn't track stats over max. This means that if you have a stat at 9 (max) and then gain and immediately lose a stat, your stat will drop to 8. This can happen if picking up and dropping Loki's Bargain when a stat is maxed.
Other upgradable variables
During a playthrough, the player can also upgrade two other variables - maximum HP and clip size. They are not tracked like official stats, but nonetheless increase incrementally similar to stats.
Maximum HP can be temporarily increased by Midgard Bracelet, and is permanently increased by Heart Container or by using Shield Converter while having armor. Maximum HP starting value depends on the character and maxes out at 400.
Clip size acts as a bonus added to a weapon's normal ammo capacity, and is kept between different weapons. This bonus starts at 0 and has no known upper limit (it can reach at least +46 and likely any number achievable in normal gameplay). Clip size can only be increased by collecting Clip Up items or by using a Tribute altar.