Statistics Help Needed
 

I've got a problem that I'm hoping the wealth of math talent on this board can help me with.
Our school district has recently adopted a traveling trophy program based on the district wide reading program. Initially the schools were ranked 1 to 4 in percentage on reading tests and 1 to 4 on reading points earned. They've now changed the system to this:

Reading Points x Percentage on tests = Ranked Score

This issue with this is it severely undervalues the percentages students score on tests. I think it value quantity (books read) over quality (how well the comprehend the material).

Full disclaimer, our school is typically the leader when it comes to percentages. In the old system, we had won the trophy 4 of the 5 months. Since the change, we've had situations like this:

Our school averaged 13 pts per student, averaged 90% on tests, and gets an aggregate score of 11.7.
Another school averaged 15 pts per student, averaged 80% on tests (5% below the recommended level for the program), and gets an aggregate score of 12.

So, my question is, how do you equally weight percentages with a point value? I'm pretty good at math but admit this is beyond my level of statistical analysis. Any thoughts on ways to balance the two would be greatly appreciated.

Just thinking out loud and havent ran much analysis....but if I am reading correct and an 85% is the recommended level, then an aggregate based on 85 percentile performance would make the difference.

So instead of
13 x .9 = 11.7
15 x .8 = 12

You would have
13 x (.9/.85)=13.76
15 x (.8/.85) = 14

It doesnt give you the result you want, still. But a difference of 2 points per student seems fairly significant.

Nice thought. Much easier than some sort of efficiency rating u was trying to work on. Yes, the goal isn't to make my school tops. But I know the spirit of the competition is to make sure students are gaining in their reading through age level appropriate books while maintaining strong comprehension levels. Trying to think like an admin here, and I don't want to see the program fall into the trap of simply chasing points.
Just on a side note, I grabbed the points for their ease of computing. Last month saw the winner edge out two other schools by something like 24 to 22 pts per student while finishing several percentage points lower.

Maybe express the percentages as a z-score?

.85 as a pivot and the further away from the pivot the higher the weight?

Not sure how to explain this in a more scientific/statistical rational, but a more 'fair' equation would be:

(Reading Points x Percentage on Tests) + (Reading Points x (Percentage on Tests - Recommended Level ))

This gives a bonus/penalty for those above/below the recommended level.

So in your situation:

(13*.9)+(13*(.9-.85))=12.35
(15*.8)+(15*(.8-.85))=11.25

Last 3 posts: you can normalize the test scores one way or another :)

Thanks, all. I really like formula Scarecrow. It doesn't change any of the current standings, but it does help keep outliners from being either penalized or rewarded depending on their performance. I'll pass it along to admin to see what they think. :)