OD&D is, of course, based heavily on the Chainmail Fantasy miniatures game. In fact, it is included as recommended equipment (Vol-1, p. 5; in the same category as dice and OD&D itself) and it is incorporated by reference at numerous points (e.g., Vol-2, p. 5: "Special Ability functions are generally as indicated in CHAINMAIL where not contradictory to the information stated hereinafter...").
You probably know that Chainmail's man-to-man and fantasy combat mechanics functioned by way of 2d6 rolls, whereas OD&D's "Alternative Combat System" functions by way of the ubiquitous d20. Therefore, as is obvious to pretty much anyone who's looked at it, the modifiers that appear in Chainmail would have very different effects probability-wise, if used verbatim within the core D&D system.
Intuitively speaking, a conversion from Chainmail to OD&D should more-or-less double any modifiers, in that Chainmail's 2d6 roll has a range of about 10 (11, really) and OD&D has a range of 20. But in addition to that, Chainmail's non-uniform distribution varies from point to point. Look at the table above for specifics: depending on where the initial target for success was, a +1 bonus in Chainmail might be the equivalent of anywhere from 1/2-point to over 3 points in D&D. On average, however, a +1 Chainmail bonus is worth +1.82 D&D bonus (i.e., 20/11; but easily rounded up to +2, as expected).
Nevertheless, the real issue I want to highlight is this: Throughout the entire publication history of OD&D, AD&D, d20 System, etc., the precedent was established to translate Chainmail-defined bonuses on a direct 1-for-1 basis (i.e., entirely overlooking this issue). Here are some examples:
- Goblins, kobolds, and orcs. Per Chainmail, "When fighting in full daylight or bright light they must subtract 1 from their Morale Rating, as well as 1 from any die rolled" [CM p. 29-30]; in OD&D, this translates to an identical, "when they are subjected to full daylight they subtract -1 from their attack and morale dice." [Vol-2, p. 7]. Likewise, this same modifier is carried forward into later editions [AD&D MM p. 47, et. al.]
- Weapon-vs-armor. Taking a single sample row from the weapon-vs-armor types in Chainmail, we see target numbers for a hand-axe of "7/7/8/9/10/10/11/12" [CM p. 41]; in the Greyhawk D&D supplement we see hand-axe modifiers of "+1/+1/0/0/-1/-1/-2/-3" [Sup-I, p. 13]. This is fundamentally the same progression, converting CM targets of 8 or 9 to +0, and any pips above/below that on a 1-for-1 basis. In fact, this is true for the entire OD&D weapon-vs-AC table, which is then copied forward to AD&D with only minor adjustments (for example, the hand axe modifiers are identical except for a single pip difference at AC4). [AD&D PHB p. 38].
- Missile fire. In the Chainmail man-to-man missile fire table, a target progression of -2/-1/0 is shown for each range category of short/medium/long [CM p. 41], and this coverts 1-for-1 to the D&D to-hit rule of +2/+1/0 [Vol-1, p. 20]. However, in AD&D this was wisely altered to become 0/-2/-5 [AD&D PHB p. 38].
- Mounted combat. Per Chainmail, "When fighting men afoot mounted men add +1 to their dice for melees and the men afoot must subtract -1 from their melee dice" [CM p. 26]. While this rule wasn't transcribed into the OD&D or AD&D core books themselves, it is copied unchanged into places such as the 1E AD&D Wilderness Survival Guide [WSG, p. 86], 2E AD&D [DMG, "Mounted Combat"], and 3E D&D [3E PHB, p. 138].
- Parrying. For lighter weapons, Chainmail provides the ability to parry, "subtracting 2 from the attacker's roll" [CM p. 25-26]; this is copied without change into Holmes Basic D&D: "The parry subtracts 2 from the attacker's die roll" [Holmes D&D p. 21].
- Magic swords. In Chainmail fantastic combat, "they give a plus 1 to the dice score... Excaliber [sic] and other 'Super Swords' would give a plus two or three!"; and in OD&D we also see magic swords from +1 to +3 in value [Vol-2, p. 23]. That said, in AD&D swords were expanded from +1 to +5 in value [DMG p. 124], and Arthur's sword was in fact later given the maximum +5 bonus [AD&D DDG, p. 18].
What would I want to do? Personally, I think I prefer option (b). I'm willing to chalk up these 1-for-1 translations as fundamentally an oversight and a "mistake" in D&D, and consider a more faithful conversion in probability on a 2-for-1 basis. In addition, I might make the philosophical case that no 1-point situational modifier is worth the mental effort to track. For example, if someone has a +1 Strength bonus to all melee attacks (such that it can be included on the PC card), then by all means, use that. If a weapon-vs-AC effect, or a special skill or ability, gave +2 in a given situation, then that is worth tracking. But tracking fiddly +1 sometimes-modifiers makes a difference so rarely, that it's better to entirely avoid. (3E "Bard Song": I'm looking at you and your ilk.)
In fact, this overall philosophy matches those modifiers that were freshly introduced at the time of AD&D. Cover modifiers are given in increments of at least +2 (cover AC +2/4/7/10; DMG p. 64). The bonus for charging is set at +2 (DMG p. 66). Special to-hit bonuses are in increments of +2 (opponent off-balance +2; opponent stunned or slowed +4; DMG p. 67). Likewise, if I have a shortcut system that generates results within 1 pip of the official tables (such as Target 20: see sidebar), then in my games I'm happy to call that "close enough". In short, I might argue: Situational modifiers in D&D should be at least +/-2 to be worth bothering with. And this is synchronous, I think, with the desire to double Chainmail modifiers if we opt to use them within D&D.
What's your preference? Poll results here.