Tuesday, May 15, 2012

Many people have been asking me what is an appropriate donation level for my marathon. I thought about replying "all the money you have," but that seemed greedy.

My good friend Doug spent some time thinking about how much to donate, and came up with this handy formula, which he explained to me in an email and has permitted me to share with you.

This confirms two things I have long thought about Doug:
1. he is a deeply generous and thoughtful friend
2. he may have more mental free time than is entirely healthy

Here is his email:


Kristin,

I'll be putting in my pledge shortly, but I felt I needed to explain the particular logic and conditions inherent to this particular pledge.

As I see it, a single dollar amount would be just a gift.  This is a marathon, so the real test is endurance.  A simple pledge of $ X per hour would overvalue the early easy hours and undervalue the later hours.  So here is my proposal to you: 

For the first hour, you get nothing form me.  That's the easy one, and you sit through an hour of theater on a regular basis.

The second hour, gets 25 cents.  Still easy, but you get the equivalent of 12min at a Boston parking meter (that's a full 1/2 hour here in Gloucester).

Now hour 3 gets you 50 cents, and hour 4 a full $1.  Do you see where this is going?  Each hour thereafter doubles the pledge from the previous hour.  So those last few hours are real money.  Here's a handy chart I put together.


Hour
Unit Donation
Total Donation
1
 $           -  
 $           -  
2
 $       0.25
 $       0.25
3
 $       0.50
 $       0.75
4
 $       1.00
 $       1.75
5
 $       2.00
 $       3.75
6
 $       4.00
 $       7.75
7
 $       8.00
 $    15.75
8
 $    16.00
 $    31.75
9
 $    32.00
 $    63.75
10
 $    64.00
 $  127.75

But if you quit early, I expect to get back the value from unused hours.  Admittedly, the final figure is a bit higher than I might have pledged straight off.  But once I latched onto this idea, I couldn't pass it up.

Now get out there and sit!

-Doug

(ps. My initial thought was to start at $1 for the first hour, but that would have ended up costing me $1,023.  I love you, but not that much)

3 comments:

  1. What great math! Especially for StageSource!

    ReplyDelete
  2. Clearly all theatre people need more mathematicians as friends. I love this!

    ReplyDelete