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It would be nice if someone could write down the answer to the question "How do I know who is komaster?". If I knew how to determine it I might understand it :). The above discusion really doesn't seem to clarify anything for me. It sounds an awful lot like the komaster is simply the person who has enough excess ko threats to win. There is also a lot of asigning points in the above, which seems difficult if not impossible without knowing the position on the rest of the board.
Bill: In the precise technical meaning of the term, for a player to have just exactly enough threats that are large enough so that she is komaster is against the odds. Usually one player or the other has more than enough large enough threats to win the ko without having to ignore an opposing threat, or neither player is komaster.
Simple examples can be given, however. The simplest is that of a simple one-step ko where neither player has a ko threat. The player to take the ko is komaster.
Bill: The beauty of the komaster idea, IMO, is that for the first time it gave us a way to calculate the value of single kos in a manner similar to the way we calculate the value of other plays. For that, it's vagueness in terms of what conditions need to be met on the the go board for a player to be the komaster for any specific ko fight is a virtue, just as the vagueness for calculating the value of non-ko plays about other plays on the board is a virtue.
For non-ko plays we have a good idea of the conditions on other plays that have to be met so that we can have confidence in the theoretical results. I. e., that the largest play is the best play. Furthermore, we know that these conditions are typically met, so that playing the largest play is usually correct.
For placid kos, which have the same value regardless of who is komaster, we can be relatively confident. However, komaster calculations do not provide absolute limits, so we cannot be as confident about any ko as about non-kos.
For hyperactive positions, such as approach kos, mannen kos, and positions which threaten fights for large placid kos, the story is different. Being able to calculate their value gives some guidance, where before there was none, but little is known in general about conditions for komaster, so our level of confidence is much lower.
There are other ways, which I pioneered, of theorizing about such positions by analyzing kos and threats together in what I term a ko ensemble. However, that theory is so complex that it is not yet of any real practical use.
There's plenty of "more correct" explanation already, maybe this could be a simple starting point to get in:
"If White is komaster, then this position has a mean score of 7.5."
is roughly equivalent to
"Assuming that White can win the ko for free, we get a mean score of 7.5 for this position."
When talking about local positions, scores are meant to be local scores. That is, if not explicitely defined otherwise, the shown part of board is scored, with peripheral groups treated as alive and marginal areas as neutral.
Note that, knowing the score for the case of White being "komaster" is useful even if White, in fact, cannot win the ko for free, but has to accept some damage elsewhere in exchange. The score is then corrected according to that loss.
Bill: Well, that depends on what we mean by, for free. Being komaster means that we can take and win the ko in exchange for ordinary plays elsewhere. It does not cost us any more than that. It does not cost us anything extra.