[Bug-gnubg] Game Statistics

[Christopher D. Yep]

Within a match, gnubg gives game statistics.  However the last 3 lines of 
the game statistics may be confusing to users (see below).  While I don't 
consider it a "bug", perhaps we can debate a possible change.

Sample output (game statistics):

                                      Player1              Player2
Actual result                         81.00%               19.00%
Luck adjusted result                  55.17%               44.83%
Relative FIBS rating                  34.08                -34.08

Interpretation (correct me if I'm wrong):

If Player1's match winning chances (mwc) change from N to (N+D), then 
Player1's "Actual result" is listed as (50% + D).  Similarly, if player1 
experienced net luck of L, his "luck adjusted result" is listed as (50% + D 
- L).  Finally, the "Relative FIBS rating" uses the "luck adjusted result" 
over the length of the match.

More explanation:

1. Player1's mwc was 69% at the beginning of the game and 100% at the end 
of the game, therefore his "actual result" is listed as 50% + (100% - 69%) 
= 81%.

2. Player1 had net luck of 25.83% mwc according to the luck 
adjustment.  His "luck adjusted result" is thus 50% + 31% - 25.83% = 
55.17%.  The interpretation of this is that of Player1's 31% jump in mwc, 
25.83% mwc can be attributed to net luck and 5.17% can be attributed to net 
skill.

3. The above is from a 7 pt. match.  A 55.17% to 44.83% edge in a 7 pt. 
match corresponds to a 68.16 point rating edge (i.e. 34.08 to 
-34.08).  Note that a 5.17% mwc edge (or 2 * 5.17%, depending on how you 
define "edge") in one game generally corresponds to much more than a 5.17% 
edge over an entire 7 pt. match.  Here gnubg just assumes that Player1's 
edge over the entire match is 55.17% to 44.83%.

To avoid user confusion, I suggest the following output for the above example:

                                      Player1              Player2
Actual result                         +31.00% mwc          -31.00% 
mwc
Luck adjusted result                  +5.17% mwc           -5.17% 
mwc

Note that if "Luck adjusted result" is calculated (in the code) as "Actual 
result" minus luck adjustment, then changing "Actual result" from (50% + D) 
to D will automatically generate the desired output for "Luck adjusted result".

Finally, I'd suggest deleting the "Relative FIBS rating" line for game 
statistics (but include it for match statistics), since it's too difficult 
to interpret what a +5.17% mwc edge in a particular game means to the 
rating difference between the two players.  For example a 5.17% mwc edge in 
the first game of a long match usually implies a huge rating differential, 
whereas a 5.17% mwc edge in the final game of a long match often implies a 
somewhat smaller rating differential.

Chris