1:40 barrier broken I always find enjoyment in breaking artificial barriers / round numbers / thresholds. I wasn’t expecting this much improvement (particularly as there was some weight gain), but it was pleasant to see a 3 in the ‘tens’ place at the end of the swim.

07 October 2018
Zoltán’s 100m Time [1]	1:05.8 (no change)
My 100m Time	1:39.1 (0:05.1 improvement)
Percentages and Factors
Percentage Improvement [2]	4.89%
Percentage Faster [3]	50.61%
Percentage Slower [4]	33.6%
Speed Factor [5]	1.51
Additional Statistics
Total Strokes	48
Average Stroke Rate	29 strokes per minute
Maximum Stroke Rate	32 strokes per minute
Weight	108.2 kg (238.5 lbs)
Pool Length	25 meters
Training Distance (per week)	1200 meters

Statistics: Percentages and Factors

I was thinking about how to represent improvements and distance away from my goal as a meaningful statistic, something a bit more than just “I’m 0:33.3 away from Zoltán’s 100m Time”.  I then started down what I thought was an easy path of a “simple” calculation of “percentage off pace”.  Which seemed easy until I sat down and went to do the calculation, what should be subtracted from what, what should be divided by what, what does it mean to say I’m x% slower than Zoltán’s 100m Time.  I then opened the can of worms that is the differences of opinions on how to calculate values like this, what they mean, and what should be done.  As a result I’ve come up with four values that I’ll define here and then use on-going to help track progress.

A General Note on Percentages

There are obviously a number off different methods of calculating values like this, and below I’ve outlined four ways of doing calculations on the data set I’m creating.  It is worth noting though that the general calculation for percentage change / percentage difference is of the form ^{[6] [7]}

[Change of Value] divided by [Original Value] times 100
with [Change of Value] equal to [New Value] minus [Original Value]

^[2] Percentage Improvement

Percentage improvement was the clearest value to calculate and provides a nice gauge of overall improvement for each month.  The calculation aims to answer “How much did I improve?”.  As such this was the clearest use of the general percentage change calculation.

[Prior Month 100m Time] minus [Current Month 100m Time] divided by [Prior Month 100m Time] times 100

So for this month the calculation was

1:44.2 minus 1:39.1 divided by 1:44.2 times 100 equaling 4.89%

Percentage Improvement is a great calculation overtime, but it will have some expected interesting effects.  For example it is expected that it will be “high” for a period of time, but as my fitness increases I won’t be able to reduce my time as a percentage each month and it should “stall out” at some point and flatten out.

Percentage Faster and Slower

With the expectation that percentage improvement will have an interesting slope / diminishing return as a calculation (with the occasional spike here and there) I also wanted a bit more of a universal “How close am I to my goal” type statistic.  There were sort of two natural calculations available there, the percentage Zoltán is faster than me and the percentage that I am slower than Zoltán.

^[3] Percentage Faster

How much faster is Zoltán than I am? This is the standard calculation with Zoltán’s time being the original value an my time being the new value

[My Time] minus [Zoltán’s Time] divided by [Zoltán’s Time] times 100

So currently

1:39.1 minus 1:05.8 divided by 1:05.8 times 100

So Zoltán is 50.61% faster than me (for now)

^[4] Percentage Slower

The opposite side of the same coin: How much slower an I than Zoltán? This is just the same calculation, but with my time being the denominator.

[My Time] minus [Zoltán’s Time] divided by [My Time] times 100

It is worth noting that in both instances I use [My Time] minus [Zoltán’s Time] and this is to keep the numbers positive, while it would make sense to be negative as well, in general it isn’t as clear, the calculation result remains the same just without a negative sign.  So the calculation would currently be

1:39.1 minus 1:05.8 divided by 1:39.1 times 100

So I am currently 33.6% slower than Zoltán (for now)

^[5] Faster by a Factor of (aka Speed Factor)

Finally I wanted just a straight number that was sort of all encompassing, that would change consistently over time with improvement (even though rate of change might slow down) and would show if I was getting closer (as well as have the nice feature of not having to change language if I actually hit my target; percentage slower and faster would switch if I were to pass Zoltán).

To this I did a “faster by a factor” ^[8] calculation along the lines of Zoltán is faster by a factor of X compared to me, where that value would be 2 if Zoltán was twice as fast as me (i.e. if my time were 2:11.6 (aka 1:05.8 times 2).  This has the very nice benefit of being both meaningful and easy to calculate with the formula

[My Time] divided by [Zoltán’s Time]

So currently we have

1:39.1 divided by 1:05.8

Making Zoltán faster by a factor of 1.51

Enough Math for One Day

So that is how I came to some of the calculations displayed above. I plan on utilising these values to track some progress over time (with some data visualisations to come) as well as using these items to track some of the differences in technique, progress, fitness, and other variables (i.e. if I change my breathing technique these numbers can provide some insight into how much of a difference that change enables.

References: External Links

^[1] 100m Freestyle World Record Progression
^[6] Wikipedia: Percentage Change
^[7] Skills You Need: Percent Change
^[8] Math Stack Exchange: Faster by Factor and Faster by Percent