To be fair, I find the value given for a knight (alone) in Omega Chess in that link I gave (i.e. just 2 pawns worth) to be very unlikely - I'd put it around 3 pawns, personally.
If I recall correctly, I once estimated a Champion as worth 4.75 pawns on 8x8, with my 'standard' value for a rook on almost any square/rectangular board size being 5.5 pawns. On larger board sizes I figure a single wazir (W) is worth less than on 8x8, and I think the same in the case of an alfil (A) or dabbabah (D), so that affects my value for a Champion (WAD) adversely.
How to understand that more concretely? Well, a wazir power enhances the power of a spider (AD), but using the wazir power on a bigger board only benefits a Champion the most when it takes certain paths, in terms of number of moves spent getting to a certain square (if it luckily is a relevant one). It is a similar story sometimes even for alfil and dabbabah powers, say compared to some paths a knight can take. Note that an alfil has one more 'binding' than a dabbabah, but the former is generally speedier and so gets a bonus, one making them about equal in value in my eyes.
edit: for what it's worth, here is a diagram to help illustrate that a Champion is sometimes slower than a knight. It takes it 3 moves to reach the N on b4 (which can reach it in 2 moves) and it takes 5 moves for it to reach the N on b8 (which can reach it in 4 moves) - on bigger boards there would be more such cases than on smaller ones, I'd think:
For wide boards, a Champion can go deep faster than on a deep board, it's true, but sometimes the Champion would want to go from one side of the board to the other. I do generally give a bishop a higher value on a rectangular board than on a square board, though on square boards greater than 10x10 I think a B's value should be put higher - though I balk at making a B worth 4 pawns or more as a general rule (restraining 3 pawns in an endgame can be tough enough). Thus for me, single B=3.5 on 8x8 or 10x10, but B=3.75 on 10x8 (based on cases of number of squares reached from each board square) or 12x12, for example. I have no set formula for estimating Bs values otherwise, but put it at 3.99 if a board is really huge. I have a more precise-value-oriented way of calculating a N's value on square or rectangular boards up to 16x16, but at that point my method + formula break down completely, not just because I think that on a board that big a N's value should be tiny.
Aside from all that, arriving at a precise average value for any piece type (even chess ones) I regard as something not to be completely sure of, even if it becomes the consensus. In WWII the main Axis powers were sure their codes were unbreakable, and may have had plenty of inductive reasoning to back that feeling up. Yet, they were eventually proven shockingly wrong, in more than one instance.
To be fair, I find the value given for a knight (alone) in Omega Chess in that link I gave (i.e. just 2 pawns worth) to be very unlikely - I'd put it around 3 pawns, personally.
If I recall correctly, I once estimated a Champion as worth 4.75 pawns on 8x8, with my 'standard' value for a rook on almost any square/rectangular board size being 5.5 pawns. On larger board sizes I figure a single wazir (W) is worth less than on 8x8, and I think the same in the case of an alfil (A) or dabbabah (D), so that affects my value for a Champion (WAD) adversely.
How to understand that more concretely? Well, a wazir power enhances the power of a spider (AD), but using the wazir power on a bigger board only benefits a Champion the most when it takes certain paths, in terms of number of moves spent getting to a certain square (if it luckily is a relevant one). It is a similar story sometimes even for alfil and dabbabah powers, say compared to some paths a knight can take. Note that an alfil has one more 'binding' than a dabbabah, but the former is generally speedier and so gets a bonus, one making them about equal in value in my eyes.
edit: for what it's worth, here is a diagram to help illustrate that a Champion is sometimes slower than a knight. It takes it 3 moves to reach the N on b4 (which can reach it in 2 moves) and it takes 5 moves for it to reach the N on b8 (which can reach it in 4 moves) - on bigger boards there would be more such cases than on smaller ones, I'd think:
For wide boards, a Champion can go deep faster than on a deep board, it's true, but sometimes the Champion would want to go from one side of the board to the other. I do generally give a bishop a higher value on a rectangular board than on a square board, though on square boards greater than 10x10 I think a B's value should be put higher - though I balk at making a B worth 4 pawns or more as a general rule (restraining 3 pawns in an endgame can be tough enough). Thus for me, single B=3.5 on 8x8 or 10x10, but B=3.75 on 10x8 (based on cases of number of squares reached from each board square) or 12x12, for example. I have no set formula for estimating Bs values otherwise, but put it at 3.99 if a board is really huge. I have a more precise-value-oriented way of calculating a N's value on square or rectangular boards up to 16x16, but at that point my method + formula break down completely, not just because I think that on a board that big a N's value should be tiny.
Aside from all that, arriving at a precise average value for any piece type (even chess ones) I regard as something not to be completely sure of, even if it becomes the consensus. In WWII the main Axis powers were sure their codes were unbreakable, and may have had plenty of inductive reasoning to back that feeling up. Yet, they were eventually proven shockingly wrong, in more than one instance.