Yes, they literally DO play a third more games. More actually. You ARE aware there are 24 teams in the championship right? Its really basic math, 24 teams x 46 games each is right around 1100 sides. In the premier league 20 teams x 38 is 760. A third of 760 is 253 games. So the premier league(760) plus a third more (253) would be 1013, less than they play in the championship.
Want to work it the other way to help your numbers? If the championship played 30% less, it would be 770 games, still more.
Your making it easy Davek