The quality of a game is not determined by the height or depth of the total score. A great example is a soccer match where the total score is 25 goals. Obviously, one or both teams did not know how to play defense very well. Does 25 goals indicate that the game was good? Not necessarily.
Let's examine a three games where we got a total score of 25.
- One team scores 25 points and the other scores 0
- One team scores 12 points in a row, and then the other scores 13 in a row
- One team scores 13 points and the other scores 12, but the scores are interwoven
If we judge on total score, all three games are of equal quality. Obviously the first game is not a quality game, because one team was stomped and the other was not given a challenge. What are some other ways to measure quality? Let's try these metrics:
- Closeness of the scores of each player at the end of the game
- Closeness of the scores of each player throughout the game
- The strategy and/or tactics of each player
A strategy of saving useful tiles may lead to a lower beginning score, but a large payoff at the end. A more aggressive strategy of grabbing points when you can may nab you the win, but you may be surpassed by a more patient player. My conclusion is that the quality of a game is based on closeness of the final score and the strategies each player employed to get there.
A commentator asked that I provide ideas on measuring good strategy. I can only provide a lower bound, as well as some additional notes.
- A player who mulligans his hand repeatedly until losing, or simply concedes every game as soon as it starts, has employed the absolute worst strategy
- A perfect players employs the absolute best strategy
All strategies in between are subjectively good or bad. Often in Chess, strategy employed in a game is reviewed by panels of experts. Books are written about good strategy in Scrabble. The strategy of a professional Scrabble player is probably good. The quality of a game between a guy and his grandmother may be undeterminable if neither player possesses expert knowledge on good Scrabble strategy, and a panel of experts is not available.