How do game developers decide what scale of numbers their system will use, I.E. how large the “base” numbers are? For example, in MTG a 15/15 creature is a world ending menace while in Yu Gi Oh a 300/200 creature, Skull Servant, is noted on the card’s flavor text to be individually weak. What are the advantage of using large numbers versus small ones and vice versa?

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The size of the number affects how things feel to the player. When it comes to system design, what really matters is how many hits it takes to defeat an opponent. However, humans also have feelings associated with big and small numbers relative to the "normal" expected number. The relation of the number to the "norm" is what makes something feel big or small within the game. The base numbers exist primarily for a game to differentiate itself from other games.

Let's take a look at Magic first. The majority of creatures in Magic are somewhere between 0/1 and 5/5, meaning that their (unanswered) presence typically means an opponent will die within some number of turns (usually 5 or more). Their size relative to each other gives players a strong sense of relative strength too - a 1/1 is much weaker than a 4/4 and needs some kind of help in order to survive a fight with one. This makes any card significantly larger than a 4/4 feel much stronger like the 15/15 world ending menace.

YuGiOh started after Magic and immediately needed to differentiate itself from its competitor in order to establish itself as its own game. The entire scale is different - life points are measured in the thousands and monsters have attack points in the thousands as well. Most normal summoned monsters have an attack power of around 2000 at most, and special summoned or tribute summoned monsters tend to top out at 3000-3500. This means that a player can usually withstand maybe two turns of hits from a powerful top-end monster, but can only survive maybe four turns from a single unanswered monster. This generally makes YuGiOh's individual cards larger plays than Magic's - they are larger relative threats than most Magic cards.

If YuGiOh had started with its numbers at 1/100th of where it started (e.g. players start at 80 life, attack power for Blue Eyes White Dragon was 30, etc.), it would have felt a lot more like Magic and likely not have felt as different. But since everything is in the thousands, player brains immediately grasp that they aren't playing the same game anymore - everything is at a completely different scale (even though the overall numbers relative to each other are similar in terms of number of cards played per turn, number of turns per game, etc.). The numbers within the game establish the relative power of the cards to each other. The baseline numbers tend to be there to differentiate the game from competitors and set an overall feeling for the player as to the sense of scale the game is.

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