not the best comparison to be fair on EA (thanks, I'm sympathizing with EA). Valve has 1-3 "major projects" outside of games, live updating 2-3 games, maintaining 2 others, and then maybe has some misc. developers here and there for R&D. then you can muliply that by 3 or 4 for art, support, legal, and other stuff.
EA works on and releases a dozen games in house a year, if not more. And the studios are scatered all over the world, not all in WA. Then it maintains a few dozen more that still makes big money. Then has publishing wings to publish more 3rd party games. Then has a mediocre store to manage, then has sales and outreach, and probably a few more wings I'm forgetting.
They spread out a lot more, so they'll need more staff for that.
That does go along with article I just saw on Valve that they operate their systems with 350 admins, versus EA with 10,000 people.