Calculation for the Chess SE question: http://chess.stackexchange.com/questions/13137/whats-the-average-piece-density

piece_densities.py

#!/usr/bin/python
import pgn
import numpy as np
from matplotlib import pyplot as plt
import sys

initial_piece_density = 0.5
decrease_per_capture = 0.015625

pgn_file = open(sys.argv[1], 'r')
pgn_text = pgn_file.read()
pgn_file.close()
games = pgn.loads(pgn_text)
results = []
for game in games:
	halfmoves = game.moves
	densities = [0] * (len(halfmoves) + 1)
	densities[0] = initial_piece_density
	for index, halfmove in enumerate(halfmoves):
		if 'x' in halfmove:
			densities[index+1] = densities[index] - decrease_per_capture
		else:
			densities[index+1] = densities[index]
	results.append(densities)

density_values_at_each_halfmove = dict()
for dens in results:
	for indx, value in enumerate(dens):
		if indx+1 in density_values_at_each_halfmove.keys():
			density_values_at_each_halfmove[indx+1].append(value)
		else:
			density_values_at_each_halfmove[indx+1] = [value]

average_densities = [round(np.mean(dens),5) for dens in density_values_at_each_halfmove.values()]
plt.plot(range(1, len(average_densities)+1), average_densities)
plt.title("Average piece densities by halfmove", size=18)
plt.xlabel("Halfmove", size=14)
plt.ylabel("Piece density", size=14)
plt.grid(True)
plt.savefig("piece_densities2.png")