What are some common statistical analyses we can run on many games (~20k games)? I have a list of around 20k games played on a popular online website. I would like to run some statistical analyses on these games. I'm not talking about analysing specific games, but rather finding common patterns that arise.

I've looked at some popular sites on the internet that provide such statistics, but I'm wondering if there might be any more. So far I've got:


Popular openings grouped by ECO.
Most common endgames.
Average rating difference between opponents.
Frequent players.
Longest streak (rematch count).


What other kinds of statistics might reveal something about the community, players, tendencies and more?

Thanks.

EDIT:

Thanks for the suggestions so far. I apologize if I wasn't very clear with the question, so let me clarify some things: I would like to avoid analysing all the games (such as finding the point at which its +-2, or finding recurring tactical motifs, as these require going through each game and running it by an engine). I'm more interested in getting information and statistics about that particular collection of games, so having access to more games isn't necessarily a better thing. I hope this can steer the answers in the intended direction.

Thank you.
You can find posistional themes and other interesting info from SCIDvsPC software. Sample of output-

4.3 Positional Themes

Frequency of themes in the first 20 moves of each game:
Same-side castling:             73%    White Isolated Queen Pawn:       8%
Opposite castling:               8%    Black Isolated Queen Pawn:       8%
Kingside pawn storm:            15%    White Pawn on 5/6/7th rank:     52%
Queens exchanged:               40%    Black Pawn on 2/3/4th rank:     34%
Only one side has Bishop pair:   6%    Open c/d/e file:                50%


I had answered the same on this question: Chess Olympiad statistics