n = total number of days
x = total on given day
1 Day = Always 0% improvement
Even Days (2, 4, 6, etc)
𝑛
( )
2
𝑛
∑
𝑛
( )+1
2
(𝑥(𝑛) + 𝑥𝑛−1 + ⋯ ) − ∑
1
(𝑥(𝑛) + 𝑥(𝑛)−1 + ⋯ )
2
1
2
𝑥 100
𝑛
( )
2
∑
(
1
(𝑥(𝑛) + 𝑥(𝑛)−1 + ⋯ )
2
2
)
Odd Days (3, 5, 7, etc)
𝑛
𝐴𝑏𝑠( )+1
2
𝑛
∑
𝑛
𝐴𝑏𝑠( )+1
2
(𝑥(𝑛) + 𝑥𝑛−1 + ⋯ ) − ∑
1
2
1
2
𝑥 100
𝑛
𝐴𝑏𝑠( )+1
2
∑
(
(𝑥𝐴𝑏𝑠(𝑛)+1 + 𝑥(𝐴𝑏𝑠(𝑛)+1)−1 + ⋯ )
1
(𝑥𝐴𝑏𝑠(𝑛)+1 + 𝑥(𝐴𝑏𝑠(𝑛)+1)−1 + ⋯ )
2
2
)
Whenever a leaderboard is created the %improvement is always calculated down the middle from start to end.
So, using an example of a 5 day challenge with leaderboard every day:
Day 1 - 0 % improvement
Day 2 - %improvement -> ((d2-d1)/d1) * 100
Day 3 - %improvement -> (((d3+d2)-(d2+d1))/(d2+d1)) * 100
Day 4 - %improvement -> (((d4+d3)-(d2+d1))/(d2+d1)) * 100
Day 5 - %improvement -> (((d5+d4+d3)-(d3+d2+d1))/( d3+d2+d1)) * 100
Team 1
Num Steps
% Improvement
Mon
2000
Tue
4000
100%
Wed
5000
50%
Thu
6000
83.33%
Fri
9000
82%
Mon
2000
Tue
5000
150%
Wed
4000
29%
Thu
6000
43%
Fri
9000
73%
Mon
2000
Tue
6000
200%
Wed
4000
25%
Thu
5000
12.5%
Fri
9000
50%
Mon
2000
Tue
9000
350%
Wed
6000
36%
Thu
5000
0%
Fri
4000
-12%
Team 2
Num Steps
% Improvement
Team 3
Num Steps
% Improvement
Team 4
Num Steps
% Improvement