How can I best assess the quality of a game of Scrabble?

Question

As a child, I played Scrabble with my grandmother. At the end of each game, she would tally the total score (i.e. both players' combined), and consider the game a good one if the total was high, a worse game it was lower.

• Is that a common way to determine whether a game of Scrabble is good? Is it the common way?
• Are there any other common ways to determine a good game? (Perhaps — and, as a novice player, I'm just guessing — number of bingos, number n-ple-word squares covered by tiles, how many times the expensive tiles were used (across and down or just once), how many tiles were left unused at the end, how many squares were used along the edges of the board, vel sim.)

Either of those may depend on the level of play, in which case I'd like to know answers both for the novice level I played her at and for more advanced levels.

Answer 1

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).

Answer 2

I always thought a good game was one that was fun!

Answer 3

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.

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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.

Answer 4

All of those suggestions you proffer for judging the quality of a game are excellent ones. Remarkably, an extremely accurate mechanism for weighting them all appropriately, so as to correctly assess the total quality of a game, has already been invented.

Surprisingly, this mechanism ha been around since the game's inception, and is in fact a fundamental component of the game.

It is called the score.

Yes, just go back to your grandmother's knee and accept her worldly wisdom. By definition, the quality of each participant's play has already been judged, weighted by defensive and offensive maneuvers, and use of board bonuses and bingoes, and calculated to be their score on each play. Adding them up is in fact the way to judge the quality of a game.

Answer 5

Here is another interesting thing Nigel Richards perhaps the best Scrabble ever, has at the time or writing played 2549 internationally rated games. He has scored more than 300 in all but 10 of them. It's more than likely that in those 10 games he had sequences of incredibly bad racks. His average per game is 461.37 and average against him is 390.26 which makes up approximately 852 points per game.

How do more mortal players stack up? The current #8 rated David Eldar manages 442.95 per game and against him it's 401.08 he has gone past 300 , 98.7% of the time.

300 is a good benchmark. In my country the national scrabble league only allows players with an average score of more than 300 to take part in certain tournaments.

Answer 6

Yes, total score is a good way to assess the quality of a scrabble game.

In fact, in the instructions for an old scrabble set that my parents have, this method is specifically recommended. I can't remember all the cut-offs, but they say that a points-total of 700 or over represents an excellent game (presumably in the context of casual, home play).

Why is this an effective measure? If you add up the points on all the tiles in a scrabble set, there are a total of 187. So this is the absolute minimum total score achievable (in practice a bit higher, since it is impossible to avoid scoring some tiles twice when adding words to the board). Players use their skill to get "added value" out of their tiles. They can do this by the use of bonus squares, perhaps targeted specifically at their high-scoring tiles, by scoring letters more than once (e.g. adding an S to existing words on the board), and by getting 50-point bingo bonuses. In general, the greater the skill of the players, the more value they will be able to add to the base score of their tiles.

As @TimLymington mentions, the measure is not perfect, since a good defensive player may be able to restrict their opponent's score. But in my experience this contributes only a small amount to the flow of high-standard games, since expert players are able to make good plays out of all but the worst situations. The more complex method described by @Ricky provides one way of, at least partially, taking this into account, but is clearly considerably more difficult to apply, and adding up a total score is a good approximation.

Note also that of the other possible measures that are suggested in the original question, most do in fact contribute to the final points score, and so are also useful, but coarser measures.