I think that I can recreate An's calculations. And I disagree.
- Click Here To Show Diagram Code
[go]$$Wc White first.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . X O . X |
$$ | . . . . O O . . . . C C C O O O O O X |
$$ | . . O O X . O . . , O 5 O . O X X X . |
$$ | . . O X . X O . . . O X O O X O X . X |
$$ | . O . X . X X O . O X O X X X O O X . |
$$ | . . X . X . O . O O X 1 3 8 . O . O X |
$$ | . . . . . . X O . O X 2 4 X X O X X . |
$$ | . . X . . X . O . X C C C X O O X . X |
$$ | . . X O X . . . . X . . . X X X O . . |
$$ | . . O . O . . X O X O O O O X O O . . |
$$ | . . O . O . O O X . . X X X O O X . . |
$$ | . . . O O . O X X X X . . . . O X X X |
$$ | . . . O . X X O O O O X X O O X O O X |
$$ | . . O . . . . . X O . O X O X X O . O |
$$ | . O O X X . X . X O O O . X X , X O . |
$$ | O X X O X X . . X O . O X . X X X X . |
$$ | . X O O O O X . X X O . O X O X . . . |
$$ | . O . . X X . . . . . . . O O O . O . |
$$ ---------------------------------------[/go]

fills
If

extends, we get

-

. Later

is sente, forcing White to fill. For convenience I am counting the

points, three for each player. White scores the captured stone and the result is then -1, or 1 pt. for White.
- Click Here To Show Diagram Code
[go]$$Bc Black first.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . X O . X |
$$ | . . . . O O . . . . C C C O O O O O X |
$$ | . . O O X . O . . , O . O . O X X X . |
$$ | . . O X . X O . . . O X O O X O X . X |
$$ | . O . X . X X O . O X O X X X O O X . |
$$ | . . X . X . O . O O X 1 C C . O . O X |
$$ | . . . . . . X O . O X C C X X O X X . |
$$ | . . X . . X . O . X . C C X O O X . X |
$$ | . . X O X . . . . X . . . X X X O . . |
$$ | . . O . O . . X O X O O O O X O O . . |
$$ | . . O . O . O O X . . X X X O O X . . |
$$ | . . . O O . O X X X X . . . . O X X X |
$$ | . . . O . X X O O O O X X O O X O O X |
$$ | . . O . . . . . X O . O X O X X O . O |
$$ | . O O X X . X . X O O O . X X , X O . |
$$ | O X X O X X . . X O . O X . X X X X . |
$$ | . X O O O O X . X X O . O X O X . . . |
$$ | . O . . X X . . . . . . . O O O . O . |
$$ ---------------------------------------[/go]

is gote, of course. Now there is a gote left that gains 2/3 point.
- Click Here To Show Diagram Code
[go]$$Wc Black first. Then White.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . X O . X |
$$ | . . . . O O . . . . C C C O O O O O X |
$$ | . . O O X . O . . , O 1 O . O X X X . |
$$ | . . O X . X O . . . O X O O X O X . X |
$$ | . O . X . X X O . O X . X X X O O X . |
$$ | . . X . X . O . O O X X C C . O . O X |
$$ | . . . . . . X O . O X C C X X O X X . |
$$ | . . X . . X . O . X . C C X O O X . X |
$$ | . . X O X . . . . X . . . X X X O . . |
$$ | . . O . O . . X O X O O O O X O O . . |
$$ | . . O . O . O O X . . X X X O O X . . |
$$ | . . . O O . O X X X X . . . . O X X X |
$$ | . . . O . X X O O O O X X O O X O O X |
$$ | . . O . . . . . X O . O X O X X O . O |
$$ | . O O X X . X . X O O O . X X , X O . |
$$ | O X X O X X . . X O . O X . X X X X . |
$$ | . X O O O O X . X X O . O X O X . . . |
$$ | . O . . X X . . . . . . . O O O . O . |
$$ ---------------------------------------[/go]
If White plays next, we count 3 1/3 pts. for White, the three marked points plus 1/3 pt. in the ko. We count 7 pts. for Black, the six marked points plus 1 pt. for the captured White stone. The net count is 3 2/3 (for Black). Since the White play gained 2/3 pts., the count for the
Black first diagram is 4 1/3.
The
White first diagram has a count of -1, so the swing is 5 1/3 pts., as advertised.
I have claimed that the White response gained 2/3 of a pt. If so, the result if Black continued should be 5.
- Click Here To Show Diagram Code
[go]$$Bc Black first. Then Black again.
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . X O . X |
$$ | . . . . O O . . . . C 2 C O O O O O X |
$$ | . . O O X . O . . , O 1 O . O X X X . |
$$ | . . O X . X O . . . O X O O X O X . X |
$$ | . O . X . X X O . O X 3 X X X O O X . |
$$ | . . X . X . O . O O X X C C . O . O X |
$$ | . . . . . . X O . O X C C X X O X X . |
$$ | . . X . . X . O . X . C C X O O X . X |
$$ | . . X O X . . . . X . . . X X X O . . |
$$ | . . O . O . . X O X O O O O X O O . . |
$$ | . . O . O . O O X . . X X X O O X . . |
$$ | . . . O O . O X X X X . . . . O X X X |
$$ | . . . O . X X O O O O X X O O X O O X |
$$ | . . O . . . . . X O . O X O X X O . O |
$$ | . O O X X . X . X O O O . X X , X O . |
$$ | O X X O X X . . X O . O X . X X X X . |
$$ | . X O O O O X . X X O . O X O X . . . |
$$ | . O . . X X . . . . . . . O O O . O . |
$$ ---------------------------------------[/go]
Black has 7 pts. as before, while White has 2 pts., for a net count of 5. Check.
So that is how I think that An got 5 1/3 pts. for the swing.
Why I disagree.
You may have noticed that the point for Black at L-11 disappeared when Black played first. That is because of a protective play. In the game Black made one by capturing a White stone at L-11 after a cut. In the White first diagram no protective play is needed because Black can atari that stone at L-10 instead of M-11, and the center Black stones are in no danger.
- Click Here To Show Diagram Code
[go]$$Bc Protection needed?
$$ ---------------------------------------
$$ | . . . . . . . . . . . . . . . . . . . |
$$ | . . . . . . . . . . . . . . . X O . X |
$$ | . . . . O O . . . . . . . O O O O O X |
$$ | . . O O X . O . . , O c O . O X X X . |
$$ | . . O X . X O . . . O X O O X O X . X |
$$ | . O . X . X X O . O X O X X X O O X . |
$$ | . . X . X . O . O O X 1 . . . O . O X |
$$ | . . . . . . X O . O X . . X X O X X . |
$$ | . . X . . X . O . X . . . X O O X . X |
$$ | . . X O X . . . a X . . . X X X O . . |
$$ | . . O . O . . X O X O O O O X O O . . |
$$ | . . O . O . O O X . . X X X O O X . . |
$$ | . . . O O . O X X X X . . . . O X X X |
$$ | . . . O . X X O O O O X X O O X O O X |
$$ | . . O . . . . . X O . O X O X X O . O |
$$ | . O O X X . X . X O O O b X X , X O . |
$$ | O X X O X X . . X O . O X . X X X X . |
$$ | . X O O O O X . X X O . O X O X . . . |
$$ | . O . . X X . . . . . . . O O O . O . |
$$ ---------------------------------------[/go]
Even though a protective play was required in the actual game, it seems to me that four things had to occur besides the Black capture at

. White had to save the White stone at "a", preventing an eye for Black there. White had to cut at "b". White had to play atari at "c". And White had to take the resulting ko. To try to calculate the position taking all of that into account would take some time and effort. But I think that we can say that

gains around 3 pts., either as a gote or as a reverse sente.