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BGonline.org Forums
Proposed new scoring system for quizzes
Posted By: Timothy Chow
Date: Friday, 2 June 2023, at 1:48 p.m.
The Othello Quiz has a simple scoring system: 1 for a correct answer, and 0 for an incorrect answer (or no answer).
Every backgammon player has experienced the difference between knowing that a play is correct, and luckily guessing the correct play. Can this difference somehow be captured in a scoring system? I propose the following modification to the scoring of quizzes such as the Othello quiz. In addition to submitting an answer, you indicate whether you are "confident" or "not confident." ("Not confident" is the default answer, if you say nothing.) Then you are scored as follows:
2 points for correct and confident
1 point for correct and not confident
0 points for incorrect and not confident
–2 points for incorrect and confident
A frequently asked question is, "Doesn't this mean I can earn extra free points just by lying and claiming that I'm confident when I'm not?" The answer is that just as with any system, it is always a possibility that you can score high as a result of lucky guessing. However, indiscriminate claims of confidence come at a cost, because there is a penalty for an incorrect claim of confidence. Note that a claim of confidence carries a bonus of 1 point if you are indeed correct, but a penalty of 2 points if you are wrong. In effect, you are offering 2 to 1 odds that you are correct, so if you are less than 66% confident, then it's a bad bet to claim confidence.
A few examples may help clarify. Suppose you get 6 out of 10 questions right and you indiscriminately claim to be confident of all 10 answers. Under the proposed scoring system, you would earn 12 points for your correct answers and –8 points for your incorrect answers, leaving you with an overall score of 4, which is lower than the score of 6 that you would have earned if you had not claimed to be confident of any questions.
As another example, suppose you're a strong contestant and you get 7 right. You feel pretty confident in 5 cases and not so confident in the remaining 5 cases, so you mark your ballot accordingly. It turns out that of your 5 "confident" claims, 4 are correct and 1 is incorrect (whoops!). You therefore score 8 points for the 4 correct+confident problems, –2 for your incorrect+confident problem, 3 points for your 3 correct+not-confident problems, and 0 points for the remaining 2 incorrect+not-confident problems, for a total of 9 points. This is better than the 7 points that you would have gotten with no declaration of confidence, and also better than the 8 points that you would have gotten with indiscriminately claiming confidence on all 10 problems. Even though you were only 80% correct and not 100% correct with your claims of confidence, it paid off to declare confidence only on those problems rather than on all problems.
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