At the outset, this may become a long essay. We'll see.
Let's take a look at one aspect of each of four editions (0e, 1e, 2e, and 3e).
0e: requires (ie, promotes) house rules, gives no guidance for house ruling, rules cover very few specific circumstances.
1e: Forbids house rules entirely (at the time it was written), thus gives no guidance for house rules, but rules cover many specific circumstances without a streamlined method of resolution hardwired into the character sheet.
2e: Encourages house ruling and provides lots of ways to personalize the character sheet. Rules cover roughly the same number of specific circumstances as 1e and still don't have a streamlined resolution method, but more methods appear on the character sheet (ie, outside the DM's purview).
3e: Encourages house ruling but the amount of specific methods hard-wired into the character sheet makes it more difficult to make rulings that don't impinge on the character generation system. Rules cover a very large number of specific circumstances, but this is done by giving characters a wide variety of generally-usable skills to address most circumstances (drowning, climbing, finding food, negotiation, appraising items, etc). The contrast to 1e (and a bit less to 2e) here is that in 1e/2e the rules were not linked to the character sheet, which reduced the chance that a DM deciding to use different resolution methods didn't mess up the results of character generation.
I'm indebted to Matthew Stanham for pointing out something that made this taxonomy come together; the fact that 2e encourages house ruling more than 1e did.
This all helps to explain why there were once savage edition wars between 0e and 1e, and also why those evaporated after a decade to be replaced by virulence between 0e/1e on one hand, and 2e on the other hand. The reason is that once 1e was no longer "official," those who stuck with 1e started to view it more like the 0e players had viewed 0e ... as a vehicle for house ruling. House ruling is easy with 1e because the extensive rules aren't hardwired into the character sheet -- they are still all within the DM's internal system. But the official word had been not to house rule. Clearly, people had been house ruling since the dawn of 1e, but the message of officialness was very, very strong from EGG and TSR.
Once 1e is seen as a vehicle for house ruling, the very fact that there's no advice for how to do it suddenly makes it a pretty open system for modification. It's hard to break the system with house rules since only the DM is really given much in the way of rules. All of a sudden, 1e is no different from 0e except in terms of complexity.
2e, on the other hand, even though it encouraged house rules and tailored campaigns, once it's also out of print can be seen as a bit more restrictive than 0e/1e precisely because at one point it embraced the concept. By standardizing (some) of the ways to personalize a character sheet, 2e no longer looks quite as freewheeling as 1e, even though at the time of its publication it represented a huge step away from standardized officialness and toward a more freewheeling style. The passage of time actually reversed the way things operated when read as written.
Then there's 3e. Here, although house ruling is definitely encouraged, the amount of hard-wiring into the character sheet becomes very significant, to the point that if a DM changes much, he'd be invalidating choices that the players made at the time of chargen. ("Wait, if you make all negotiation into roleplaying, WTF did I take "negotiation" as one of my skills?"). Personalization of a gaming table was encouraged in terms of new monsters and details WITHIN the system, but personalization of the system ITSELF suffered precisely due to the fact that the system was so unified, streamlined, and hard-wired into the character sheet (as opposed to having lots of disjointed rules residing almost exclusively behind the DM screen).
There are a lot of implications to the fact that there are structural differences between these editions. The disjointedness of rules as opposed to streamlining/unifying, their location on the character sheet (as opposed to behind the screen), and whether the rules contain official rules for house-ruling (ie, official options), are three structural axes around which D&D editions have shifted.
It explains why a divide between 0e and 1e suddenly disappeared once 1e was no longer the official version. It explains why the flexible character generation system of 2e had less difference with 3e, even though 1e and 2e shared lots of other characteristics -- why it seems that the 1e players are such a hold-out against "modern" games as opposed to 2e players, who already worked with a much more personalized character sheet. All that 3e added to 2e was a more streamlined (and more complex) method for personalization. This also explains why 2e DMs seemed to get more irritated with 3e than 2e players did. The players had more of the same, but the DM faced an entirely different structure (unified methods vs. disjointed rules that could be cut or altered without screwing with the game's hardwiring).
Don't know if any of this makes sense, but I think it's going to become very relevant now that 5e is trying to create a modular system. Who's going to like it best? It might be that 5e is the big gift for the 2e players, who are most comfortable with personalized character generation, but whose DMs are used to modular (disjointed) rules.
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