Power/Difficulty Curves

This weekend I played a flash fantasy adventure game. Its content runs through nine levels, but it has a Diablo-style level generator that provides random maps with scaled up enemies, presumably endlessly. Many games have a version of that: levels keep rising with pure procedural content. Infinite levels show an issue common to many games: competing scaling of character power and enemy difficulty.

If power scales more quickly than difficulty, the game becomes trivial. If power scales more slowly than difficulty, the game becomes impossible. If power scales exactly the same, the game becomes very boring as you are doing the exact same thing for potentially infinite levels (“I hit for 25% damage yet again!”)

Any scaling system that runs sufficiently long will be dominated by the subsystem that scales the best. A 1% difference in scaling rate becomes very significant. You may not have noticed it in beta testing: 1.01^30=1.35, so a 35% shift over 30 levels. It is +64% at 50, +170% at 100, +345% at 150 +632% at 200. Wow, those numbers really started jumping, didn’t they? Behold, the power of compound interest. And there are games like Asheron’s Call that scale that far. If melee improves slightly faster than archery, melee will dominate the late game; if one weapon type improves slightly faster, it will be the only one worth taking.

D&D players are very familiar with how this happens in only 20 levels. A level 1 Wizard is a sleep spell in a dress, while a level 1 Fighter can take out quite a few goblins. A level 20 Wizard is a nuke-tossing god who alters reality at a whim, while a level 20 Fighter can take out quite a few larger monsters.

: Zubon

4 thoughts on “Power/Difficulty Curves”

  1. The way that most non-procedural games (City of Heroes, WoW) handle this is by having abilities and enemies scale in an almost equal manner, but having the complexity of the game scale greatly as you level. A level 10 mage and a leve 69 mage (the game becomes more complex at 70) are roughly equal in power compared to the enemies they will be fighting, but the high level mage will have dozens of abilities to juggle around during a fight, while the low level mage has only a couple.

    It’s interesting how the two games handle this scaling differently. In CoX, all powers scale in the same way as you level, so while you get new powers, your old powers always remain useful. WoW takes a staggered approach – abilities sit at (nearly) the same power for several levels, then take a big (factor of 2x, often) jump upwards, only to remain unchanged again. This forces the player to adjust his playstyle as different abilities wax and wane in relative power. WoW is the more interesting system, but CoX is easier to balance, and is why CoX is more friendly to be played with high or low level friends.

    EVE is a nice example of a game with an extremely shallow power curve. Skills take forever to train, and give only minimal direct benefits – I once spent over a month training only to get a 5% increase in my drones’ attack power. Since the PVP game is more developed than the PVE, fights are often won and lost with tiny advantages, but this does mean that the PVE game also has a very shallow difficulty curve. This shallow curve does allow players of all ‘levels’ to play together and puts the emphasis on player skill, but removes most sense of advancement. It’s also why I quit the game – once you can fly a battleship, the game is pretty much over unless you’re heavily involved in manufacturing or a strong corporation.

    A good leveling curve (from the standpoint of the players and the developers) is one where the player is constantly looking just over the horizon – “one more level, and THEN I’ll be mighty!” – without the treadmill effect becoming too obvious. Of the games I’ve played, WoW does this best.

  2. Another neat thing from WoW was achieving higher ranked spells every few levels. So, for example, at level 10 you get Nuke1a but you must use Nuke1a until level 14 when you get Nuke1b. Nuke1a’s damage was scaling downwards from level 11-13 because you were fighting targets with increasing HP but by level 14, things got easy again. The cycle would repeat every few levels so you were always in a cycle of increasing and decreasing difficulty.

    This was more noticable in solo play.

  3. One way to make a game with scaling content interesting is to have monsters get stronger faster than the player, but make other resources available that become more available over time. This is what Rogue did: monsters generally get stronger faster than the player, but the items the player finds through the game can just barely enable him to survive long enough to win. Those items are made available linearly: each level has the same item generation odds. On level 1, the player has no magic items, but he doesn’t need them. On level 26, most monsters can vaporize an empty-handed player in two or three turns, but the player has had lots of time to build up his state and resources by that time.

    My point is, it doesn’t have to be magic items. By playing around with the rate at which different advantages improve, the designer can allow the player to find different ways to survive without making the game impossible for him.

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