Greetings. Some office workers have joined together in a competition
to lose weight. The period of time is three months, but each person
wants to lose a different amount of weight - absolute or percentage,
they are all different. How can we create a system to measure progress
equally and fairly?

Regards,

mrlg

Greetings mrig,

Certainly a worthy endeavour you're undertaking here...I believe I
have come up with a system that meets your requirements of equality
and fairness.

The common thread between people measure weight loss sbsolutely versus
by percentage is the rate of weight loss. This is essentially the
progress that each person has made towards their goal weight (ie. Jim
has progressed 78% towards his goal weight).

It seems that an Excel spreadsheet is a good way to keep track of all
this information...you will need to set up the following columns:

Name - person's name
Original Weight - on the date when the competition began
Absolute/Percent - whether their goal is an absolute value (A) or a
percentage (P)
Absolute Goal - value in pounds if goal is absolute for this person,
blank otherwise
Percentage Goal	- percentage value if goal is a percentage, blank
otherwise
Current Weight - the weight of the person when comparisons are being
made
Overall Progress - how far the person has progressed towards their
goal

The last two of these columns can be copied if you want to track
everyone's progress over several intervals, but for the purpose of
this example we will only have one (the weight at the end of the
competition for each person).

The only column that requires  calculation is the "Overall Progress" -
in Excel the formula is as follows:

=IF(C2 = "A", (B2-F2)/D2, IF(C2 = "P", (B2-F2)/(E2*B2/100), "Bad
Option in Column C"))

This formula is conditional based on whether the person chose to
measure progress by percentage or absolute weight. You can copy the
formula down in Excel so that you only need to enter it once. Let's
use some sample data to illustrate this (corresponds with column
descriptions above:

Example #1

Jim
173
A
23

161

Since Jim wants to track with an absolute weight, his value in
"Overall Progress" is calculated like this:

(Original Weight - Current Weight) / (Absolute Goal)

(173 - 161) / 23 = 52.17%


Basically it can be broken down as follows:

Calculating progress for absolute weight loss:


Name	Original Weight	Absolute/Percent	Absolute Goal	Percentage
Goal	Current Weight	Overall Progress
Jim	173	A	23		161	0.52173913
Joe	182	P		10	174	0.43956044
Jack	158	P		12	150	0.421940928
Jill	141	A	21		130	0.523809524

Example #2

Joe
182
P

10
174

Since Joe wants to track by percentage, his value in "Overall
Progress" is calculated like this:

(Original Weight - Current Weight) / (Percentage Goal * Original
Weight / 100)

(182 - 174) / (10 * 182 / 100) = 43.96%

Hopefully this system will encourage everyone to stay health and fit
in the grips of competition! If you have any questions about the
information above please do feel free to post a clarification.

Cheers!
answerguru-ga

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Request for Answer Clarification by mrlg-ga on 28 Jul 2003 19:49 PDT

Thanks. The spreadsheet does seem to be the way to track progress.
Could you explain in greater detail how we can compete as well as
track our progress? Your answer clearly explains how to track
progress, but we need a method for declaring a "winner" or ranking
progress. For example, assume every week each person puts $5 in a pot.
The weekly "winners" take the pot. To compete in this way, we need a
ranking system, somehow weighted to account for the different weight
goals. Some folks only want to lose 5-10 pounds while others are
seeking to lose 40 or more.

If this has turned multi-part or should be a separate question, let me
know and I will make adjustments.

Regards,

mrlg

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Request for Answer Clarification by mrlg-ga on 28 Jul 2003 19:51 PDT

Upon re-reading your answer, it appears you are expressing progress as
a percentage of individual goals. I will accept this answer and create
a new question if my office mates do not agree.

Thanks for your help.

Regards,

mrlg

---

Clarification of Answer by answerguru-ga on 29 Jul 2003 08:09 PDT

I'm glad you were satisfied with the answer - I will stay on the
lookout for follow-up questions to this one :)

answerguru-ga

The researcher provided complete details for implementing his answer,
a helpful contribution.

if i were the one loosing 3 pounds and others much less during one
week (or 35 pounds and others much less during 3 months), then i would
prefer this formula:
my goal-related percentage + a multiple of my group-contribution
percentage.

my goal-related percentage being the one suggested in the answer; 
my group-contribution percentage being: 3 devided by the group's total
weight loss during that week;
 the multiple should be determined by group decision.

(if the group's total weight loss is zero or less, then adjustment is
required or just order pizzas.)

correction of previous comment:

my goal-related percentage + a multiplication of a factor by my
group-contribution percentage.

my goal-related percentage being the one suggested in the answer; 
my group-contribution percentage being:
100 times my wieght loss devided by the group's total weight loss
during that week;
 the factor is a fraction or integer and should be determined by the
participants.

another one:

(my goal-related percentage) devided by (1 - my group-contribution ratio).
 
my goal-related percentage being the one suggested in the answer;  
my group-contribution ratio being: 
 my wieght loss devided by the group's total weight loss
during that week;

(my goal-related percentage) devided by (1 - f *(my group-contribution ratio)) 
  
my goal-related percentage being the one suggested in the answer;   
my group-contribution ratio being:  
 my wieght loss devided by the group's total weight loss 
during that week;
the factor f is a fraction or integer and should be determined by the
participants.