Simple to try. Less simple to write up with confidence.  An outline of the four searches that I ran is below.
Simply put there were LOTS of kos. However, I am not sure that there were no systematic errors. I clicked through a sample of the games selected and everything I checked was a legitimate ko shape. However, with nearly 150,000 hits on the fourth search, I obviously did not check too many. The four searches are independent so there is no way to tell about duplicate games counted. The safest approach is to assume that the result in search four, 47,780 games, is a reasonable approximation of the total. That means that about 2/3 of all games in GoGoD feature ko shapes, on average something like three of them per game. I say shapes because there are many cases where such shapes arise but are immediately connected in normal play. For example...
This standard invasion sequence produces a ko shape after  but Black normally connects immediately so no ko fight occurs. Nevertheless the position after will appear in my search 4 below.
- Click Here To Show Diagram Code
[go]$$Wc
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . 9 6 . . . . . . . |
$$ | . . . . . . . . . 7 4 1 8 X . . . . . |
$$ | . . . , . . . . . X 3 2 . . . O . . . |
$$ | . . . . . . . . . . 5 . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . , . . . . . , . . . . . , . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . . . . . |
$$ ---------------------------------------[/go]
Entire game list 72,645 games
Note in all the search diagrams below a stone of either color is optional on the points marked 'a'.
- Click Here To Show Diagram Code
[go]$$B Search Pattern 1 - On the Edge
$$
$$a O |
$$O X |
$$X . |
$$a X |
$$[/go]
Result 47,755 hits in 23,318 games.
- Click Here To Show Diagram Code
[go]$$B Search Pattern 2 - Along the side
$$
$$a X O a |
$$X O . O |
$$a X O a |
$$[/go]
Result 10,293 hits in 9,436 games
- Click Here To Show Diagram Code
[go]$$B Search Pattern 3 - In a corner
$$- - - +
$$O . O |
$$a O X |
$$a X . |
$$a a X |
$$[/go]
Result 1,107 hits in 1,086 games
And last the big guy!
- Click Here To Show Diagram Code
[go]$$B Search Pattern 4 - The Open Board
$$
$$a X O a
$$X O . O
$$a X O a
$$[/go]
Result 147,764(!) hits in 47,780 games.
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) who could do something similar across GoGoD?