It’s important to remember that game design is about crafting an experience for a player. Good designers can elicit emotional reactions from players by tuning specific numbers. The number that a player is shown does not exist in a vacuum. By taking the context of that situation into account, the number conveys specific meaning to the player. Let’s consider a practical example.
Let’s say that you hit an enemy at full health with Attack A and this is what the enemy life bar looks like before and after the hit:
Now compare that with hitting the same enemy at full health with Attack B and seeing this result:
Assuming that all other attributes of these attacks are the same (startup time, recovery time, ammunition, cooldown, etc.), which of these attacks is more effective at defeating these enemies?
If you consider the number of these enemies you defeat over time using only attack A or attack B, both attacks are actually functionally identical. It still takes two attacks to defeat an enemy, no matter if you use A or B. That B deals more damage per hit doesn’t matter - overkill doesn’t count for anything. However, if you think about which of these attacks feels stronger, then clearly B wins because the number is bigger, even if that bigger number doesn’t actually make a difference in the speed at which you defeat enemies. It is the context - that the attack deals more damage - that makes the number feel like it’s stronger and more powerful.
This principle remains true if the amount of damage dealt is 5 or 5,000,000,000. Damage dealt is handled as a percentage of the enemy’s health and the amount of time said enemy takes to defeat, the numbers are really only for the way it makes players feel. It feels like you’ve gotten a lot stronger when you started hitting for 5 damage per hit and now you hit for 50,000. The enemies feel tougher than ones from the start if they can take 50,000 damage without dropping. It’s this noticeable difference when engaging enemies of various levels that set the context for players to feel like they’ve gotten stronger and can take on “harder” challenges.
This has all been a long and roundabout way of saying “designers use bigger numbers to make players feel like they’ve gotten stronger and are taking on tougher challenges”.
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