Some (Interesting) Statistic on London Cycle Hires

Disclaimer: I have never cycled in London.

Let’s try to use a very small data set ( the number of cycle hire every day since 2010 from TFL ) to find some trends about cycle-hiring in London.

Primary Data

We can observe a similiar concave-like trend every year. The number of cycle hires increases gradually from January to May, remains faily constant till September, and decreases till December.

The total number of hires is gradually increasing from 2011 to 2014, with a drop from 2012 to 2013.

2011 7,142,449
2012 9,519,283
2013 8,045,459
2014 10,023,897
2015 (up to July) 5,747,362

Aside from that, the signal obtained from this data seems like random fluctuations / noise that does not exhibit any interesting local patterns (aside from a very large peak in July 2015). Hence, let’s try deriving some secondary data!

Secondary Data

I have calculated the proportion of hires in a day-of-week (eg: Monday, Tuesday) over the last 5 years. For example, if there are a total of 100 bicycle hires at the week starting 5 July 2010 and there are 20 hires on Monday, the value of Monday for the week starting 5 July 2010 will be assigned a value of 0.20. In case you still do not understand what proportion in our context mean, please refer the appendix.

Interestingly, this simple data transformation seems to present us some additional information:

Here are the average proportions by day of week over the last 5 years:

Day of Week Average Proportion
Sunday 0.1115
Monday 0.14389
Wednesday 0.159627
Thursday 0.157135
Friday 0.15016
Saturday 0.12195

The average proportion of hires on weekends (0.116725) is noticable lower than (0.1533), a difference of approximately 27%.

The following is the varience and average deviation (note, not standard deviation to prevent numerical problems) of the above entries:

Day of Week Varience Average deviation
Sunday 0.0010001 0.02439
Monday 0.0006385 0.01820
Tuesday 0.0005254 0.01585
Wednesday 0.0005739 0.01546
Thursday 0.0006224 0.01662
Friday 0.0005045 0.01686
Saturday 0.0008424 0.02288

The varience in proportion of hires on weekends (0.00092127) is much higher than those of weekdays (0.0005730) 46.61%.

Over the course of 260 weeks, there are approximately 13 significant peaks / statistical outliers. I will leave finding them a challenge for the readers.

Interpreting the Statistics

The following section will be biased towards how I interpret the statitstics above.

Based on the timeseries graph above, Londoners prefer not to cycle when the weather is cold, especially during winter.

The number of cyclists over the course of 4 years (2011 - 2014) is gradually increasing. The slight drop in 2013 might be due to air pollitions problems (ref: airqualitynews ). [ You probably won’t agree with this if you are a Londoner, because air pollution simply became worse in the following year , read on more a better argument! ].

The average proportion on weekends are significantly lower than those on the weekdays. This suggest that the borus bikes are indeed hired as a mean of transport by the general populus. (This might sound obvious, but in some places (eg: my hometown, Penang, Malaysia) there are specialized public transports for tourists).

An interesting little observation can be made from the average deviation. A much higher average deviaion suggest that cycle hiring on weekends a more likely for non-recurring purposes (eg: meeting a friend for coffee).

Throughout the years, a proportion peak is observed during Christmas. This is probably due to the closure of tube stations. In 2011 and 2013 (i.e. Christmas is in 2011, so by 2011 i mean end of 2011), the maximum peak at Christmas is followed by a minimum peak on new year. In other years, the cycle hires at New Year is near the week’s average. This may suggest that the populus prefer not to cycle during the festive season or holidays whenever possible. This in turn explains the size of the small peak during Christmas, despite the tube closure. (Although a more proper argument is Londoners prefer not to travel during holidays, we can’t draw that conclusion without referring to data from other forms of transportation).

A small peak during christmas

There is a very large peak in 9 July 2015. It turns out that the London Underground was suffering from one of the worst tube strikes in years (ref: BBC News). In fact, the highest number of cycle over the last five years was achieved that day (see timeseries graph below) at 73094 hires, more than three times the average over the last 5 years (23336.57 hires / day)!. There is a high chance that a high proportion of the 73094 hires are first timers. My argument will follow shortly.

A large peak due to tube strike

Similiarly, the closure on 28 November 2010 is due to a less severe tube strike (ref: BBC News). As consequences of it was much more insignificant than that in July 2015, the peak is less sharp. It may also be coupled by the fact that people prefer taking longer tube routes than cycle when the winter approaches.

A tube strike in 28 November 2010 also featured a peak, but it's much smaller than those of 9 July 2015

Furthermore, @tmhrtly also suggested that before 3 December 2010, resgistration is required prior to cycle hiring (ref: http://road.cc/content/news/27682-barclays-cycle-hire-scheme-opens-non-members-next-friday).

Comparing the two tube strikes (2015 vs 2010):

Cycle hiring required prior registration in 2010. This prevents people from simply rolling up to a bike by the road without previously registering.

Besides that, another implicit factor is technology. Smartphones are not as widespread in 2010, preventing people from getting first hand information about tube strikes and hence, planning journeys in advance efficiently.

(I’d take this opportunity to appreciate how much technology has changed in just 5 years!)

Conclusion?

From interpreting the data, with some biased subjective opinions:

Londoners cycle primarily when: (In the order of significance)

  • Tube strikes occur ( causes sudden peaks in the proportion graph )
  • They need to get to work ( more cycle hires on weekdays than weekends )

Londoners adjust their cycling schedules based on the weather, prefering not to cycle during winter. ( more cycle hires on summer than winter )

Londoners prefer not to cycle during holidays. Occasionally (inpredictable how often), Londoners prefer to hire cycle for non-recurring visits. ( the higher average deviation during weekends )

Londoners will prefer to cycle during a scheduled closures, but the effect is much less significant than tube strikes. ( trends in christmas and new year )

EDIT : It doesn’t end here, read the follow up section below!

Edit: A Little Follow Up

After sharing this article at reddit , I have got some pretty interesting feedback and suggestions. I did some extra research on the data and here is what I have found:

Summer Olympics 2012

Firstly, thanks /u/greymutt for pointing out Summer Olympics in Summer 2012. Somehow, it has completely slipped through my eye.

The summer olympics does have some impact on the july-august data.

Year July Hires August Hires Difference Percentage change
2011 708454 642440 -66014 -9.31803%
2012 1014174 1163171 148997 14.691%
2013 998755 904155 -94600 -9.471%
2014 1183182 1055206 -127976 -10.816%

NB: I dropped 2010 and 2015, because they lacked July and August data respectively

In the other years, the number of hires dropped from July to August consistently by approximately 10% every year but 2012. (I find the consistency rather intriguing; ping me @fyquah95 if you know why). The summer olympics took place in August 2012, which saw a rise in the number of hires from July to August of 14.691%.

Studying the upward trend

While I have mentioned that there is an upward trend, there seem to be an sudden surge in 2012. The graph below shall graph a little more context:

Although there is an upward trend, we can observe a large surge in Summer 2012 (especially August).

To save you from time from scrolling up, here is the annual total number of cycle hires again:

2011 7,142,449
2012 9,519,283
2013 8,045,459
2014 10,023,897

I initially argued that the disruption of a upward trend was caused by the surge in Summer 2012 due to the olympics. It turns out that I might be right, but only partially.

Let’s make an assumption : assuming we hypothetically remove all the cycle hires during both the summer olympics and paralympics. The numbers are 642,000 and 442,000 respectively (ref: House of Commons) which sums up to 1,084,000.

NB: Of course, this assumes that noone are hiring cycles during the olympics, which is of course a wrong claim. However, it should be a reasonably good estimate, factoring the traffic caused by the the pre/posts-olympic events.

Substract that number from the current table, we get:

2011 7,142,449
2012 8,435,283
2013 8,045,459
2014 10,023,897

There is something fishy about the upwards trend. A safe assumption of an upward trend would be somewhere between 8,006,889 to 8,198,979. I calculated the range via:

(+- (+ (/ (- 10023897 7142449) 3) 712449) 0.1)

Or, in more familiar mathematical notations:

delta = (10023897-7142449) / 3;
lowerbound = 7142449 + 0.9 * delta;
upperbound = 7142449 + 1.1 * delta;

The best possible explainations for the 2012 number I can think of are:

  • officials / workers visiting London to prepare for the Olympics before the event
  • some players staying in London after the tournament
  • tourists visiting the olympic stadiums

My above explainations are based on the fact that the higher number of cycle-hires are pretty evenly distributed throghout the year. Here are the data from randomly chosen months of the year:

From 2011 to 2012, these months, 3 of which are not associated to the Olympics, has shown increase in number of hires

You can see data of the other months (though I feel it is probably not necessary) here:

The Summer olympics has answered part of the question.

What happened in 2013? Why did most months show a decrease in cycle hires?

NB: most means 10 out of 12, including two of the olympic months. Even if we remove those two, 8 out of 12 is a fairly large portion of the year

We see a decrease from 9,519,283 to 8,045,459. I did argue that an air pollution warning might the reason for the sharp decrease, but that argument might be invalid

  • air pollution simply worsen in 2014.

/u/matstace pointed out (in the reddit post) that the borus bike double there access charges at New Year 2013, due to inflation (ref: standard.co.uk).

Initially, I suspected the number of Borris Bike usage will decrease to a minimum peak for the week at New Year 2013. It turns out the claim was invalid:

The Proportion chart, zoomed in to the week starting 30 December 2012. New Years’ day is the green line on the week starting 30 Dec 2012

Instead of doing a one-day protest on the price change, Londoners simply started usingh the bikes less frequently over the course of the year. Londoners might have opted for purchasing their own bikes in response to the price increase (In my opinion that’s probably the most rational course of action, both emotionally and mathematically). Since we do not have (and are not going to) use such data, we will not explore it further.

Free Access Weekend

/u/FrancisField suggested that there are dates where the borrus bikes are free for access. Logically, I’d expect those dates to be during winter, simply because people are less likely to cycle.

I tried looking for the proportions graph for a maximum peak and found it with some effort.

Notice the (rather small) pale red peak

At first glance, this peak doesn’t seem peaky enough to qualify as one. However, if you remember the proportion table from one of the sections above:

Sunday 0.1115
Monday 0.14389
Wednesday 0.159627
Thursday 0.157135
Friday 0.15016
Saturday 0.12195

This peak we have here falls on a weekend. By default, most people are less likely to cycle on weekends. The introduction of a free access scheme will increase the number of cycle-hires, but the proportion difference will not be as noticable as doing such on weekdays.

The peak was due to a free acess weekend on the 16-17 August 2014. (ref: TFL)

Wrapping Up

Thanks for spending time reading this little data analysis. I have published the code I have used for analysis on github.

However, I wish to clarrify that my statistical reasonings above are very less related to the code - The code simply aids my data visualization.

That’s it for now folks!

Appendix: Understanding the Week Proportion Transformation

This is best explain by an example:

Assume on the week starting 1 June 2012, and we have the number of hires as follows:

Day of Week Number of hires
  • Sunday 1
  • Monday 2
  • Tuesday 3
  • Wednesday 4
  • Thursday 5
  • Friday 6
  • Saturday 7

The total number of hires of the week is 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. We will have the following values on the line chart:

  • Sunday 0.0357 (1 / 28)
  • Monday 0.0714 (2 / 28)
  • Tuesday 0.1071 (3 / 28)
  • Wednesday 0.1423 (4 / 28)
  • Thursday 0.17857 (5 / 28)
  • Friday 0.2142 (6 / 28)
  • Saturday 0.25 (7 / 28)

Using such proportion patterns, we can capture “micro-patterns”, at the expense of information about the general trend of the data. In other words, we can capture local trends within a small time frame which are hardly noticable by looking at the original graph.

To illustrate this claim, consider Christmas 2011 / New Year 2012:

Even up close, a peak might be dismissed simply as a random fluctuation in the case of time series data. From a larger scale, it is simply impossible to notice the existence of this peak.

However, in the case of the proportion graph, finding the peak is trivial.

This method, as with most statistical methods, has it short comings when the usage over the week is consistently high (eg: a festival) or low. The proportions of days-of-week will simply be too equal to produce a spike.

In those conditions, it would be more appropriate to refer the original time series graph.