Team ratings question

[Days of Grace]

Have had a bit of a conundrum in the past few days deciding how to apply a team's batting/bowling rating (as seen in my thread on top 100 test batting and bowling performances) to a working batting/bowling average.

The best teams for both batting and bowling have a rating around 750, whilst the absolute worst teams have a rating around 250. If 500 is the mean (say a batting/bowling average of 30.00), then what do 750 and 250 correspond to?

Before, I thought it should be 750-500-250 would equal 1.25-1-0.75 (37.50-30.00-24.00), but of course the mirror of 1.25 is not 0.75. It is 0.80.

Should it be x1.25-1-divided by 1.25

Or something else?

It's doing my head in, so any help would be appreciated.

P.S. to those concerned, I do get out quite often. Got a date with a Chinese bird this weekend.

 

[cnerd123]

Got a date with a Chinese bird this weekend.

Maybe she can help you with the math then

 

[Zinzan]

Maybe she can help you with the math then

Or at the very least make you some Egg foo young, which is good brain food.

 

[indiaholic]

Some kind of a logarithmic scale should allow you to maintain symmetry.

 

[Days of Grace]

Some kind of a logarithmic scale should allow you to maintain symmetry.

Ok. So far I've only used linear scales, so could you help me out with an example?

 

[vcs]

I'm not sure I understand your problem correctly, but if

is your mean, and you want

and

to be symmetrically represented, you take log of your data. Hence

and

. So it becomes symmetrically distributed about 1.

EDIT : The math tags seem to **** up the alignment of the text, but you get the idea.

 

[Days of Grace]

I'm not sure I understand your problem correctly, but if

is your mean, and you want

and

to be symmetrically represented, you take log of your data. Hence

and

. So it becomes symmetrically distributed about 1.

Sorry, mate, that is way over my head. Can you explain it in layman's terms?

 

[vcs]

It is not as complicated as it looks.

The log function gives you the power that you need to raise the base to in order to get the argument. For example, log to the base 2 of 16 would be 4, since you need to raise 2 to the fourth power to get 16. Similarly, log to the base 2 of 1/8 would be -3, since you need to raise 2 to -3 to get 1/8. Now, by the rules of exponent, we can easily get the rules for finding logarithms of products of numbers, which is what I have used here.

log(a*b) = loga + logb
log(a/b) = loga - logb

 

[Days of Grace]

Well, this is what I have so far. Whearas, a batting team rated 750 would have a batting average of 37.50 (30x1.25) and a batting team with a rating of 250 would have an average of 24.00 (30/1.25)

Is this a sound formula, or should I try a log?


750 1.25
745 1.25
740 1.24
735 1.24
730 1.23
725 1.23
720 1.22
715 1.22
710 1.21
705 1.21
700 1.20
695 1.20
690 1.19
685 1.19
680 1.18
675 1.18
670 1.17
665 1.17
660 1.16
655 1.16
650 1.15
645 1.15
640 1.14
635 1.14
630 1.13
625 1.13
620 1.12
615 1.12
610 1.11
605 1.11
600 1.10
595 1.10
590 1.09
585 1.09
580 1.08
575 1.08
570 1.07
565 1.07
560 1.06
555 1.06
550 1.05
545 1.05
540 1.04
535 1.04
530 1.03
525 1.03
520 1.02
515 1.02
510 1.01
505 1.01
500 1.00
495 1.01
490 1.01
485 1.02
480 1.02
475 1.03
470 1.03
465 1.04
460 1.04
455 1.05
450 1.05
445 1.06
440 1.06
435 1.07
430 1.07
425 1.08
420 1.08
415 1.09
410 1.09
405 1.10
400 1.10
395 1.11
390 1.11
385 1.12
380 1.12
375 1.13
370 1.13
365 1.14
360 1.14
355 1.15
350 1.15
345 1.16
340 1.16
335 1.17
330 1.17
325 1.18
320 1.18
315 1.19
310 1.19
305 1.20
300 1.20
295 1.21
290 1.21
285 1.22
280 1.22
275 1.23
270 1.23
265 1.24
260 1.24
255 1.25
250 1.25

 

[harsh.ag]