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Subject: How Much is a Bingo Worth? rss

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Randy Cox
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Just how much value is there in playing all seven letters from your rack in one turn?

The answer seems obvious--50. After all, you get a 50 point bonus for doing so. But there are plenty of times where some shorter word generates more points than a bingo, so the 50 extra points doesn't necessarily mean you performed 50 points better than you would have without that play.

You may play seven 1-point letters and get something like 58 points. But you may have been able to play four of those common tiles elsewhere and get 20 or so (e.g. parallel words). In that case, the bingo was worth 38. Right?

I really don't know. I do know that S/He Who Plays More Bingos tends to win more often. But just how much is that big bonus worth in real points?

Well, I keep track of our plays and went back and analyzed our scores for all games in May (30 days, 30 games). One way to look at the value of the bingo might be to see how much difference it makes in the final outcome of the game. Makes sense, right. If the winning player tends to win by about 80 points, how much of that was the (often, but not certain) extra bingo?


According to the numbers, our average game was decided by about 66 points plus an extra 22 for each excess bingo the opponent had. In this case, we're just assuming that one player is going to win by about 66 points. Well, that's a failing assumption, since a good portion of that 66 points is made up from bingos. Therefore, I'll tentatively say this one isn't much of a valid way to look at things. (You'll note that the R-squared figure is pretty low, too).

So let's just tackle it the way that seems most logical. Look at each person's score and number of bingos. That should tell us something.


And this does show that a bingo is worth about 50 points atop our base average bingoless score of 295. This sure is looking like the right answer.

But what effect does your bingo have on the overall board. I mean, if you have seven great letters, what are the odds that your opponent will have great letters? Probably not that great. As such, your great play might be followed up by a sub-par play by your opponent. So what happens when we graph total board score (both players combined) against total number of bingos?


This seems to say that the board gains only about 40 points for each bingo played.

So what I think I'm seeing is that the individual player gets about 50 extra points per bingo AND that the board as a whole only gets a 40 point advantage. Therefore, I'm guessing that the opponent suffers those extra lost 10 points. Thus, the bingoing player should net a 60 point advantage, right (50+the other player's loss of 10)? I guess I could argue the other side that the non-bingo player still scores about average but that the bingoing player also has lower scoring turns either before (setting up for) or after (due to new random letters) the bingo. Thoughts?

I realize that the numbers don't directly show me this. It does show that a one-bingo advantage game should be about a 89-point victory. Is 60 of that spread made up of the extra bingo? Are the other 29 points just the typical swing in a game score? I really don't know. I do know that our average game had a 0.6 bingo differential in favor of the winner and an average spread of 80.2 points. Let's see (from the first graph): 66.7+.6*22.5 = 80. That's about right, but you'd expect it to be, wouldn't you?

Anyway, I don't have an answer, but I'm going to say that a bingo is worth about 60 points. No, 50. No, 40. No, 22 1/2. Yeah, that's it. 22.5. The rest is just luck and non-bingo skill. :)
 
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Wim van Gruisen
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You should have added a dummy variable, indicating who plays. If the bingos are mostly played by the same person, and that person scores significantly better than the other person, it might just be possible that the bingo player is better at the game than the opponent, and that his or her scoring better has not so much to do with the seven letter words as with the better skill.


I don't believe that laying a seven letter word gives you an advantage of more than 50 points. Because when you lay that word, you open up possibilities for the other player. When you play defensively, that other player may have more problems laying down words or reaching bonus squares. The 50 point bonus is especially put in to encourage players to put down long words and so break open the board. That bonus is a compensation for the added scoring possibilities that you give your opponent.
 
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Chris Martin
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Randy Cox wrote:
So what I think I'm seeing is that the individual player gets about 50 extra points per bingo AND that the board as a whole only gets a 40 point advantage. Therefore, I'm guessing that the opponent suffers those extra lost 10 points. Thus, the bingoing player should net a 60 point advantage, right (50+the other player's loss of 10)? I guess I could argue the other side that the non-bingo player still scores about average but that the bingoing player also has lower scoring turns either before (setting up for) or after (due to new random letters) the bingo. Thoughts?

Perhaps I've misunderstood your methodology, but to me it would appear that the 10-point gap can't be explained by the bingoing player having bad surrounding turns, since you have already established that the bingoing player scores 50 points more across the game per bingo. That 50 points already includes any bad surrounding turns.

What you're saying is that, where a is the score of all (both) players, b is the bingoing player's score, c is the competing player's score, n is the number of bingos the bingoing player scores and x is the effect on the competing player's score of each bingo:

a = b + c
a + 40n = (b + 50n) + (c + xn)

a + 40n = (b + c) + (50n + xn)
40n = 50n + xn
40 = 50 + x
-10 = x


I think that that proves that your initial hypothesis, that the competing player loses 10 points for every bingo that is played, is correct.
 
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