How can I best assess the quality of a game of Scrabble?
Another measure of a good Scrabble game, used amongst serious tournament players: equity points loss. Let me explain.

As another commenter highlighted, sometimes strategy determines that you should play defensively and get lower score instead, in which case high-score may not measure how well the player plays (if that's your definition of good/quality, as opposed to excitement). Similarly, a game where a player has lousy tiles but played well given the circumstances may score lower than one where a player has abundance of easy bingos and can afford to miss one or two good plays and still win.

If what you want to measure if how well the player plays, one other way is to benchmark it against the theoretical best play. Usually what is used is the play made by a powerful Scrabble-playing software in similar circumstances. This is a common practice amongst serious Scrabble tournament players who are trying improve their play quality.

A couple of popular software that can be used for this are Quackle and Elise. I personally use Quackle so my explanation will be based on that, but the same concept applies for all software (and Elise plays better, albeit slower, than Quackle).

What I do is I will key in the racks (i.e. the 7 letters held by a player) for every turn, and also the actual move played, into Quackle. I will ask Quackle to also choose its optimum play (or list of possible plays, ranked in descending order from the best). Quackle can then run a simulation on what happens for the various plays, and calculate the equity point for each move.

Equity point is the nett point for a move, instead of the score itself. By nett point usually it means the score, minus the score of the opponent's reply, plus my score for the next move. This will account for both defence (reducing opponent's score) and tactics (sacrificing current score for me to score bigger next move). Since Quackle can calculate equity points for all moves, I can then compare the equity difference between my move and Quackle's best move. The number of equity point my move is lower than Quackle's best move's equity point, is the equity loss. The lower the equity loss, the better the play was. Sum up the equity loss for each play, and you have the equity loss for the whole game.

A 0 equity loss means a perfectly-played game (even if it's one which is lost to an opponent with better luck in that particular game). This is rare but has been achieved by a few top-flight players. I myself would be very happy with an equity loss below 50 for a whole game. To give a bit of a sense, missing a bingo can easily lead to equity loss of 50 in a single move. Similarly, failing to restrict opponent from scoring an extra 5 points each turn may add up over the 10 moves to be a 50 point loss (not accounting yet for suboptimal scoring on my part).

There are two flaws to this approach of benchmarking against a software:


it assumes the software used plays a perfect game. They don't - Elise
is better than Quackle, for example, and occasionally top players
have identified a better move than the software can (typically for
very unorthodox situations). But by and large, it's safe to say vast
majority of the times, measuring loss of equity is a good indication
of quality of play in a Scrabble game.
it takes effort to get the figure. One must key in the information
into a software to do its calculation. Serious players may put in the
effort, but casual players won't have this information and may prefer
a measure that can be seen at a glance (e.g. score).