Design Tidbits – Numerical Nuance

This is the first of a type of post I’m calling “Design Tidbits.” Rather than focusing entirely on a single game, system, or concept, Design Tidbits will touch briefly on several small elements from a variety of games, all based around a common theme. This post, as the name implies, focuses on how a few games handle their numbers in interesting ways.

The first game we’ll be looking at today is one of the first console role-playing games released on the NES, Dragon Warrior. A massive hit in Japan, Dragon Warrior codified many of the common themes seen in the genre to this day. Many RPGs that followed use static growth rates for each character’s stats (Strength, Agility, Defense, etc.), where an equation runs at every level to determine which stats increase, and by how much. Games which use this method include Final Fantasy, Mother, and Dragon Warrior III, as well as the majority of the Fire Emblem series. This method has the advantage of variety, but can lead to tricky spots if a necessary stat hasn’t increased enough to keep up with new challenges.

The other common method is a carefully defined stat table. In this case, each character’s stats increase by a set amount at each level, so the numbers will always be consistent. Games which utilize this method include Chrono Trigger, Dragon Warrior II, and—though modified by allowing the player to choose—Zelda II. As one may expect, this method is about the inverse of the prior, ensuring consistency but losing variety. Dragon Warrior largely uses this method, but it has an interesting twist to it: some stats are modified based on the name chosen by the player at the beginning of the game. More specifically, two of the hero’s four stats are penalized by a set amount based on the first four letters of their name. Different combinations of letters have different effects, and some result in less significant penalties in the long run, but it adds a personal touch not seen frequently in other games.

  • Loto, the hero's ancestor's name in Japan, is one of the strongest options, and has a definite bonus in both strength and agility (defense) early on.

The next topic of interest lies in one of the series mentioned above: Fire Emblem. Whenever a character attacks, be they friend or foe, the game generates a random number between 0 and 99. This is compared to a calculation based on the stats of the attacker and the defender to determine whether the attack hits or misses, and whether the hit is a critical hit or not.

What you see is what you get in Fire Emblem Gaiden.

In the early games, the calculated number was the exact chance of the attack hitting; the game generated one number, and if the number was lower than that chance, the attack hit.  Newer games in the series, from right before the first localized game until Awakening, made a few changes to the system. Rather than generating one number, each attack generates two numbers and calculates the average of the two. Because of this, numbers above 50 have a higher chance of appearing, and numbers below 50 have a lower chance of appearing. The table below reflects some of the results of this, with calculations made using Wolfram Alpha.

Given 10% 20% 30% 40% 50%
Actual 2.1% 8.2% 18.3% 32.4% 50.5%
Given 60% 70% 80% 90% 100%
Actual 68.4% 82.3% 92.2% 98.1% 100%

The purpose this serves is complex. For a start, this gives the player the impression that the stakes are more dire than they actually are, particularly when it comes to critical hit chance. Critical hits in Fire Emblem deal three times as much damage as a normal attack would, and the looming threat of permanent character death makes even a small chance of an enemy critical hit intimidating. To preserve both engagement and entertainment, players should feel that they are in danger, but should not be forced to suffer a loss. The difference between reported and actual chance is enough to strike that balance, both with critical hit chance and accuracy.

Eirika probably isn’t taking that hit from the enemy soldier, though she’s also unlikely to land a critical hit this time.

Additionally, the balance of stats between player and enemy characters means that enemies are likely to have a low hit chance and players are likely to have a higher hit chance—particularly in Awakening and Sacred Stones, two of the most beginner-friendly games in the series. For those who may be wondering, Fates uses a modified version of the two-number system in which the second number has less weight than the first, and Shadows of Valentia—a remake of the second game in the series—uses the one-number system.

The final game for this post was the focus of the last one: Earthbound. There’s plenty to discuss in Earthbound, but today’s topic is numbers, so we’ll take a look at how Earthbound’s battle system presents player health in a dynamic way. At a glance, the most eye-catching thing about the battles may be the multi-colored, constantly shifting backgrounds.

A cop and his retainers aren’t even close to the strangest foes the game has to offer.

However, there’s another detail worth paying attention to: the health and psychic point displays. Both of them take the appearance of rolling number counters, similar to odometers in the dashboard of cars. It makes for a smooth stylistic effect, but it has a couple of properties that affect gameplay as well.

Whenever a player character takes damage, their health counter ticks down to the resulting value. If the player acts quickly enough, they can heal up before the counter reaches the bottom, allowing the character to survive otherwise mortal damage. This becomes more achievable the more damage they sustained in a single blow, because the speed doesn’t increase enough to match the longer countdown. The countdown also allows the player to survive an enemy’s final attack should they get through the end-of-battle dialogue quickly enough, adding an element of strategy to fights with volatile foes. As a final note, characters also have a chance of surviving mortal damage based on one of their stats, giving players just a bit more of an extra edge.

The absence of the word “mortal” before damage shows that Ness would have survived the hit even if the damage had time to calculate.

That concludes this first Design Tidbits post. There are certainly other games that make make interesting use of their numbers, and still more that quietly work in the player’s favor, but more examples will have to wait until another day. The blog posts are going to start working a little differently from here on out, but there will still be something here every two weeks, so look forward to that.



Dragon Warrior Name Effects:

Fire Emblem Hit Chance Details:

Leave a Reply

Your email address will not be published. Required fields are marked *