Like about a third of my posts, this one is inspired by Dan, specifically his comments on this article. I'll quote for ease of reference. I'm going to talk about differences between combat and knowledge skills, and how this results in it being easier to make combat monsters than polymaths, though as I have no solutions to present it's perhaps not very useful.
For reference, I'm using "skill" in a very general sense below - things like Base Attack Bonus, feats, attribute points and so on can be considered skills here.
There *are* Sage characters in DH (I think they're even called Sages) and they have exactly this problem. You generally can't make a knowledgey character in a 40K RPG that does knowledge as well as a fighty character does fighting, partially because of the generalist/specialist issue rearing its head again.
It strikes me that part of the problem with sages is that, because most games model combat with a small number of skills that often support each other, wile they model knowledge with a large number of skills that are unrelated to each other, a Sage is necessarily a generalist character. They might seem specialised, because their role is specifically "knowledge and research" but in reality you're a generalist who is spreading their skills over (say) Accounting, Anthropology, Biology, Chemistry, History and so on while the combat characters just need to invest in Fist and Shotgun. You *could* design a specific class/splat/specialisation to get massive bonuses to all knowledge-related tasks, but games tend not to do that.
Because of the way knowledge is handled in most RPGs, you can't really have a character who is *generically* good at knowing about lots of stuff, because knowledge is almost always based on a wide variety of completely unrelated skills. A character who wants to be good at fighting usually has to invest in a single weapon, which they can then use to kill anything they meet. A character who wants to be good at knowledge has to invest in everything you might every conceivably want to know about. About the only exception I can think of to this in a mainstream RPG (and it's only partial) is the way Call of Cthulhu uses Library Use and Know Rolls as generic Find All The Knowledge skills.
Interestingly the one-and-a-half exceptions I can think of are World of Darkness, which has one skill covering all of Academics and to some extent Call of Cthulhu if you assume that all you really need to find stuff out are Library Use and Know.
This strikes me as a very good point.
I think a large proportion of the issue breaks down into two aspects: synergy and granularity (I talk about granularity way too much).
Combat resolves a low-granularity challenge with a lot of granularity. The challenge is, more or less, "do I win this fight, and by how much?" and this is resolved with multiple rolls, potentially involving multiple skillsets. Because multiple rolls are involved, the outcome falls somewhere on a spectrum of success from ignominious defeat to effortless victory. Moreover, your actual performance will tend towards your paper performance: if you have a 70% chance of Swording things, you'll generally end up performing at about 70% Sword in a game. A 70% Sworder will tend to reliably beat a 50% Sworder, demolish a 20% Sworder and be pwned by a 90% Sworder.
Knowledge skills generally resolve challenges as a single roll. The challenge is "do I know this fact?" or "do I solve this intellectual problem?", and often a binary outcome is offered, although some games (or GMs) build in degrees of success or failure. Because of the small number of rolls, performance will tend to be more erratic both within a challenge and across the character's lifetime. A single bad roll can leave you failing an entire challenge even though you're a world-class expert, in a way that rarely happens in combat challenges, where luck tends to even things out across the rounds. It's also relatively likely that an ignoramus will pass a difficult challenge by fluke.
As Dan pointed out when we chatted about this, if you play the botanist, you don't want to fail the one or two botany rolls that come up because you roll two really bad dice; you don't want the boxer to pull technical botanical knowledge out of thin air because she rolls a 1% chance; you don't really even want both of you to pass, because it's your time to shine. This was a point in favour of Trail of Cthulhu.
The combination of individual knowledge skills occurring rarely, and being handled with small numbers of rolls, makes the ones that do happen crucial for establishing the in-game reality of a character's abilities.
Discrepancies of granularity
Why this discrepancy in how challenges are resolved?
I think a large part of it is that (as fiction illustrates) we find the minutiae of combat intrinsically interesting, and it's obvious how to model these things (be that individual blow or as a set of manoeuvres forming a "turn"), whereas there's no very obvious way to model knowledge interactively. Many applications of academic skill involve pitting your wits and memory against a static obstacle. Others involve practical applications of skill that can change the current situation, like powering-down a machine or reading the hieroglyphs that will tell you which door leads out of the collapsing building, where breaking them down into smaller chunks may feel artificial.
Often, knowledge skills are used to try and create a change from the status quo, by gaining information or affecting the environment; combat skills generally change the possibility space instead. Referring back to an earlier post, combat is generally fork-in-the-road and knowledge skills are often something else.
The details of many academic skills are not considered enthralling. Modelling library searches, lab experiments or gathering of biological samples in detail probably doesn't inspire many people, while there's really nothing you can do for factual recall or comprehension of a clue, which is how these skills are very often used.
It's perhaps also relevant that combat is intrinsically dangerous, whereas many skill applications are not. The combination of an intelligent adversary, an activity that people generally find compelling in itself, and danger to the PC, provide strong incentive to model combat in detail.
One step removed
I think there's an argument you could make that combat skills and academic skills work differently because of how they achieve things (which is a result of the points above). I reckon combat skills tend to contribute to a broader overall goal: the purpose of the Sword skill is to damage things using swords, and the purpose of Dodge is to avoid attacks, but the overall objective of using these skills is typically to win fights. Academic skills tend to blend purpose and goal more closely: the purpose of Botany is to do botany, and the mechanical objective of using it is typically to discern botanical information, which will provide a clue or otherwise contribute to moving the plot forward.
As Dan points out, very often combat prowess requires only that you put lots of effort into one specific weapon skill, and obtain that weapon. It's a little broader, because as I said, combat often includes more than one skill. At its most basic level, you may have an offensive and a defensive attribute. A third skill may be useful for feinting, seeing through feints, manoeuvring for advantage (or to escape a fight that's going badly) and other direct combat factors. Stepping back a moment, a stealth skill may help you get the drop on enemies, a perception skill help avoid ambushes, a raw strength skill help you use surroundings to your advantage by climbing or pushing scenery.
These skills all feed into the same objective: winning fights. They may have other uses too, of course. Not having most of these skills will reduce your options for winning fights effectively, but you can still be highly effective at winning fights. Synergies between the skills strengthen your position: at the most basic level again, being better at avoiding damage makes you better at winning fights, just as being better at dealing damage does. Combining Perception, Stealth and Tactics allows you to detect enemies, determine the most advantageous approach and get into position - essentially decreasing the difficulty of the challenge.
In comparison, knowledge skills are almost universally isolated from everything else. There is one skill which allows you to do Botany, and if you don't have it, you cannot do Botany. Having points in other knowledge skills like Physics or Ancient Egypt does not provide any benefit. Because of the low granularity of knowledge challenges, there is rarely any opportunity to establish and exploit advantages by using multiple skills.
At the same time, knowledge skills are non-fungible, which is to say, you must have the designated skill to be able to complete a knowledge challenge.
Why yes, I am a colossal pseud.
This contrasts heavily with combat skills, which are often very fungible. There may be fifty weapon skills, but you only need one weapon to complete fights. There may be several useful secondary skills, but these generally provide alternative (and sometimes mutually-exclusive) tactical options, rather than enabling completely different activities. A warrior is likely to specialise either in berserk rampaging, heavily-armoured patient plodding, or evasive swashbuckling - any of these can be used to win fights, and some will suit particular battles better than others, but it's very unlikely that you'll be completely unable to partake of a fight because you chose a different option. The only likely example is a warrior with no ranged weapons facing enemies they can't reach. At the same time, there's very little point trying to be good at all three schools of combat: excelling at any one of them is generally enough, and you may as well spend any spare points on something else you're more likely to use. Logically speaking (and simplifying things massively), if you have an overall 80% in Berserk Fighting stuff, then even if you have 50% in Swashbuckling stuff, there will be very few situations where it's mechanically better to use your Swashbuckling at full strength, than your Berserk Fighting with a penalty.
In knowledge skills, however, you need to have a broad range of skills so you can cover as many situations as possible, because your 80% Botany is no use at all for Archaeology. Games are not generally very forgiving about substituting knowledge skills in this way.
Moreover, skills that are useful for winning fights are often useful in other situations too. Being strong, agile and tough protects against many hazards, allows you to force past obstacles, endure difficult conditions, perhaps evade pursuers or pick pockets, and so on. Secondary skills like stealth let you avoid combat altogether, tail suspects or escape. Perception skills help you spot not only ambushes, but hidden treasures, good campsites, signs of burglary or wanted criminals. Some knowledge skills are relatively flexible, such as those relating to "general knowledge" or (in a fantasy game) wilderness survival skills; many others are quite specific. Overall, in most games, combat skill will be useful far more frequently than any given knowledge skill, or even several.
On the whole, there also tend to be significantly more knowledge skills than combat-related skills; many systems also give relatively generous initial combat skills because it's so significant to the game. Call of Cthulhu, for example, gives everyone 15%-30% with various firearms, even though many people have never touched a gun in their life, but offers only 1% to 5% in knowledge and hobby skills. This sort of thing means it's relatively simple to become very good at combat and do well in most kinds of combat situation - equipment is often the deciding factor in what range of situations you can handle. In contrast, it's typically difficult to have good scores in more than a few knowledge skills, which means even if you work very hard at knowing stuff, there are likely to be many knowledge situations you can't handle.
World of Darkness
The WOD system presents an interesting counterpoint here. It has (depending on your definition) about half-a-dozen academic skills, a similar number of social skills, and a similar number of combat skills. All skills typically start out with no dots, and all skills are equally expensive to buy up. It's not noticeably more difficult to be a scientist than a brawler.
However, the synergy issue still applies to some extent. Someone who has Brawl and Athletics is better at combat that someone with just one of those; someone who has both Academics and Science will be more broadly successful, but not better at achieving the tasks each skill is used for. The issue of granularity still applies, with combat being resolved blow-by-blow and non-combat interactions typically based on a single roll; as such, swing is more substantial in knowledge skills. All that being said, the WOD Attributes + Skills system for determining competence does compensate to an extent, as does the use of a dicepool.
By comparison, Deathwatch is unusually bad for characters wanting to develop any skills but combat. All skills use the same percentile system, based on the tabletop stats - this results in percentages of around 40%, while many skills begin untrained, so characters roll on half skill or simply cannot roll. As a result, success for even trained characters is far from assured, while the success rate for untrained characters isn't much worse in many cases. To put it another way, what you might call the False Positive rate is a very substantial proportion of the overall successes, and the False Negative rate is a very substantial portion of the overall failures.
Moreover, there are a large number of knowledge and technical skills covering specific areas: individual sections of history and culture are broken down, as is knowledge of the various enemy races characters may face; general technical knowledge is separate from ability to hack locks; medical and chemical knowledge are separated.
To further exacerbate the situation, as I explained in this article, your skill options are severely limited based on your chosen class-equivalent, level-equivalent and origin. Some skills or skill boosts are impossible to buy at all, others very difficult or extraordinarily expensive. While all skills are based on attributes, attribute upgrades are priced according to class-equivalent, making it even more difficult for most characters to enhance their knowledge skills because they pay over-the-odds for Intelligence upgrades. You could easily spend several thousand XP getting a handful of knowledge skills to the 50% mark, while your battle-brothers pump combat skills to 70% for a fraction of the cost. Considering how often each of these is actually used, it's a poor exchange.
The system also has various modifiers built in that can enhance your odds of success in combat, such as a flat +10% chance for aiming before a shot, +10% for charging, the +30% applied against Surprised targets, and equipment bonuses. There is a small amount of equipment that can aid in specific non-combat tests, but this is very limited, and there are no built-in modifiers to increase success in such tasks.
This combat-centricity isn't intrinsically bad, since it is a game specifically about supersoldiers, but it does affect the type of characters you can build within that framework.
As with about 60% of my posts, this one has no clear conclusion, and this wasn't it.
No, c'mon, I can do this. Let's see. Even games which intend to support a wider variety of characters than the classic adventurer tropes, such as Call of Cthulhu, are inclined to leave it very difficult to be a successful sage-type character; the limited incidence of many knowledge skills, together with the swinginess that results, and the large number of discrete and non-synergised knowledge skills, mean that such characters are prone to be less effective and less likely to have their moments of awesome.
Unintuitively, World of Darkness, with what seems a mere handful of knowledge skills, is probably the game that best enables players to portray a highly competent knowledgeable character.