Shield's +1 AC bonus a relic of Chainmail

Its no secret that before Dungeons&Dragons there was Chainmail. D&D took shape from the fantasy rules in the back of that booklet. The combat rules in Chainmail are based on 2D6 and the alternative combat rules in D&D are based on D20. Chainmail fantasy combat was weapon vs armour combination rolling on 2D6. In many examples the addition of a shield increased the number to roll for a hit by one. In Men and Magic the alternative combat rules use a straight D20 vs armour to hit without including the weapon type. This time the shield grants a flat bonus of 1 across the board. But the two systems are not really similar. The bell curve of the 2D6 makes a +1 bonus worth a different amount in percent depending on where on the curve it lay. The odds of rolling a 7 or better on 2D6 are 58%. The odds of rolling 8 or better are 42%. A 16% difference for a plus one bonus. But the odds of rolling 10 or better are 17%, adding that +1 bonus for a roll of 11 or better changes the odds to 8% for a difference only 9%. Clearly its better to have a bonus in the middle of the curve than the ends. If you average it out to say a 15% bonus it still is better than the lowly 5% you get with the D20 roll. The shield has been short changed in the conversion from Chainmail to D&D. I might adopt the idea of three types of shields; small bucklers +1AC, the classic knight's heater +2AC, the large body shield +3AC. The standard +1 is simpler but has always seemed lacking. My alternative goes well I think to correct something that wasn't exactly wrong rather a relic of an earlier rule system.