Parabolic Power Curve

A design flaw that shows up mainly in RPGs, but also in other games where the main characters' abilities are supposed to improve over time. The Parabolic Power Curve is a situation where, beyond a certain point, increasing your character's power actually makes him less effective. Not Crippling Overspecialization, nor the milder situation where characters simply stop getting more powerful at a certain point. This is a situation where a character that should, on paper, be less powerful actually has an easier time with a given challenge.

Often shows up when a game uses elements of Dynamic Difficulty, such as scaled encounters, but doesn't get the balance right. Occasionally a designer will put this in a game deliberately, as a kind of Anti Grinding, but this is not wise as it tends to infuriate the players - especially if they've gotten so powerful that the game has become Unwinnable. Sometimes this can be defused by advertising it as a feature, but not always.

In games where the level and difficulty caps are changed through updates, the parabolic curve may become a sine curve instead, with one parabola for each interval between caps.

Contrast Elite Tweak. Compare Empty Levels, where it's all downhill from the start. Unrelated to Linear Warriors Quadratic Wizards, which is about a parabola opening upward rather than downward.

Action Game

 * While it isn't completely fatal, larger bombs and faster fuses can make it very difficult to avoid killing yourself in Bomberman.
 * Shmups with speed power-ups. One or two are usually necessary to dodge maneuver properly. Some, however, allow you to stack speed-ups far past the point when your ship handles with any sort of controlability. (The Gradius series is a prime example; though a few games have a method to speed down, they either cost many more power chips than to speed up or are only accessible at maximum speed.)

Gamebooks

 * In the Fighting Fantasy books, players have to determine Skill, Stamina, and Luck scores at the beginning. Normally, the higher these are, the better. In Magehunter, however, due to body-switching, it's an advantage to start with the lowest Skill and Stamina scores possible.
 * In Black Vein Prophecy, you need to fail the first luck check, or you're doomed to wander through the book without a hope of beating it. If you rolled a 6 for your luck (the maximum), it is literally impossible to win.

MMORPGs

 * In the ultimate difficulty of Phantasy Star Online, the temporary invincibility after being hit is taken away unless you get completely knocked over. Thus, it's only possible to survive some attacks until your defense gets high enough.
 * World of Warcraft uses this intentionally. Stats granted by items (in particular, ratings that convert to a percentage increase in effectiveness like armor, critical strike chance, dodge chance, etc.) lose relative power as characters level up, encouraging players to seek better gear. This was actually done to avoid the problem of Power Creep, Power Seep where, given a logical progression of gear at higher levels, players would eventually be running around with 100% crit, haste, dodge, etc., severely breaking game balance.
 * One side-effect of this is that items and enchants converted from the old rating system could be absurdly overpowered in the hands of low-level characters -- thus spawning a whole culture around twinking characters for battleground play. (Ironically, this made it so hard for normally leveling characters to compete in PvP that Blizzard eventually created a new bracket just for twinks.)
 * A variant of this situation occurred with Rage-based tanks (Warriors and Feral Druids), who count on being hit to generate power for their own attacks. With sufficient gear levels, these characters would get hit so seldom that they could not earn enough Rage to generate threat. Again, Blizzard addressed the issue by adding talents and skills that generate Rage (or Mana/RP for Paladins and Death Knights, respectively) when an attack is avoided.

Role Playing Game

 * The Elder Scrolls 4: Oblivion raised quite a furor over this. Due to how the Level Scaling worked, it was reputedly easier to fight the Final Boss at level 1 than at level 20.
 * The problem (or lack thereof) is based almost entirely on the player's class. If you spent your twenty levels being nice to people and stealing their stuff when they aren't looking, the above is true when you get into areas where none of the entities around want to talk to you. If you're a combat-oriented class, you won't have the above problem, because you've spent twenty levels killing things.
 * Also, NPC equipment never scales and they all have the artificial intelligence of a suicidal lemming on crack. Escort missions become difficult at level fifteen, borderline impossible at level twenty, and unwinnable at level twenty-five.
 * It gets worse. Damage, both weapons and magical is capped (stats only go so high), but health is level dependent. So as you level beyond a certain stage, you and your enemies grow more durable, but your damage stays the same, leading to long, drawn out slug fests. Worse still, monster damage does scale with level, forcing the player to rely on a Game Breaker to kill anything at the higher levels, which in turn make things too easy instead.
 * Fallout 3 does it as well. While completing quests gives you better and better perks, to the point that a BB gun in the hands of a level 30 character is better than a minigun in the hands of a level 5, enemy health scales much faster and much farther than the increased damage you can do even with the best perks and weaponry. The major changeover starts to occur around the time Super Mutant Brutes replace most of the normal Super Mutants. After that, enemies with sky-high health become bog-standard. Some people build specialty characters who can still waste them, but this is difficult and takes a lot of knowledge of the game and usually just the right gear and tactics.
 * It gets even worse if you have the Broken Steel DLC installed. Once you pass level 20 some new monsters start showing up (Albino Rad Scorpion, Feral Ghoul Reaver, Super Mutant Overlord, etc...) who are much tougher than anything that came before them, with the sole exception of the Super Mutant Behemoth.
 * Final Fantasy VIII is another famous example. Your characters had levels and increasing them gave you slight bonuses to stats, but the enemies were scaled and got powerful much faster than the player. The player was supposed to use the Junction system - which provides a much better time to earnings ratio - to increase his own power, but obsessive grinders often didn't realise until it was too late.
 * Those who understood the junction system well had little difficulty beating the game at the party's starting level.
 * Geneforge 3 gives the player canisters that can increase his attributes, but using too many makes him suffer violent mood swings. Although this doesn't make the game unwinnable, eventually the player will not be able to take certain quests due to the character flying off the handle and attacking the quest givers. What makes this all the more annoying is the fact that the player was warned of this in the previous two Geneforge games, but due to Gameplay and Story Segregation nothing significant ever came of it. So when the warnings show up here for the third time, the player is likely to disregard them until past the point of no return.
 * Geneforge 2 did have a few encounters that forced the PC into fights if they had used too many canisters.
 * In all 5 games it will affect the ending. It's really hard to do a no-canister game, but it will make some bittersweet or even good endings better. In game 1 it lets you rejoin shaper society.
 * The US and EU releases of RPG The 7th Saga altered level-up stat gains waaay downward, resulting in lots of Forced Level Grinding. It also had boss battles with other characters at the same level as yours - but with the old stat gain formula. If you leveled up too far, their stats would outmatch yours to an unbeatable degree.
 * Final Fantasy VII had a multi-layered version of this: Sephiroth's stats during the final fight are determined by a number of flags activated by the player. The more of these flags activated, the stronger he became. Gaining levels above level 90 were among these flags, as were defeating either or both Ruby and Emerald Weapon, acquiring Knights Of The Round, acquiring each character's best weapon, and a couple other possibilities. Note that the fight is still fairly easy if you've achieved any of the above.
 * Due to a glitch, this can happen to seriously overleveled characters in Phantasy Star IV. Once a character's level gets a few levels away from 100, their stats begin to drop sharply and they lose skills. This isn't an issue in normal play, however; you can beat the game at around level 45-50, and the experience required to get that high of a level is so massive that it takes very deliberate effort to get that high (XP requirements for a single level up when in the 90s range are more than the total XP need to be able to beat the game).
 * The web RPG Dragon Fable recently had to rebalance their entire battle scaling system because fights at high levels were getting so tedious people would get bored trying to get through quests where every one of the 10 or 15 battles took 2 minutes to finish. It's been fixed now, though.

Turn Based Strategy

 * The Fire Emblem games and many of their cousins, some of the units have this problem. You can eventually build some of your characters to the point where they can one-shot most enemies easily, at which point they become nearly impossible to keep alive. What happens is, an enemy will move into position and attack. He'll get blown away on the counterattack, but the character will still take some damage. Once the attacker dies, the space he currently occupied is now free and another enemy will move into it, swing for some damage, die on the counterattack, etc. Repeat six or seven times a turn and many characters, particularly the more glass cannon sorts, can end up dead. It is particularly obnoxious with mages, who can easily kill many melee units (due to their low resistances) but having low defense against physical attacks themselves, can easily put themselves in this situation. Some very powerful units, however, either have so many hit points, such high defenses, or are so likely to dodge that they annihilate groups of enemies single-handedly.
 * Ditto Battle for Wesnoth. Paladins vs. walking corpses and magi vs. almost anything are particularly poignant examples.
 * In the strategy RPG Ogre Battle, your units get universally more powerful with levels, however a crucial element of the game is keeping the populace's faith in you. If you defeat enemy units with higher-level units, that faith goes down because you look like a bully, so other characters help you out less along the way. This was meant to encourage players to level less, but it didn't work because the players instead identified and exploited loopholes in the system.
 * Ogre Battle 64 also had one nasty problem with leveling. Dragons are particularly powerful enemies, and in order to get several powerful magical crests, you've got to defeat two dragons, and a dragon tamer (strengthens dragons) in a random battle in a certain place. If you don't do the battle early enough, the dragons are all extremely strong. Smart players would bring a strong multi-attacker, and two Pumpkin Heads (HP Halving attacks), but those are late game enemies, and only available by recruiting a special character.
 * Final Fantasy Tactics sort of falls under this trope. While Level Grinding would allow you to easily win the normal missions, which all have a preset difficulty, it would actually make random battles far more difficult. This is because the enemies in Random Encounters scaled to match both your level and the equipment you're supposed to have at that level. Players that overleveled would find themselves in the frustrating position of either having to save before around the overworld map and hoping not to get into a random battle, or training their characters in the thief class and stealing stronger gear from the few human enemies they encounter (a very tedious task, and quite difficult, considering how weak thieves are).

Anime & Manga

 * Kinda happens in Dragon Ball Z, surprisingly enough. During their time in the Hyperbolic Time Chamber, Goku and Gohan learn to remain in their Super Saiyan forms either indefinitely, or for days at a time. While this is useful for fighting, as it saves them the time and energy required to transform, it leaves them too strong for normal household stuff. For example, they tend to accidentally crush mugs when they try to have something to drink. After the Cell arc ends, they stop using Super Saiyan as default, though they can still maintain it outside of a fight if they choose. High-school was awkward enough for Gohan as it was; bright gold hair would've only made things worse.