Consider first the fighter. Fighters make an easy target, because they have a simple progression: d10 hp, full BAB, 1 good save, 2 poor saves, 2 skill points/level, and 1 feat/level (+1 at 1st). Thus, a 5th level fighter will have roughly 5 times the bonuses of a 1st level fighter (give or take some constants and rounding errors).
There are some minor quirks. BAB grants an extra attack every 5 levels. And feats aren't neccessarily linear: Spring Attack is a much more powerful feat than Dodge. However, even these only nudge the super-linearity a little.
Now consider a spellcaster, say the wizard. His standard abilities increase linearly like the fighters (d4, 1/2 BAB, 2 skill points, 1 feat/5 levels, etc). But he also gets spellcasting, and that is a whole different story.
For starters, let's just consider direct damage are effects.
A level 1 wizard gets 2 spells/day which deal (say) 1 die of damage each. Using just that same spell, a level 2 wizard gets 3 spells/day which deal 2 dice of damage each. A level 5 wizard gets 9 spells/day which deal 5 dice of damage each. A level 10 wizard gets 21 spells/day which deal 10 dice of damage each.
Under this simple model (which includes a +1 "bonus spell" at each level), at level 1 the wizard can deal 2 dice of damage per day, at level 2 they can deal 6 dice of damage per day, at level 5 they can deal 45 dice of damage per day, and at level 10 they can deal 210 dice of damage per day. Tabulating for all levels 1..10:
In basis, if the DM rules consistant reaction of the NPCs in the game world to the PCs actions, keeps the power spiral in line (by not skipping those low levels for instance) and aims for a heroic fantasy genre style, the Fighter keeps a certain parity he otherwise might not maintain based on societal issues and "role play". Yes, out in the wilds the groups 9th level Wizard (or Cleric, or other primary spell caster) is at a decided advantage, all else being equal, in combat situations, but in situations where societal interaction is needed, if the DM uses the heroic fantasy model, the footing swings almost as drasticly away from the Wizard (or even Cleric), even in societies where magic is "accepted" as "not necessarily evil", a rarity in heroic fantasy.
The problem comes in more in "video game role playing" styles, where the same is true in the video games too...magic is simply too much of a trump card. Take the old Morrowind vgRPG. You CAN run through the whole thing, even with ramped up difficulty factors from mods and from the game settings, with a straight Warrior of any (basic atleast) race. You'd better have plenty of scrolls and magic items though, after the mid point in the main sceanrio against Dagoth Ur atleast, turning the Warrior into a sort of weak pseudo mage. At the same time the straight vanilla Mage (especially a Breton Mage) will waltz blithely through the same situations with nary a problem if you use your spells intelligently, even with a derth of scrolls and magic items. The only differences are the thought required for one type copared to the bulling ahead the warrior allows for.
It is much the same with vgRPG style game play in the present incarnation of D&D. Magic (or Psionics) simply provides too much of a trump card for the non-magic utilizer to ever over come without skewing the way the system works because of the linear way in which the Fighter and non-magic classes progress in comparison to the unlimited trump card of magic and the cumulative effect it has on power.
Isshia
What to do? One could make fighter types equally quadratic, but that creates a powerful disincentive for multiclassing and increases the need for "hybrid" PrCs (which I consider to be clear symptoms that the multiclass system has major problems).
I think the real issue with multi-classing is the checks and balances to prevent a single class "multi-classing" or essentially stepping over additional roles.
Take a rogue for example. Rogues are supposed to be lightly armored skill monkeys. That's fine. And if you want, you can pick up Medium Armor proficiency, and have them running around in breastplates. But there's another check that provides incentive against doing that. Armor Check Penalty. A number of Rogue skills (at least 2 of the most important ones) get hurt by that. On top of that, movement penalty as well. Thirdly, max dex, something that does happen to be a concern for rogues.
So, he has multiple reasons to NOT wear heavier armors, on top of having a d6 hit die, and some other effects. As a general rule, the rogue isn't going to take over for the tank job anytime soon.
Now, in terms of JUST being a rogue, that's fine. But multi-class to a fighter level. Fighters generally rely upon heavier armors, something that arguably hurts rogues. Additionally, class skill lists and limited skill points hurt your rogue abilities further (or at least keep them from advancing).
That's the short version of it. I think the real problem with multi-classing is that the constraints within a class to stay in its intended role makes the blend between different classes harder to do.
The opposite of that, for the most part, is the cleric however so...
Mathematically, you are correct: The Wizard should exceed the fighter at higher levels. The thing you are forgetting though, is that this is D&D. The emphasis is more on roleplaying, and the spell lists and feats make the fighter and the wizard equally fun to play. A Gust of Wind, while still a low level spell, could contribute signifigantly to the encounter, and the Improved SUnder feat, while attainable by a low-level fighter, could greatly affect his fighting style.
A Wizard's Cone of Cold may take out a swarm of opponents, but a Great Cleave could do almost the same.
Another aspect you falied to address was the fact that Fighters were designed to be less complex, wereas with a Wizard, it was unavoidable. Some people just don't want to be Wizards, but are happy swinging their Greatsword at a Goblin or a Balor, regardless of the level.
Altogether, D&D players need to accept the classes as what they are, vital to another important aspect, teamwork. Without the fighter, the Wizard would be dead, at 1st level or 20th, and Vice Versa.
Sorry if that seemed harsh. Otherwise, it was an excellent article.
A +1 to-hit bonus is more valuable at lvl20 than at lvl1, it has a much larger effect on your damage per round. When your average hit is 50 or so, and you get 4 of them +1to-hit is worth 10 damage per round(Actual numbers have no relevance outside the example.) while the level 1 fighter hitting an average hit of 11 nets a paltry .55 damage per round. So you can see that there that linearly stacking % modifiers has a higher effect as the base numbers go up and the base numbers do.(A +1 to-hit is really 5%, remember that.)
Because of the built in obsolescence of magic, the fact you get more and better spells will not have as huge an effect as you assume on game balance. A fighters feats never become obsolete, they just build on top of each other and get better via stacking and altering the base.
I'm not denying the problem, I'm stating your assumption that fighters grow linearly is a false premise there actual combat effectiveness grows exponentially as well.
Being more direct, I think the manoeuvre system is designed to do the opposite of what you suggested, and make the fighter non-linear too. Seems to make sense to me, as the player should double in power every 2 levels. Why? Because someone with class levels has an encounter level equal to that, and a party of 4 should be able to fight 4 encounters of their level, or 2 encounters at +2 of their encounter level. This must surely mean that each level 7 threat should be worth 2 level 5 threats. Whether this is the case in practice is debatable, but it leans towards an even more extreme power progression: exponential! To be exact power=base*2^((level-1)/2), however on earth you manage to quantify "power".
Whew, I have been doing way to much essay writing!
But then there's also the question though of whether this idea carries forward: Is one level 7 fighter worth 8 level 1 enemies? Most likely, but is a level 15 worth 128? I think it would start to play quite oddly, although I think a lv 11 wiz could probably take 32 1st level wizards quite easily, very easily if they stood within a cloudkill radius.
Anyway I get the feeling we're retreading old ground here, so I'll leave it there for a bit.
The in-game effect of this is that wizards are very weak in the early levels and very powerful in the later levels. In the early game (which might run for months real time), the wizard doesn't feel like he can contribute much.
I disagree, wizards are very powerful at low levels; just look at spells like sleep and colour spray. The only thing they don't have going for them at low levels is endurance. After a few spells, all of their resources are gone, whereas a fighter can go on and on.
You ought to take this a step further and apply some probability theory to consider the expected damage values of the wizard vs. the fighter, which will change depending on the defense of the target (mostly spell resistance, saves, armor class). Depending on the defenses of the target, sometimes a fighter will be more effective, even at higher levels (I've seen a fighter with Great Cleave effectively kill a ten-headed hydra in one round).
I think you're discounting the effect of the extra attacks from BAB that a fighter gets. A level 20 fighter will have well more than double the expected damage value of a level 10 fighter because even his second and third attacks are overwhelmingly likely to hit. Fighters also have equipment advantages that aren't being taken into account, and when selected carefully his feats can make him very dangerous (consider again the fighter vs. the hydra).
Lastly, even though the wizard probably does in the end deal more damage than the fighter, he benefits from having a meat shield. While this does relegate the fighter to what might feel like second banana, his hit points and AC help the entire party and should have considerably more weight than anyone else's in any mathematical analysis.
(Note: I haven't commented on the psionics because I don't typically play with them and admittedly don't know very much about them.)
Good article, if a bit of an old argument, you present it in a new way from what I've seen.
Another thing is that the fighter's main purpose at higher levels is not to cause damage, but to absorb damage so that the caster does not get mauled, beign of great offensive power but brittle as glass with his d4 hit die.
However, the mathmatical explanations put aside I think you have forgotten one very important item: Magi alter reality.
Magic, psionics, whatever you call it... its about translating thought and intent into physical reality. This will always be a greater power than marshaled combat skills. It is by conception superior. Its no wonder that the math reflects that.
To change the math you must change the premise of the game. Limits must be put in place, and gamers loathe limits dear friend. DnD is so vastly popular because of its lack of limits.
In a world of computer gaming and simulation, DnD survives because it is _less_ restrictive.
The solution is not more restrictions, but more powerups.
I vote for the warrior quadratic scaling solution rather than limiting the powers of magic or psionics.
Ignoring cantrips, bonus spells and specialisation, the Wiz 20 gets 36 spells (4 each level) at caster level 20 with a max spell level of 9. The Wiz10/Clr10 gets 37 spells (9/9/7/7/5) at caster level 10 with a max spell level of 5. The only benefit that the split classing brings is a slightly larger spell selection; the actual number of spells / day is identical, but those spells are at half spell level and half caster level. Again, the linear vs exponential effect comes into play.
In contrast, if I hybrid a fighter and a rogue, or even a fighter and a ranger or barbarian, I actually get an "average". I miss out on some of the high level abilities, but otherwise it's fairly workable. In the fighter/rogue example, the character has a weaker sneak attack than a full rogue and fewer feats and hp than a full fighter, but his attacks are more accurate than a straight rogue, he has more special moves (feats), and he is more survivable. In contrast, an even multiclass of two casters leaves the character in a rather barren valley gazing up at the two peaks.
Admittedly, the "hybrid" caster PrCs do alleviate this problem somewhat, but the very existence of this inelegant workaround testifies to the scale of the problem.
(Yes, I still haven't proposed a solution. That will need to wait for more thought and a discussion of the effect of resource use models on D&D design.)
I am currently playing two characters in a long running RPG. One is a human fighter of 7th level, specialized in bastard sword and wielding it two-handed, with a strength of 20. The other is a halfling wizard of 8th level with a plethora of scrolls and a very nasty temper. This is a ROLE-playing game, not a war-game or ROLL-playing game where math makes up the sum of your character.
My fighter does an average of around 18 or 20 points a swing, with two attacks per round. He has a scarab of enraging enemies, and his weapon does double damage against true giants. He's got 90 hit points, and he's not afraid to use them. He's also insane. He believes his name is Colliseur LePetimagne, and that he is the Arch-mage of Lanseur, who's spellbook has been stolen by the evil Baron Von-Shtupp. He is most certainly nothing of the sort, but YOU try telling him that and walking away with your head on your shoulders.
My wizard loves her fireball spell. She's also quite fond of stoneskin, ice storm, mage armor, and burning hands (even though it's a lowly first level spell). In battle, her first move is either a protective spell like blur or stoneskin, or a fireball. She has 46 hit points and gets rather vicious when cornered. A band of brigands chased her up a tree at one point in the game and set it on fire to force her out. After that traumatic experience, what was once a cheerful and helpful hobbit called 'Toot', became a revenge-driven and calculating creature with a desire to inflict her personal pain on anyone crazy enough to get in the party's way.
And if she knew my fighter was coming and got first initiative, Tuterina could kill Colliseur easily. But if it were the other way around, it would be her head rolling away.
Fighters are not a weak class. The decisions you make regarding stats, weapons, feats and magic items you acquire can make or break your fighter. If you choose wisely, a fighter can stand up to any class in the PHB or supplimental books and hold his own. Playing a wizard makes playing a fighter no less interesting, either. My fighter contributes just as much to the party as my wizard does, and both have saved the other over and over.
In my opinion, neither class needs changing. Both are balanced enough for a clever ROLE-player to stay interested and stay useful as they advance in level. A good DM also helps to ensure that all of his or her players are enjoying the game and feeling like they can contribute.
Perhaps people should spend less time worrying about whether the math adds up and just play the game.
You have a bit of an error, you say that fighters have 1 feat/level, when they actually only have 2/level.
Quite correct. Unfortunately, I can't edit the original source post.
Just a nitpick, not directed any anybody in particular: Note that quadratic and exponential are two very different things.
The terminology was chosen carefully in the original post, though I messed up in my follow-up.
Good article, if a bit of an old argument, you present it in a new way from what I've seen.
More pertinently, I'm not actually trying to argue that "fighters are more powerful than wizards" or "fighters are weaker than wizards". Rather, I'm looking at the underlying mechanics to focus on the root problem. Namely, that comparing a linear advancement to an exponential advancement must inevitably lead to inequities.
It also inevitably makes a mess of multiclassing, since 2 * K * X will only approximate 2 * J * (X/2)^2 for a very limited range of X.
You say: "The in-game effect of this is that wizards are very weak in the early levels and very powerful in the later levels."
I am currently playing two characters in a long running RPG. One is a human fighter of 7th level, specialized in bastard sword and wielding it two-handed, with a strength of 20. The other is a halfling wizard of 8th level with a plethora of scrolls and a very nasty temper.
I don't consider 7-8 to be "later levels". If I was wanting to actually compare wiz vs fighter (which I'm not), I'd say that 5th - 10th was the range where they can make approximately comparable contributions. You're smack in the middle of that range.
This is a ROLE-playing game, not a war-game or ROLL-playing game where math makes up the sum of your character.
Ultimately, this is a restatement of the so-called "Oberoni fallacy". That you can modify your application of something so that the brokenness is controlled doesn't make it not-broken.
Sure, if your play-style is such that mechanical utility isn't an issue, then differences in mechanical utility isn't an issue. However, if mechanical utility is part of your enjoyment of the game (and for D&D, mechanical utility is an important game feature, whether or not your group highlights it) then an underlying advancement mechanic that must inevitably create a wide disparity over time is not a "good" feature.
Another thing is that the fighter's main purpose at higher levels is not to cause damage, but to absorb damage so that the caster does not get mauled, beign of great offensive power but brittle as glass with his d4 hit die.
And this gets to the heart of my dissatisfaction. As a stereotype: At extremely low levels, the fighters "fight" while the casters occasionally contribute. At high levels, the casters "fight" while the fighters act as bodyguards. If I wanted to spend my adventuring career being the backup, I'd play a bard (and on occasion do).
If you stay in focused classes, the problem can be hidden because you're operating in different domains. However, when you try to play a hybrid it rapidly becomes clear. Discussion of the Psychic Warrior is not accidental.
The psychic warrior is (IMO) fairly balanced compared to the fighter, and its magic capabilities are way below the psions. This wasn't a problem, until I noticed that if I tried to pick up a few psion levels I was playing with quadratic magic point totals; grabbing a few levels of a pure caster class could actually leave me with fewer magic abilities than a pure hybrid. The next logical step was "psion is as to wizard as psychic warrior is to cleric", whereupon you notice that the cleric is very close to the psychic warrior in combat but is a full caster rather than a half caster. This led me to thinking about why it's so hard to make fighters and magicians comparable at higher levels, and thus to the quadratic vs linear issue.
However, the mathmatical explanations put aside I think you have forgotten one very important item: Magi alter reality. ... It is by conception superior. Its no wonder that the math reflects that.
Again, that's fine for a wargame, but it's mechanically broken for a one-character-per-player advancement-driven skirmish game. It can be fun to voluntarily play the supporting cast, but the game mechanics shouldn't inshrine endemic imbalance between supposed "lead roles".
I vote for the warrior quadratic scaling solution rather than limiting the powers of magic or psionics.
Except that this breaks multiclassing for all classes, not just spellcasters (as per currently).
Getting more into the content
I think you're discounting the effect of the extra attacks from BAB that a fighter gets. A level 20 fighter will have well more than double the expected damage value of a level 10 fighter because even his second and third attacks are overwhelmingly likely to hit. Fighters also have equipment advantages that aren't being taken into account, and when selected carefully his feats can make him very dangerous (consider again the fighter vs. the hydra).
Defining a "linear" increase can be tricky in this context. For example, did you realise that simply doubling the number of units on a side actually results in a x4 better result. Dealing 2x the damage doubles his attrition rate, which halves his ability to attrition you, which means that as the battle progresses your attrition rate slows while his increases (relative to the reference battle), and thus you end up taking far fewer casualties.
Calculating the exact scaling factor for a D&D Fighter is tricky. HP is roughly linear on HD (with a boost at level 1). Damage per hit gradually increases, due to Str increases, magic, and feats. Similarly, number of hits also slowly increases, with jumps each 5 levels.
In that sense, one could argue that a fighter's full attack remains approximately balanced with a wizards single attack. At least if that single attack is a hit-point dealing single-target damage spell. But I put it to you that fighter mean full attack damage is less than 1:1 with fighter level, while wizard damage single attack damage is 1:1 if we don't consider the scaling effect of spell level.
But that's still linear scaling. They key balance problem is that the cost of those wizard attacks drops with level even as their power increases. This next post both gets and misses the key point: resource usage
I disagree, wizards are very powerful at low levels; just look at spells like sleep and colour spray. The only thing they don't have going for them at low levels is endurance. After a few spells, all of their resources are gone, whereas a fighter can go on and on.
At level 1, a wizard has 2 shots (more if he takes daze
). Each shot can contribute, neither is likely to win the battle outright, but he only gets two of them.At level 20, that same wizard has a decent chance of winning the battle outright. He may need 3-4 spells to do it, but at this level he has spells to burn (over 40 per day without magic). He goes from having a scarce resource of limited effectiveness to having an abundant resource of potent effectiveness.
And this is the issue. The fighter at any level has an unlimited resource (except hp, but they are easy to replace between fights) of ~ linearly increasing effectiveness (not exactly, but on average). The wizard starts out starved of both power and usages, and ends up with excellent power (or more) and almost no usage limit, with a non-linear increase. It's mathematically impossible to align those two progressions on the same graph.
It seems to me that the correct solution is to make spellcaster power more linear. In practice, this probably means stronger at low levels and weaker at higher levels, but I'm not so concerned about the exact balance as the underlying mathematical model. Heck, you might put up a convincing argument that a Ftr20 and a Wiz20 are of comparable utility, but it must follow from that that a Wiz1 is massively weak compared to a Ftr1, because the Wizard is growing quadratically while the fighter grows near linearly. Similarly, I'm not so concerned about whether a Clr20 is more powerful than a Wiz20, since they are both growing on approximately the same quadratic curve. Rather, I'm concerned that a Wiz10/Clr10 can never even approximate the effectiveness of either pure character, due to the quadratic nature of their growth curves.
Note again that I'm not performing a competitive analysis - "Ftr10 vs Wiz10, who would win?" doesn't really prove anything. Rather, I am concerned that the utility of many classes at low levels doesn't relate well to their utility at higher levels; it's hard to build a PC that will remain equally able to contribute to the party's success throughout his or her career.
It's a game, and despite the poster's thesis that wizards are "more powerful", many people still absolutely love and enjoy portraying the fighter character, and have for over 30 years now.
Analyzing the rules using mathematics gives one an understanding of the rules, but not the associated roles.
I most appreciated the response that said, "It varies by campaign."
Real world, U.S. Marines might be considered "More powerful" than say, U.S. Coast Guard. So what. Both are necessary, as are restaurant workers, stockbrokers, nurses, and television news reporters.
Some, given the varied choices out there, choose to do no work, and rely on the kindness of others.
Some are forced into homelessness, and when offered the choice to join the military, balk. (Even though it would give them work, and money = power).
So, Nom is saying Wizards are more powerful, over time.
Yeah, all right, and that means... what, exactly, in a roleplaying game?
Note that quadratic and exponential are two very different things.
True.
If one assumes that the wizard starts out weaker than the fighter, and that the wizard's power growth is faster than the fighter's (whether exponential vs. linear, or quadratic vs. linear), then it is easy to prove that at some point the wizard must overtake the fighter.
Given this, the design issue is: Choose the difference in power between the fighter and the wizard at level 1, then choose a level (say X) at which they are roughly equal. From this, the wizard will be weaker than the fighter until level X, after which he is stronger. The difference between quadratic growth and exponential growth for the wizard will be in how far apart these two classes will be at very low and very high levels. If the two start off at roughly equal power, then the slower the non-linear growth (quadratic < cubic < ... < exponential) of the wizard's power, the more "balanced" things will be.
It's almost impossible to completely quantify things, but to me it "feels like" the wizard's power growth is exponential, since at mid-to-high levels the wizard has so many different things it can do, while the fighter has relatively fewer things it can do. Not that the fighter doesn't do what it does do well, it's just that the wizard can do more. And magic is the reason -- you can pretty much do anything with magic. So, it seems appropriate that the wizard's power is modeled by exponential growth.
Even if we could prove that the fighter's power grows linearly and that the wizard's grows exponentially, it really shouldn't make much difference since the typical party is a team. Challenges that require magic should demand exponential (or whatever) resources from the magic-users, while more mundane challenges should require linear resources from the non-magic-users. This is the challenge for the DM, and if done properly everyone has fun.
Some will say that magic-users can do both jobs, to which one might reasonably reply: So what? A well-designed adventure should have something for everyone and make it difficult for one character to do everything (e.g. the magic-users use up all of their resources before the adventure is over), not to mention that in this case the magic-users aren't being very good teammates.
Fighters are not a weak class. The decisions you make regarding stats, weapons, feats and magic items you acquire can make or break your fighter. If you choose wisely, a fighter can stand up to any class in the PHB or supplimental books and hold his own.
I was with you until you made the "supplemental books" comment. I have ever stood in shock and awe at the fact that truly, the players handbook's classes are truly balanced. I don't feel the same way about all those supplemental books. I've stood in with my mouth gaping for minutes at some of these classes, where the author never once appeared to give a nod to balance.
Of course, I have always played with power-gamers, so maybe a few loop-holes have skewed my judgment. (lousy awaken spell, don't even get me started on Eldritch Blast
Of course, everything that's put here is discussed elsewhere and someone posted this, and I'm putting it here to hopefully prove the person I'm quoting false:
That discussion fills me with despair. The basic conclusion that Wizards > Fighters is well established, but the reasoning presented is completely irrelevant.
Having more spell slots per day with burning hands in them doesn't make you more powerful, and thus that entire line of comparison is irrelevent. But on the other hand, the people who are attacking his analysis are pulling dumb crap like saying "Altogether, D&D players need to accept the classes as what they are, vital to another important aspect, teamwork. Without the fighter, the Wizard would be dead, at 1st level or 20th, and Vice Versa." - which is just mouth diarrhea.
There's relative power (how effective your character is against the enemies you are facing), and there's irrelevant power (how good your character is against enemies you aren't fighting any more or are not fighting yet). And while the specifics of what is and is not irrelevant will vary game to game, I can pretty much discount a magic missile as ever having relevance to anything.
Things aren't very linear in D&D. They aren't quadratic either. The math is actually really complicated. At first level, a Wizard can expect to blow away perhaps two or three enemies in a single spell (sleep or color spray) and a Fighter may be able to take an entire hit from an enemy without dropping. Either one of them can grab their weapon of choice and bonk a kobold over the head and drop it. The Fighter's only interesting class abilities are "six extra hit points" (which allows him to take about one hit from a crossbow without falling down), his BAB is really small cheese that you might not even notice against the Wizard's +0 BAB.
What you do notice at first level is attributes. The Fighter's Strength looms large in this equation. His +3 damage may not sound all that big against the d8 of his Longsword but since that's +3 minimum damage it's actually really important - most enemies only have 4 HP. The fact that the Fighter put a 16 into Strength makes his sword into a death effect at first level. It's not the area of effect death effect of a color spray, but it's pretty damned impressive. But that's not a quality of the Fighter class. Nothing is stopping you from playing a Cleric with a Strength of 16, and indeed if you do that you're pretty much indistinguishable from the Fighter. Your Morningstar is good enough for goblin hunting and your hit points are plenty to survive a blow from a sharpened stick (and still not enough to stay concious after 2, but that's nothing new).
As levels go up you get more bonuses, but you also get more kinds of bonuses. Going from 5th level to 6th level doesn't just see you get a +1 BAB. It sees you get a better magic sword. And you pick up some gauntlets of Ogre Power that increase your Strength bonus by 1. That one level gives you like a +3 shift in attack and a +2 shift in damage, and you might even get an iterative attack (which will occassionally come up even though they suck).
And yet, while those bonuses are impressive, and impressively non-linear - they aren't near enough because even though you are stacking all these bonuses together your opponents are getting HP faster than that. An Orcish Warrior has like 5 HP, and a Hill Giant has over a hundred. I don't care how you look at the linearity of the Fighter's attacks, the fact is that against the higher level opposition the Fighter's Magic Sword simply lacks the impact of the 1st level character's dull length of steel.
And Mages experience the same thing - for a while. At 1st level, or even 2nd level, sleep makes you win against an entire group of enemies. But at 6th level your spells like web and stinking cloud are simply very useful. They tilt the battle in your team's favor, but they don't make you straight-up win outright. You don't get to cast your spell on a group of enemies and straight up hear the XP-dance song play again until like 13th level. But at 13th level they do get that mojo back. Fighters don't get back to clearing away level appropriate enemies ever.
So yeah, it's really complicated. Really complicated. And the first level comparison (Wizard can kill two enemies, Fighter can take two hits) is completely different from the 5th level comparison (Wizard can control the battlefield to make his team win, Fighter can DPS and soak about as well as an animal companion). And it's really saddeningly different from the 15th level comparison (Wizard controls time, space, and infinity and can destroy all enemies by glaring at them, and the Fighter can fight as well as a contingent summoning).
So seeing people come out with simplistic mathematical analyses that then get argued against on the grounds that they are poopy heads is just saddening. It's a multi-layered construct of opening and closing options with an arms race of attacks and defenses running sidelong an arms race of raw numerics that are all continuously growing at different rates as one progresses trhough levels. The flaw with the Fighter is that he never really gets any new options, so the parts of the game where his numerics happen to be on top make him boring and the parts where his numerics don't make him useless.
The Wizard continuously gets new options that have a reasonably effective tactical role at every level. If you go through the spells that kill people list you'll note that there really are levels in which you are very dominant over your enemies (1st and 17th, for example), and there are levels where you are merely pretty good (5th and 8th).
There aren't any tactics in D&D that don't eventually go sour as enemies continue to get more weird defenses. People who don't get new attacks are structurally incapable of mattering.
- "..."
The problem with the above was a post that followed:
"...", the thing is, if you went and posted what you just did on the WotC boards they would flat out tell you "no." It doesn't matter that you're right, it only matters that your opponents have enough rhetoric, red herrings, and outright lies that your argument isn't even valid there anymore.
A +1 to-hit bonus is more valuable at lvl20 than at lvl1, it has a much larger effect on your damage per round. When your average hit is 50 or so, and you get 4 of them +1to-hit is worth 10 damage per round(Actual numbers have no relevance outside the example.) while the level 1 fighter hitting an average hit of 11 nets a paltry .55 damage per round. So you can see that there that linearly stacking % modifiers has a higher effect as the base numbers go up and the base numbers do.(A +1 to-hit is really 5%, remember that.)
Your parenthetical (and thus the rest of your paragraph) is not precisely true; this is a common error made on these boards that amounts to what you mean when you say that something increases by X%: plus X% or times (100+X)%.
If your attack bonus already equals (or exceeds) your opponent's AC minus two (because a natural one never hits), then increases in to-hit will not increase your expected damage.
Conversely, if your attack bonus is your opponent's AC minus 20, then +1 to attack bonus actually doubles your chance to hit (from .05 to .10) and (the expected value of) your damage.
A +1 to-hit adds .05 (5%) to the probability of hitting (maximum of .95 = 95%), but never actually multiplies your probability of hitting (and thus the expected value of your damage) by 1.05 (105%, an increase of 5%)—it will always be greater than 1.05 (with increasingly greater effects as the difference between attack bonus and AC increases) unless you are already at .95 probability to hit.
The consequence of all this is that the +1 to attack bonus probably doesn't benefit the level 20 fighter's first and second attacks, but it does help his third and fourth. Even in a full round, it will rarely add up to a multiplier of 1.05 to (the expected value of) damage.
(1) the fighter does not only has a base attack bonus. much of his damage depends on his weapon and other items:
- base attack bonus : linear
- (magic) weapon and items (gauntlet of strength, ...): ALSO linear.
so the total damage done by a fighter would also be quadratic.
(2) you compare one hit of the fighter, with the total firepower of a wizard?
You compare the total number of spells from a wizard. this is quite strange since a wizard can only cast 1 spell per round (2 if he quickens - lets disregard that, since the fighter gains multiple attacks)
(3) (perhaps its me, but ) I'm reading your post as
- fighters got feats, but lets not look at that
- fighters get multiple attacks, but lets not look at that
- spells get capped, but lets not look at that
your not looking at positive effects of one class, and negative effects of the other. how can you then come to the conclusing that the second is stronger?
It comes down to this:
- no mather how you say it, or how many spells he gets, the wizard deals 1d6 damage per round per level,
--> which is linear.
- the fighter deals damage per round, dependant of the magical weaponry and items he has.
--> which is linear.
when you take time into account (like the total of spells the wizard has). BOTH, become quadratic
(it's not because the wizard has a limited amount off spells, his damage becomes quadratic)
On a last note: DnD is not the same as math: its not because something moves quardatic, that it will be beter then something linear. the most logical cap is level 20.
The Wizard continuously gets new options that have a reasonably effective tactical role at every level. If you go through the spells that kill people list you'll note that there really are levels in which you are very dominant over your enemies (1st and 17th, for example), and there are levels where you are merely pretty good (5th and 8th).
This is an interesting comment, and follows into my thoughts on why number of spells is relevant.
Straight martial characters mostly don't have a resource issue other than hit points. Everything is measured in "damage per round", and what you can do on round 1 you can do on round 6 as long as you're still alive and kicking.
In contrast, spellcasters are heavily constrained by resource usage, at least at low levels. The problem a level 1 wizard has isn't that his spells are rubbish, but that he only gets two of them. As he increases in level he gains more slots, until eventually he has little practical limit on the number he can throw across 4 encounters. It is interesting to consider whether a spellcaster eventually becomes so resource-rich that he can be treated as having "infinite" spells and thus attains a linear progression.
Let's also consider a direct attack progression. Let's be generous and say that attack bonus increases by 2 every level and damage increases by 1 every level.
Terms: N = level, T = target AC, An = attack bonus at level n, Dn = base damage at level n, En = expected damage per attack at level n.
Thus, we get the following:
En = (1 + (An - T + 1)/20) * Dn
= (21 + An - T)/20 * Dn
An = A1 + (n-1)*2
Dn = D0 + (n-1)
En = (21 + A1 + (n-1)*2 - T)/20 * (D1 + n - 1)
= 5% * (19 + A1 + 2*n - T) * (D1 + n - 1)
= 5% * (2*n + 19+A1-T) * (n + D1-1)
For arguments sake, let's set A1 to 4 (Str +3, BAB +1) and D1 to 10 (2d6 + 4.5 Str). Thus, En = 5% * (2*n + 23-T) * (n + 9).
Thus, the expected damage (for fixed AC) is actually quadratic, but heavily dominated by constants for much of its life over the 1-20 range.
Eg:
For simplicity, set T = 16 =>
En = 5% * (2*n + 7) * (n + 9)
Eg:
E1 = 5% * 9 * 10 = 5% * 90 = 4.5
E2 = 5% * 11 * 11 = 5% * 121 = 6.05
E3 = 5% * 13 * 12 = 5% * 156 = 7.8
E4 = 5% * 15 * 13 = 5% * 195 = 9.75
E5 = 5% * 17 * 14 = 5% * 238 = 11.9
E10 = 5% * 27 * 19 = 5% * 513 = 25.65
E15 = 5% * 37 * 26 = 5% * 962 = 48.1
E20 = 5% * 47 * 29 = 5% * 1363 = 68.15
Rate of chance at early levels isn't that impressive, but level 20 is over twice level 10. Of course, this assumes that our numbers aren't too generous.
Thus, if we assume that casters deal linear 2d6/level damage per round (no resource limit) then a fighter's mean single attack damage will eventually catch up and overtake them. However, we don't take into account non-direct damage spells, nor the relative rates of scaling of (to-hit vs AC) vs (DC vs saves).
Of course, none of this alleviates the problem with multiclassing a pure spellcaster. Martial classes can mix and match. Magic classes just end up crippled.
I was with you until you made the "supplemental books" comment. I have ever stood in shock and awe at the fact that truly, the players handbook's classes are truly balanced. I don't feel the same way about all those supplemental books. I've stood in with my mouth gaping for minutes at some of these classes, where the author never once appeared to give a nod to balance.
Of course, I have always played with power-gamers, so maybe a few loop-holes have skewed my judgment. (lousy awaken spell, don't even get me started on Eldritch Blast
Funny how the PHB classes are unbalanced and the supplemental classes are mostly balanced. Ask the people who know about balance - the Char Ops boards. They will tell you that a Druid is a better tank then a Fighter once they get Wildshape. That's 3/4 of the game. The spellcaster is a better melee combatant - and they have spells. Also funny how balanced warlocks are - they get to do a reasonably effective thing every round, and have a few out of combat skill areas.
WOTC estimates approximately 15 rounds per day. If spellcasters were balanced so they had about 15 round's worth of things to do per day at every battle, all on a level of equal-to-slightly-better compared to what a fighter can do (fighters have more HP), at every level, that would be balanced. But they don't. They have 2 at 1st level and 40+ at 20th. Playing a 1st level wizard is maddening because you can only do anything twice a day.
I would say spell growth is exponential. When you get to 20th level you're flinging wail of the banshee and time stop and wish and gate and other ridiculously broken things. And that's just your 4-ish good rounds. The other rounds you're using 1-hit-kill spells or polymorph or buffing the heck out of the druid or teleporting past challenges. And your druid friend is tanking while your fighter ex-friend sits in a corner and cries.
I was with you until you made the "supplemental books" comment. I have ever stood in shock and awe at the fact that truly, the players handbook's classes are truly balanced. I don't feel the same way about all those supplemental books. I've stood in with my mouth gaping for minutes at some of these classes, where the author never once appeared to give a nod to balance.
Of course, I have always played with power-gamers, so maybe a few loop-holes have skewed my judgment. (lousy awaken spell, don't even get me started on Eldritch Blast
ummmm.... the most powerful class in the game is the Druid. Warlocks are balanced. The following has nothing to do with in-play balance, but it is symbolic:
Barring wealth cheese, wizards get Pun-Pun at 14th. Psions get it at 7th or 11th or something. Wildshape gets it at 5th.
If you find a 1st level warlock dealing 1d6 and a 19th level warlock doing 10d6 unbalanced, please look at Exhibit A, 1st level Fighter with Greatsword Dealing 2d6+4 and Exhibit B, 19th level Wizard with Meteor Swarm dealing 24d6.
Eg:
E1 = 5% * 9 * 10 = 5% * 90 = 4.5
E2 = 5% * 11 * 11 = 5% * 121 = 6.05
E3 = 5% * 13 * 12 = 5% * 156 = 7.8
E4 = 5% * 15 * 13 = 5% * 195 = 9.75
E5 = 5% * 17 * 14 = 5% * 238 = 11.9
E10 = 5% * 27 * 19 = 5% * 513 = 25.65
E15 = 5% * 37 * 26 = 5% * 962 = 48.1
E20 = 5% * 47 * 29 = 5% * 1363 = 68.15
Rate of chance at early levels isn't that impressive, but level 20 is over twice level 10. Of course, this assumes that our numbers aren't too generous.
Thus, if we assume that casters deal linear 2d6/level damage per round (no resource limit) then a fighter's mean single attack damage will eventually catch up and overtake them. However, we don't take into account non-direct damage spells, nor the relative rates of scaling of (to-hit vs AC) vs (DC vs saves).
But we do not take trip, bullrush, ... in acount.
question: you create a hole damage / level system (using numbers and everything) , and as counter argument is numberless?
by default de damage spell of a wizard is 1d6 (with a safe). dissintegrate deals 2d6, but also requires touch attack.
the Wyrm red dragon (CR 20): 459 hp, his weakest save (reflex) is +19 (meaning 10+level); so the 1d20 needs to cover additional bonusses (Int, spell focus ... suppose this come to a +10; meaning 50% save chance) it has SR 26, and agains the wizard +22, thats a 20% chance to fail; and has an AC of 39
the average 70 damage from your spell (suppose it wasn't immune, lets say you're using a custom 20d6 spell that does something else)
does 42 damage (20% lost by SR, 40% full, 40 half because of safe) ...
the damage of the fighter's charge is (attack say +40 (20+STR+feats+magic (weapon / other boosts) + charge), armed with a wounding (34HD, so 1 con means in average 17 hp dissapear) 2d6+15 (+10 from 1.5 str, +5 magic) greatsword and a +2 power attack, does 43 damage.
a third point: at high level, you encounter SMART enemies! compare the wizard effeciency against the fighter efficiency: a village in a temperate climate is terrorrized by a white dragon, the village is destroyed by icy blast! you follow the tracks to a cavern and ready to kill it . you enter ... the wizard wins init ... what do you cast at the dragon
...
and then you notice the dragon used an illusion spell to look like a white dragon, and uses cone of cold (from his sorcerer list) to wreak havoc ...
at that point, a dimensional anchor is already cast by the dragon ...
a 4th point: guess how long energy resistance spells last ...
(yest stoneskin also lasts long, but by default: fighters should use magical adamantium swords (no trouble from sunder, hardness and ... stone skin) );
A wizard with a fly spell can take out a dire bear with a crossbow. Not because his damage per round is so impressive, but because that one spell makes him invulnerable to the bear.
Comparing how much damage each class can do in an arena-style shoot 'em up isn't going to prove anything. When we say that wizards are more powerful than fighters, we aren't talking about direct damage, but rather all the other stuff that only wizards can do. Fly, turn invisible, scry, etc.
Your main problem is that you assume it's going to be a fair fight.
Wizards don't fight fair.
ummmm.... the most powerful class in the game is the Druid. Warlocks are balanced. The following has nothing to do with in-play balance, but it is symbolic:
Barring wealth cheese, wizards get Pun-Pun at 14th. Psions get it at 7th or 11th or something. Wildshape gets it at 5th.
Technically, the Artificer could take the Druid, and we've got Pun-Pun at first level now.
Nom made the point with the PsiWar/Psion, but I want to look at a few other comparisons. A paladin is a lot like a cross between a fighter and a cleric, so I stated them out to 20th lvl:
- - - Paladin – BA +20, 114hp, saves +12/6/6, 12 spells/day, max spell lvl 4th, turn as 17th
- - - Clr/Ftr – BA +17, 104hp, saves +14/6/10, 21 spells/day, max spell lvl 5th, turn as 10th
It's almost pretty. The details are different, but the two function mostly at the same competence. Different flavors of the same idea. Now watch what happens if we compare a Mystic Theurge to a Cleric10/Wizard10:
- - - Mystic – 34 cleric spells, max lvl 8; 26 wizard spells, max lvl 8
- - - Clr/Wiz – 21 cleric spells, max lvl 5; 16 wizard spells, max lvl 5
I mean, wow. These aren’t even in the same ballpark. The question is, why aren’t they? Nom is suggesting that it’s because spellcasters are innately quadratic. Is it? Or, are multiclass rules to blame? Did the game designers intentionally make spellcasters resistant to multiclassing to balance their overall power?
I'm a lot more interested in figuring that out, versus a long debate over who's got the better class. (we all know it's the bard) :P
No matter what you read in my post, I am not trying to get on your bad side, my criticism is intended constructive, okay?
It's just that you spend so much time and effort (no matter how easy it comes to you) on calculating these effects, and for what? Look at the games all over the world. You can see them reflected here on the boards; there are some who constantly whine and argue about differences in power and that something is broken, yet there are so many others posting here who swap stories, ask for rules clarifications and otherwise have great games going on. Many (if not most) of those games have a fighter and a wizard, or to speak generically, a clobberer and a spellcaster. They enjoy the game. How, if it is sooo broken?
[...]Ultimately, this is a restatement of the so-called "Oberoni fallacy". That you can modify your application of something so that the brokenness is controlled doesn't make it not-broken.[...]
You're assuming that wizards did not want this discrepancy in power distribution. It ain't broken if it is intended this way, you know. In laymen's terms: it's not a bug, it's a feature!
Now I am not a stalwart defender of wizards' policies, and I differ with them very often on specific rules, but I wouldn't play the game if I didn't think the mechanics would work! That said, I think any of these discussions, be it simple "who wins"-arguments and playtests against core mechanic analyses, is moot if it works for those that like to play it.
Plus, to me it was always a given that a wizard of a given level is far superior in "power" to a "simple" fighter.
Having all that said, I get down to one consideration you seem to have left out and which, admittedly, is very hard to put into numbers: the wizard is VERY dependant on the spells he gets. The GM has every right to limit access to certain spells, and even if the wizard can learn ANY spell, he has to get his hands on a scroll or a spellbook to actually learn it (copy it into his spellbook)! The best argument doesn't hold if the wizard simply doesn't get the great mean uber-spells ;)
The other VERY IMPORTANT aspect you seem to forget is that a spellcaster has to memorize in advance. It doesn't really matter how many great cool powerful disintegrating spells he has if he hasn't prepared them for the encounter. Even with scrolls (which a wizard is seen with frequently, but which nonetheless are quite expensive and can not be that easily created on most prolongued journeys), he might simply not have the right spell handy at any given point and make do with what he has - which in my (non-mathematical) mind should make up for the exponential power difference.
Final statement: any given adventure (or encounter, if you will), are simply not cut out to be played by just any class; they are precisely cut around a certain class. You can't send a fighter against a powerful spellcaster, and you can't send a spellcaster into a simple "kill-em-all" galore of monsters/orks/whatevers. Apart from the point that they might not survive encounter for which they are not cut out, the players might not enjoy it, because they might have taken a certain class for a reason. The wizard's player might not want simple hack and slay, whereas the fighter player might want a break from complex world-altering magicks and return to a simple physical workout deal for his character.
I hope I wasn't being rude in your eyes, let me know if I was out of line, please.
I'm finding myself in agreement with AT and JE. That post JE quoted was very insightful and put into words a lot I've been thinking over for a long time.
Technically, the Artificer could take the Druid, and we've got Pun-Pun at first level now.
OK, OK, D&D economics gets it at 1st. But.... D&D economics is as balanced as a car with 1 wheel on a post. It's just a fun metaphor.
I always thought spells were exponential. Otherwise Empower Spell wouldn't make sense. I don't think a 9th level spell is as good as 9 1st level spells. Actually the curve is complicated. 1st-3rd is very fast, then it's exponential to 9th, then flat to epic.
Having all that said, I get down to one consideration you seem to have left out and which, admittedly, is very hard to put into numbers: the wizard is VERY dependent on the spells he gets. The GM has every right to limit access to certain spells, and even if the wizard can learn ANY spell, he has to get his hands on a scroll or a spellbook to actually learn it (copy it into his spellbook)!
Yeah, and the DM can never give the Fighter any weapons. The fact that you can DM around a problem doesn't mean it's not a problem, it means that Rule 0 still works. But it shouldn't have to. Invoking Rule 0 is pretty much the worst thing to do as a DM; sure, it may solve the problem, but that doesn't make it right.
Nom's point that casters scale exponentially is correct. In fact, he actually gave a weaker argument than he could have, by using damage-dealing spells as his benchmark. If you've visited the CO boards much, or read LogicNinja's "Being Batman" guide, you know that the worst way to spend a wizard's spell slots is with direct damage. If you want to kill something, use a save-or-die. Wizards get them at almost every spell level (in core!) and Clerics and Druids get a fair number as well.
The key difference between damage and saves is that monster HP scales exponentially; saves do not. Sure, the wizard's damage potential is increasing exponentially, but so is the amount of damage he needs to inflict. On the other hand, a 50% chance of instantly killing a monster bypasses all that- and at higher levels, the wizard can do that all day, with a much better chance than 50%.
Of course, the funniest thing is that "being a fighter" is a 6th level spell.
Final statement: any given adventure (or encounter, if you will), are simply not cut out to be played by just any class; they are precisely cut around a certain class. You can't send a fighter against a powerful spellcaster, and you can't send a spellcaster into a simple "kill-em-all" galore of monsters/orks/whatevers.
One problem: A caster is right at home in a "kill-em-all". In the same geographical area, laying down Evard's Black Tentacles and Solid Fog will block a choke-point, and then other area or multitarget effects can destroy the marauding horde of whatever. Against a single powerful opponent, caster or otherwise, a caster reigns supreme. Casters can target so many different aspects of their opponent. Will saves, Fortitude saves, Reflex saves, touch ACs, and no-roll effects are all options for a wizard. A fighter can only try and hit their full AC. That's it. So where a wizard has a chance to be strategic and target the enemy's weakness, the fighter is constrained to physical damage against the target's AC. As any fighter who has faced a troll would agree, the inability to use tactical options can be extremely frustrating. Put simply, the fighter can't do anything much. Any caster can access either mind-affecting abilities to bypass the fight, or fire/acid damage. A fighter's tactical options are limited to the degree of Power Attack (generally 1-3, 20 if you need a 20 to hit anyway or are CDGing).
Ultimately, casters have the options to cover their own weaknesses and target their opponents'. This includes the same weaknesses a fighter might be able to target (low AC, low HP). The fighter, on the other hand, however clever, basically only has one option: hit it. They can't force the opponent to roll saves, or set up lasting debuffs short of sundering (very expensive). Trip/disarm basically turns your attack into an attack of opportunity, and Bull Rush is less useful than Gust of Wind in the same circumstances and a wasted action in any others.
you got a nice point, but you spent a little too much time trying to convince people of the quadratic progression of a wizard. :P
Because of this, a lot of people misinterpreted your thread for a "fancy "Ftr-Wiz: who wins?" (to quote Mælstrøm). Correct me if I'm wrong, because if I am wrong, the rest of this post will be a lot of bull.
This thread is NOT about who contributes more to a party, or who would win in arena style combat; this thread is about multi classing options.
The Fighter
A fighter fights. He does this mainly by hitting things. First he attacks, then deals damage if he hits. The fighters primary "ability" will be attack bonus, with damage bonus second.
The attack bonus is based on Base Attack Bonus, which progresses linear with levels.
Having said that, I conclude that a fighters main output is based on linear progression.
--- This does NOT mean that a fighter will be useless in endgame or that his final output is linear ---
The fighters output progression is based on BAB. This is a good thing concerning multi classing, because every class gives you BAB. No matter what other class you take, you will continue the same linear BAB progression. This progression may slow down a little, but you continue to add BAB; thus, you continue to improve you main skill: hit things.
conclusion
No matter how a fighter multi classes, he continues to improve his main ability, hit things. While multi classing, this progress slows down, but continues to grow linear.
The Wizard
A wizard casts spells. First we have spells per day, then we get some sort of effect. As the wizards levels he gets more spells per day and all of his spells become more effective.
I am not a D&D mechanics guru, so I will just assume this makes his progression quadratic. Nom demonstrated this in several posts.
Now there are two reasons why you don't want to go multi classing with a wizard PC:
1) Spells are a strict class feature.
2) Quadratic progression makes the loss of later levels a lot of pain.
Spells are bound to a class
Multi classing will completely halt all progression in your main ability (casting spells). This basically limits all your multi classing options to prestige classes that grant "+1 level of existing spell caster class".
losing spell progression is pain
Because of the quadratic progression, losing only 1 level of wizard is a lot of pain in the end. I guess our major in D&D Malibu Trojan can elaborate on this, until then you will just have to accept this :P
conclusion
A fighter slows his progression a little if he multi classes, but gains a lot of cool new abilities from his new class (sneak attack or turn undead). A wizard on the other hand has to put his progression to a complete halt for these new abilities (sneak attack or turn undead), and every level that he loses as a wizard will hurt him very badly in the end.
Maybe this could be solved by making a wizards progression more linear, or base spell progression more on character level...
Psionics
A would like to add a little about psionics, because it shows more obvious than with wizards, how multi classing can hurt.
---for those of you who don't know psionics, you can find them in the SRD---
Instead of spells per day, a psion gets power points per day, it's similar to mana in computer games. Here the power points per day progression of a psion:
One problem: A caster is right at home in a "kill-em-all". [...] The fighter, on the other hand, however clever, basically only has one option: hit it. They can't force the opponent to roll saves, or set up lasting debuffs short of sundering (very expensive). Trip/disarm basically turns your attack into an attack of opportunity, and Bull Rush is less useful than Gust of Wind in the same circumstances and a wasted action in any others.
Agreed. But the fighter can go on for hours while the caster, once his spells are cast, needs wands, scrolls etc, all of which cost great amounts of money and are expendable, meaning they need to be bought anew once they are empty.
And just to be clear: I agree that the spellcaster grows more powerful, maybe even exponentially so, but I do think wizards intended it this way.
Khaim: this argument is not my strongest one, and was not intended as a carte blanche to DM-rule away the differences; I simply used it to endorse a point that it is not a true exponential growth rate if you consider these facets/aspects of the whole. A fighter depends on his weapon, but in a tight spot, he can take a club and still hash it out with the best of them while a wizard, once the spells are gone or if the wrong ones are memorized, is simply much less powerful than in a situation where the spells are "convenient" ;)
Plus, something which should not be forgotten: the power of a wizard is very much dependent on money; a poor wizard will never be able to store new spells he finds on scrolls, and how much money a party/wizard makes is again dependent on the DM. This is not to say that a DM should use the rules to circumvent imbalances or to suppress players/characters, it is simply a fact that different groups have different "party income". Some like the "poor" approach, while others want power and land at 6th level. Both is acceptable if DM and players work in concert, and neither is preferred by me; it is just a fact that the player character's power is dependent on the DM, and the dependence of spellcasting characters exponentially so (unscientifically speaking of course). ;)