Teaser 2965: Knock, knock!

From The Sunday Times, 21st July 2019 [link]

Last year a two-figure number of teams entered our football competition. With that number, it was impossible to have a straightforward knockout competition (where half the teams are knocked out in each round), so we divided the teams into equal-sized groups, each pair of teams within a group played each other once, and the overall winner from each group went forward to the second stage consisting of a knockout competition. Unfortunately our local team was knocked out in the quarter-finals of that stage.

This year a higher number of teams entered (but not twice as many). Again a straightforward knockout competition was impossible so we copied last year’s model but with smaller groups and more of them. By coincidence the total number of games played this year equalled the number played last year.

How many teams entered last year and how many this year?