TalkChess.com

[H.G.Muller]

The explanation of course is that when you are a light piece ahead, but none of your remaining pieces has mating potential by itself, you cannot trade into a won end-game. You must win additional material, while trading becomes a weapon for the defense, which you have to dodge. E.g. with 2 vs 1, when you have BB or BN, you really must win the remaining defender without any compensation, and any trade is curtains. But if you have a Captain or Man amongst your two, you merely have to trade the other. A big difference!

When a Rook-class piece is involved, the advantage is typically the exchange. (In Fruit's heuristic, a Rook is counted as 2 minors, so it also considers the exchange as being one minor ahead.) With R vs B or N you also have the problem that you have nothing to trade, because all your force is in a single piece, and must win the defender for naught. With RB or RN vs R you have B or N to trade, but you must 'trade' it for a superior piece, which in general is quite difficult (or the piece would not be very superior...).

Another remark on BN vs N is that you must win the N, while trading is fatal, which makes your own N useless for attacking the hunted N, as such attacks between equal piece type will be reciprocal. Replacing the N of the attacker by another light piece, e.g. the (1,0)+(2,2) leaper featuring in the Clobberers army of Chess with Different Armies, many more positions are won (though still quite far from nearly all). With BN vs B or BB vs B you suffer the same problem with respect to your B, while with NN you are doomed from the beginning for lack of mating potential. The only orthodox combination of 2 vs 1 minor that does not suffer from any of these problems is thus BB vs N, which indeed is a win. (The B-pair bonus probably also helps to make this possible; if you don't take for granted that the B are on unlike color, of course KBBKN is also only 50%won...)