Queen's Value

Imbalances are the heart of chess strategy, but how many pieces are equal to an active queen? I came to the position below replaying a game from the playchess server against Hiarcs 10. Black to move.





Here I played 24. ... Qg4+ and Hiarcs evaluated Kf2 as at least a half a pawn better than moving to the h-file. So, 25.Kf2 Nh3+ 26.Qxh3 Qxh3 27.Rxe8+ Kh7.





For White's queen, Black has given up a rook and knight. Earlier in the game, Black had given up a bishop for three pawns, then White sacrificed a pawn.

According to the most widely used version of point count chess, White has three minor pieces (9), rook (5), and three pawns (3) for 17. Black has a queen (9), knight (3), and seven pawns (7) for 19. But, arithmetic tells us little. How can a queen play against so many pieces? How many of Black's pawns will fall in the process?