I looked up my old comment in this topic ( https://www.chessvariants.com/index/listcomments.php?id=31222 ). There I report that the Rookies were actually strongest of all. So RR >~ NN > CC > FF. This was based on the scores in 400-game matches between each pair of armies with Fairy-Max. In a comment just before it Fergus had arrived to the same conclusion based on ChessV (but with far fewer games). Fairy-Max randomizes the first 4 opening moves of each player, which should be enough to not have significant duplication of games. (I did not actually check for duplicate games.)

My experience with this kind of materialy-imbalanced testing is that the result is not very sensitive to the piece values used by the engine. E.g. if you give one player an Archbishop instead of a Queen, and assign it a value of 900 (where Q=950), the side with the Queen will score about 62%. If you then repeat the test with A=1000), the player with Queen will still score around 62%. The reason is likely that, as long as the values are different, 1-for-1 trading is not frequent, because there is always one player that thinks it is to his disadvantage, and will avoid it. And it does not matter much which player this is. The imbalance is therefore long-lived, and you measure the relative effectivity of the imbalanced pieces for doing (or helping to do) damage to the common pieces. Which is pretty much independent of how the computer values them, as they will mostly not be traded directly for other material (2-for-1 trades are also pretty rare).

So as long as both players share the misconception on actual value, the programmed value doesn't seem to be very critical. Of course it should not be totally off; if you set the value of a Queen below that of a Pawn, it will indeed get worth as much as a Pawn, because it will be immediately traded for one. There is just no way the other player could shield all its Pawns from Queen attack, before the Queen gets to see it can force a more profitable trade. If you assign reversed values to pieces that differ very much in power, the strong one will probably succeed to force it being traded for the weak one, which it mistakenly considers profitable.

Before I did the test with complete armies, I did similar tests on all individual pieces in the armies to determine their value. E.g. use FIDE as context, and then replace Rooks of one side by (say) HFD on the other, to see whether HFD is better or worse than an orthodox Rook (and by how much). In such tests I always make sure they are self-consistent, i.e. performed with the programmed value equal to the value suggested by the eventual score. If my initial guestimate of the value was wrong in this respect, I just repeat the test with the value suggested by the outcome of the flawed test. Which then usually does not significantly alter the outcome. This should have made the individual piece values more or less OK, so that the play during the whole-army tests must have been realistic, and thus must have made the sampling of what the pieces can do representative.

I am a bit surprised about the low score imbalance you get for CC-FF. My old results table says +9% for this (meaning the match score averaged over both colors was 59% in favor of the Clobberers). You get only 52.6%. What is the Pawn-odds score for ChessV (i.e. when you use equal armies, except that one of the players gets f2 or f7 deleted)?

 

These are the piece values Fairy-Max is using (Pawn = 100):

FIDE
Knight           325
Bishop           350
Rook             500
Queen            950

Clobberers
Waffle           320
Fad              480
Bede             530
Archbishop       875

Nutters
Fibnif           310
Charging Knight  400
Charging Rook    485
Colonel          935

Rookies
Woody Rook       310
Short Rook       400
Half Duck        480
Marshall         935