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Average-Negative Score-Logic (common-sense?) prob.

It's not a game. Nevertheless, the analogy should suffice.

1) A person plays 5 games with scores of 175, 256, 13, 148, 97 averaging 137.8

2) Another player plays 5 games scoring 14, 10, -68, 45, -248 and averaging -49.4

Player one in the next game, scores 25. His average is now 119.  Because his current average is 138, he has to score 138 to maintain his average. As he has scored only 25, his average has gone down. So far so good.

Player 2 goes on to the next game. He scores -10. His average has now become -42.8.

Now player 2 has not only not made up his deficit, he in fact has lost 10 more. How do I interpret the *increase in the average*, given that a positive gain in the average is indicative of an improvement of scores?

Thanks in advance.

Saturday, July 17, 2004

I'm not sure what you're asking but couldn't you just take the absolute value of the old average and subtract the absolute value of the new average?

abs(138) - abs(119) = -19
abs(-49) - abs(-43) = +6

I'm not sure I understand your question so I may be interpreting it wrong.

Trying to be a nice guy.
Saturday, July 17, 2004

If you don't like paper, there's always

Seems like you're having a difficulty in visualizing data. ;) I haven't used it, but a numerical analyst I know does..

Unless you're French, in which case it'll just grow to be a big waste of your time: (warning -- not work-safe)

Tayssir John Gabbour
Saturday, July 17, 2004

>> abs(138) - abs(119) = -19
>> abs(-49) - abs(-43) = +6

That is what I am grappling with. How can a score that has *worsened* be reconciled with an *increase* in the average? The +6 means, at face value, an improvement in performance. But the performance has in fact been worse.

I am aware of the mathematics involved. It is the interpretation that I am not able to justify.

Saturday, July 17, 2004

I believe the players performance would have been better with a score of -10.  This is what the average indicates.

-10 is better than the players other two negative scores.  One of which was very large -248.  So a -10 would increase his performance when the numbers are averaged.

Trying to be a nice guy.
Saturday, July 17, 2004

The second player averaged -49.x in five turns.

Implication: To remain at a constant rate of success/failure, he had to score -49.x, the same as his previous average, in the sixth turn.

He scored -10 in the sixth turn, instead. Meaning, his score left a margin of +39.x (-49.x - (-10)) that he earned. If you spread this gain of +39.x over all the six turns he played, then each turn of his gains a score of 6.5 on an average, which is reflected in his _increase in average_.

Sathyaish Chakravarthy
Saturday, July 17, 2004

OK. So an increase in the average should mean "You are now expected to do X. But you have scored X+. Therefore you have improved". Makes sense now.

I was thinking along the lines of "You have scored < 0. Therefore you have worsened."

Thanks for that.

Saturday, July 17, 2004

In this case, it looks like you need to stop looking at the average, and simply look at the total.

If you can't reconcile the fact that -10 is better than -49 and hence the average should increase (indicating player 2 did better than his average), then you're using the wrong metric to measure performance.

Saturday, July 17, 2004

Ankur, actually the mistake I was making was not looking at the average at all. Just the change in it.

Today's lesson : When evaluating the change of something, it is imperative to take into account that thing as well. Evaluating the change independently will lead to wrong results.

Many thanks.

Saturday, July 17, 2004

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