Indeed, piece values are a concept that assumes an additive model for material evaluation, where the value of your army is the sum of the individual piece values. But in reality this additivity is only a (usually pretty good) approximation. The effective value of a piece is affected by what other friendly or enemy pieces are on the board. This is well known from the Bishop pair bonus, and even more dramatically demonstrated by the fact that 3 Queens lose so badly from 7 Knights (in the presence of Pawns). <p> It turns out that under 'normal' circumstances, of a varied army of opposing pieces, with widely spread values, such non-additive effects are pretty small. The dominant effect here is that stronger pieces devaluate by the presence of weaker opponent pieces, as the latter force a trade-avoiding strategy on them, reducing their usefulness. But this can be accounted for as a second-order correction to the base values of the pieces, which then makes these base values even more universally accurate. <p> The base values themselves are also not just the sum of contributions from the individual moves, as the difference in value between Q and R + B shows. Usually adding move sets causes some synergy. This is even true if the added sets are without obvious defects. E.g. the Phoenix, which moves one step orthogonally or jumps two diagonally has 8 move targets, like the Knight, and neither of them is color-bounded or suffers from the Pawn hurdle. So not surprisingly they have very similar value, ~3. If you combine their moves, however, the resulting piece has 16 unblockable move targets, which corresponds to a value of 7-7.5, i.e. a synergy of about 1 Pawn. <p> Such a synergy is to be expected, as the moves of set A help to aim the moves of set B on their target, and vice versa. A quantitative indicator for this is the number of squares you could reach in 2 moves. E.g. a 'Narrow Knight', which only has the two forward-most and two backward-most moves of the Knight, can reach 4 squares in one move and 8 squares in two moves (plus a return to its starting point). Combine it with the complementary 'Wide Knight' to a normal Knight, and it can reach 8 squares in one move, and 32 in two. So although the number of moves simply added, the number of two-step tours quadrupled. Now what you can do in two moves is not as damaging as what you can do in one, as the opponent can see it coming and gets a turn in between to take conter measures, but it is not totally unimportant. <p> Apart from this 'manoeuvrability' synergy, there are the synergies due to moves repairing each other's defects that you mentioned, like color binding or Pawn obstruction. An alternative, equivalent way to look at them is as a penaly on the unfavorable combination of moves that had the defect. E.g. color binding, and in particular higher-order color binding, can be very damaging to the performance. A Shatranj Elephant, which jumps two diagonally, can reach only 8 squares on the board, and is almost worthless (~0.5 Pawn) despite its 4 moves. A piece that moves one step diagonally forward or straight back would be worth more, even though it only has 3 moves. A non-royal King (Commoner) suffers from lack of 'speed', and adding a move with a longer stride to it would be worth a lot. These kind of deficits typically occur in pieces with very few moves. <p> As to the Ferz vs Wazir value: if you take a piece with very many moves, so that taking away a few will not introduce severe deficits in terms of speed or color binding, you can disable individual moves to measure how the value suffers from it. This revealed that forward moves contribute approximately twice as much as sideway or backward moves, (and that captures contribute about twice as much as non-captures). This explains why the Ferz is better (at least in pairs): it has two forward moves, and the Wazir only one. The Wazir also suffers from the Pawn hurdle. In fact, it turns out that all Rook-like pieces I tested so far (several limited-range Rooks, of which the Wazir is the most extreme case), starting them on the back rank behind a closed wall of Pawns makes their value come out 0.25 Pawn lower than when you start them on an open file or before the Pawns. Wazirs starting on d3/e3/d6/e6 test as about 125 centi-Pawn, while on the back-rank they hardly beat a Pawn. Also normal Rooks in the starting setup tend to test as 4.75, rather than 5. This can be seen as an 'open-file bonus', which is sort of implied in the end-game. (And the classical piece values are end-game values!) Note that a Wazir also has lower 'speed' than a Ferz. To catch a Passer the Ferz has to be in the same square area as a King would have to be, but the Wazir has to be inside a triangle half the area.