The Georgian vicar whose ideas could have saved Thameslink passengers from misery

London Blackfriars: not a Thameslink train in sight. Image: Getty.

The Reverend Thomas Bayes was born in Hemel Hempstead, Hertfordshire, in 1701. He grew up in London’s Southwark, and died in Tunbridge Wells, Kent in 1761. Had he lived 300 years later, a railway running from Hertfordshire to Kent via London Bridge would have been rather useful to him. And if the people who currently run that railway had paid more attention to him, everyone on the route would be a lot happier.

The Thameslink service links commuter towns to the north and south of London via the city centre. After a major timetable change this May, the network descended into chaos. Instead of the intended massive increase in services, the service through London collapsed.

Things got so bad that Govia Thameslink Railway (GTR) had to hire extra security staff to defend train crew from angry passengers. GTR’s CEO announced his resignation, although he’ll stay in place until the company finds someone willing to take on the poisoned chalice.

So what happened? First, some background. In the 1980s, British Rail (BR) reopened a disused freight line across London. This allowed BR to shift commuter services away from terminal stations, and free up peak hour space at St Pancras and Blackfriars.

This scheme worked so well that the railway went for a second round. This programme was called Thameslink 2000, after the year it was supposed to be finished. It’s nearly finished now (that’s another story). The timetable change was supposed to benefit from the new infrastructure.


Instead it collapsed. London Reconnections has outlined the underlying issues: in short, new trains were delivered late, so drivers didn’t know how to drive them; when GTR took over the franchise in 2014 the previous operator hadn’t been training new drivers, so it’s been playing catch-up; GTR’s training programme relies on drivers working overtime, which many of them don’t want to do; some new tunnels didn’t get handed over until far too late; and GTR didn’t transfer drivers to new depots in time. This meant that many drivers weren’t qualified to drive the new trains along the new routes in time for the change.

Some people might have decided to cancel at this point. But GTR had a cunning plan.

For a train to carry passengers, it needs to have a driver qualified to drive the route that it’s on, a driver qualified to drive the train, and a driver qualified to carry passengers. These don’t have to be the same person, so if you must, you can have three people in the cab, one of whom is qualified to do each. This isn’t ideal; but it’s safe, and it works.

GTR worked out that – between the drivers it had who were trained on the new trains, the drivers it had who were trained on the new routes, and the not-passenger-qualified drivers who had tested the new trains before they entered passenger service – it had enough drivers to run the new timetable by doubling or tripling up in the cab.

But it didn’t. Which is where the Reverend Bayes comes in.

The Reverend Thomas Bayes. Image: Wikimedia Commons.

If you’re working out the number of drivers you need based on traditional probabilities (statisticians call this ‘frequentism’), you look at five factors: the total number of trains needed, the number of drivers qualified for each part of the route, the numbers qualified for the right trains, the number qualified to carry passengers, and sickness/absenteeism rates.

Then you can work out the number of trains to run, based on the number of people likely to be around and qualified. On the evidence we’ve seen so far, GTR appear to have done this, and found that they were, narrowly, capable of running the service.

But there’s a problem here: people don’t come in percentages. Either you have a whole train driver or no train driver at all. And if you don’t have a train driver qualified to drive the train to Finsbury Park when it arrives at London Bridge at 7:30am on a Monday, then your whole timetable is stuffed.

Agent-based modelling is a more complicated way of looking at things than simple probability. But it has a huge advantage over simple statistical models, which is that it can deal with lumpy problems like train drivers. It requires a lot of hard maths, of the sort pioneered by the Reverend Bayes.

You use this maths to set up simulations of what will happen if you try and run the trains you have on the routes you have, using the drivers who you have. So your computer becomes a gigantic nerdy train simulator game, running the entire train timetable thousands of times, and seeing what happens each time you try to run it.

The conditions are slightly different each time: on run 3, the driver who’s off sick is Alan from Luton who is qualified to drive to Brighton but not Maidstone; on run 15, it’s Barbara from Brighton, who is qualified to drive to London Bridge but not Cambridge. The closer you can match the simulated agents to your real roster, the more accurate the simulation is.


Using this model, GTR would have found that having the right number of qualified crew is no use in itself: one person in the wrong place at the wrong time can make the whole thing fall over, even if there’s another qualified person on shift, because that qualified person is an hour’s cab ride away.

Because they didn’t do this kind of modelling, they took false reassurance from their data showing that they had enough crew. The first time their assumptions were put to the test was the first day of the real timetable – when it all fell to pieces.

If GTR had used agent-based modelling to test the new timetable, they would have had to ditch it at the last minute, which would have been horribly embarrassing. Maybe that’s why they didn’t do it. But looking back, it would have been much less embarrassing than what actually happened.

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Tackling toxic air in our cities is also a matter of social justice

Oh, lovely. Image: Getty.

Clean Air Zones are often dismissed by critics as socially unfair. The thinking goes that charging older and more polluting private cars will disproportionately impact lower income households who cannot afford expensive cleaner alternatives such as electric vehicles.

But this argument doesn’t consider who is most affected by polluted air. When comparing the latest deprivation data to nitrogen dioxide background concentration data, the relationship is clear: the most polluted areas are also disproportionately poorer.

In UK cities, 16 per cent of people living in the most polluted areas also live in one of the top 10 per cent most deprived neighbourhoods, against 2 per cent who live in the least deprived areas.

The graph below shows the average background concentration of NO2 compared against neighbourhoods ranked by deprivation. For all English cities in aggregate, pollution levels rise as neighbourhoods become more deprived (although interestingly this pattern doesn’t hold for more rural areas).

Average NO2 concentration and deprivation levels. Source: IMD, MHCLG (2019); background mapping for local authorities, Defra (2019).

The graph also shows the cities in which the gap in pollution concentration between the most and the least deprived areas is the highest, which includes some of the UK’s largest urban areas.  In Sheffield, Leeds and Birmingham, there is a respective 46, 42 and 33 per cent difference in NO2 concentration between the poorest and the wealthiest areas – almost double the national urban average gap, at around 26 per cent.

One possible explanation for these inequalities in exposure to toxic air is that low-income people are more likely to live near busy roads. Our data on roadside pollution suggests that, in London, 50 per cent of roads located in the most deprived areas are above legal limits, against 4 per cent in the least deprived. In a number of large cities (Birmingham, Manchester, Sheffield), none of the roads located in the least deprived areas are estimated to be breaching legal limits.

This has a knock-on impact on health. Poor quality air is known to cause health issues such as cardiovascular disease, lung cancer and asthma. Given the particularly poor quality of air in deprived areas, this is likely to contribute to the gap in health and life expectancy inequalities as well as economic ones between neighbourhoods.


The financial impact of policies such as clean air zones on poorer people is a valid concern. But it is not a justifiable reason for inaction. Mitigating policies such as scrappage schemes, which have been put in place in London, can deal with the former concern while still targeting an issue that disproportionately affects the poor.

As the Centre for Cities’ Cities Outlook report showed, people are dying across the country as a result of the air that they breathe. Clean air zones are one of a number of policies that cities can use to help reduce this, with benefits for their poorer residents in particular.

Valentine Quinio is a researcher at the Centre for Cities, on whose blog this post first appeared.