Well, have some reasoning:
- A team has 7 players on the field at once. They would have at least one backup for each position (if a game goes on for days, all players would require replacements), so that's at least 14 players per team.
- A team needs at least one coach, who (at the big-league level) is probably not a player. There might be specialist coaches as well, like a Chaser coach or Keeper coach (similar to how you have your offensive/defensive co-ordinators in gridiron football, your pitching coaches in baseball, your goalie coaches in hockey, etc). One coach per position would result in a head coach and four sub-coaches, though this seems unlikely to me. Two or three total seems more reasonable.
- A team needs an equipment manager - broom polishing, cloak patching, glove fitting, and so on. Maybe two, but one should suffice for 14 players in a sport where equipment damage seems to be mostly in the rips and tears category.
- Assuming each team has a home stadium, they need a "grounds crew" - finger quotes because in an aerial sport the condition of the ground itself doesn't matter so much. But yeah, you'd need ticketmasters, custodians, security, refreshments, and so on. I would say a stadium needs 50-100 workers.
- Then there's management and the owners. Could be somewhere between 5 and 15 depending on how "big" the team is; in a small league you wouldn't need that many top-level guys.
- Assuming pro Quidditch is anything like other sports, players would need agents for working out contracts, trades, and so on.
- Umpires. In a 13-team league you can have at most 6 games on at once, and umpires are said to get the weirdest injuries, so there's probably 15 or 20 of them total.
- The squabblers. Unions and so on. Could vary wildly depending on a bunch of factors. For the sake of a number let's say that there's a players' union and an owners' union with one member from every team (13+13), plus a couple of lawyers for an even 30. The umps probably have a union of about 5.
- Marketing. You'd need print ads and radio ads for each team, probably created by teams of 5-10 people each.
Putting all these numbers together results in a total in the range of 1220-2100; the biggest contribution is the stadium workers. Since the wizarding population of England is estimated by this answer to be in the 3000-10,000 range, this seems somewhat reasonable for higher population and lower Quidditch-career values.
