Numeric Relations in Games

In this blog post I will be discussing the game ‘Final Fantasy 13’, and discuss the relationships between the numbers in that game.

Let’s start the discussion by looking at the big picture. Final Fantasy 13 is a game with progression mechanics. Players kill monsters in the game world. These monsters drop items that can be sold for gold (or they can try to find gold in treasure chests). Players also gain ‘crystogen points (CP)’, which are similar to experience points in other games. These CP’s allow the player to upgrade their character by spending points to gain benefits such as stronger attacks, more health, new abilities, etc. On top of these resources, the player also gains technical points (TP), which are spent in battles and allows the player to use special spells. The simplest explanation for using TP points is as follows: the more TP points a player has accumulated before going into battle, the more choices they have when it comes to using spells. For example, with a full TP gauge, the player could choose to use 1 very powerful spell that depletes all or nearly all of the points, or they may choose to multiple weaker spells, which deplete less TP.

Final Fantasy 13 was a fun game overall; however, there are parts of the game that I did find frustrating. I’ve only played through the entire game once, which was a few years ago, but there was one main point about the game that had me frustrated that I still remember, which was the grinding that was required. Although the game did not specifically tell you to “go grinding”, you, the player would know you had to grind in order to progress. If you were unfortunate like me, you didn’t make all the best choices when it came to upgrading and suffered the consequences. This happens around 75% - 80% into the game’s storyline, and trying to progress is fairly difficult due to the sudden spike in enemy difficulty. With no other choice, players will be forced to grind in order to get enough CP to level up their characters to a reasonable level so that they stand a chance against the enemies in the next section. Although the area seems “huge”, if you were like me and spent several DAYS grinding enemies, that map eventually becomes small and boring. It is at this point that putting the game down is something that is not hard to do.

Let’s talk about the resources and their numerical relationships. Below, I have drawn a picture of the resources in the game and how they relate to each other.

My definition for resource comes from the book ‘Fundamentals of Game Design’, written by Ernest Adams, founder of the IGDA. This is the definition in the book:

Resources: Entities in the game world that may be created, destroyed, gained, lost, transferred from place to place or from player to player, or converted into other entities. Resources must be measured in numeric quantities. If an entity in a game never changes and cannot be traded, such as a hill in a war game, then the entity is not a resource.

Now that we’ve seen how the resources are related to each other, here are some of their relationships:

Gil and Potion: 50 Gil will buy you 1 potion, which gives 150 HP, a general case of the identity relationship and is linear. (50 to 150 linear relationship)

CP and ‘Level’: The more CP a player has, the more they can level up. Increasing CP-to-level relationship used so that more and more CP is required to gain a level, and also the game is too slow in the beginning for the player to try to camp and only kill weaker enemies.

Cie’th Stone Missions and Rewards: The player only gets the set reward for the first time they complete the mission. Afterwards the rewards continue to go down in value. There is a decreasing value relationship between the two.

Time and HP: These two resources also have a decreasing relationship. The longer a player stands around thinking or doing nothing in a battle, the more opportunities an enemy has to attack the player and decrease their HP. 

Enemies and Drops: The relationship between the two could be described as linear. Rare drops, or items that are worth a lot of Gil if sold, are only dropped by bosses or enemies with huge amounts of HP and take a while to defeat (even then there is only a random chance the player may get a rare item). Lower level or common enemies only drop items that are worth little Gil.

There are definitely more relationships between resources in the game, however, to keep this post from getting too long I think the ones above demonstrate some of the key relationships in this game.

To conclude, my suggestions for improving this game would be to increase the amount of CP received in the mid game. This will allow players to level up a bit more and hopefully they won’t run into the same problem I did: under leveled characters vs. over powered enemies. Another suggestion would be to decrease the health on some of the bosses. The bosses are usually over powered and while I agree that it is important to have some challenges in the game to keep the game fun, I think the designers went a bit far with the numbers for the bosses and should tweak them a bit to improve it. My final suggestion is to change the relationship between the Cie’th Stone missions and rewards. Although the value of the rewards decreases, there is still a level of randomness to the rewards and therefore sometimes the value of a reward may be higher than that of the previous (although it generally goes down). I think it should be a strictly decreasing relationship so that players cannot spam the missions to get more and more Gil or items for easy work.