Monthly Archives: October 2010

When will Australia’s coal run out?

Coal exports are a growth industry for Australia. A lot is being invested in infrastructure for coal production and transport to keep this growth going. But how long will this bonanza last? After all, there is only a finite amount of the stuff in the ground.

Earlier this year, the Australian Bureau of Agricultural and Resource Economics (ABARE) released an extensive report on Australia’s energy resources. The chapter on coal included the following observation about black coal:

At the 2008 rate of production of around 490 Mt [mega-tonnes] per year the EDR are adequate to support about 90 years of production.

For those unfamiliar with the jargon of the industry,  “EDR” stands for “Economic Demonstrated Resources” which means an estimate of the total amount of coal in the ground that we could feasibly dig up.

Now some of you may already be thinking that 90 years does not sound all that long, but there’s a problem. The authors of the report do not understand exponential growth! The catch is hidden in the apparently innocuous phrase “at the 2008 rate of production”. In other words, to come up with the 90 year figure they are assuming that production levels do not grow at all for the next 90 years. Is that reasonable?

A quick look at coal production over almost 50 years would indicate that it is far from a reasonable assumption.

Coal Production chart

Australian Coal Production 1961-2008

Even to the untrained eye, a growth trend is evident in this chart, a fact which is confirmed by looking at year-on-year growth, which has averaged around 5% and has only been negative three times over the whole period.

Coal Production Growth II (chart)

Annual Growth in Australian Coal Production 1961-2008

So, where does the 90 year figure come from? According to the ABARE report, Economic Demonstrated Resources are 39.2 giga-tonnes (Gt). Add to this another 8.3 Gt of “Sub-economic Demonstrated Resources”, or SDR, (i.e. reserves that are really hard to get) gives an estimate total of 47.5 Gt for Australia’s coal reserves. Now 90 × 490 Mt (the 2008 production rate) gives 44.1 Gt, which is somewhere between EDR and the combined total of EDR and SDR. Presumably the ABARE authors are allowing for the possibility that over time it will become economically feasible to mine some of the coal that is currently classified as sub-economic.

But there is no way that 2008 production rates will be kept steady for the next 90 years. Apart from anything else, there are plenty of stakeholders in the coal industry doing their best right now to see their export business grow.

To come up with a better estimate of how long the coal might last, rather than assuming zero production growth, I will assume a constant growth rate. While the annual growth rate from 1961 to 2008 averaged 5% per annum, growth has been a little slower more recently. The last 5 years have seen growth average only 3.1% (presumably the global financial crisis did not help). Working with the ABARE estimate that viable coal reserves are 90 times 2008 production levels and assuming 3.1% annual growth in production, the reserves will in fact only last for 43 years! That is less than half the 90 year figure in the ABARE report and it starts to seem like an awfully short period of time. Since the working life of coal-fired power stations is typically around 40 years, this means any new power stations built today would still work out their useful life, but they could be the last ones we build and extract the full value of their potential productivity.

Of course, if the growth rate is higher, the time to deplete the reserves will be lower, as is illustrated in the table below. In fact, if production growth returns a long run average of 5%, then reserves would only last 34 years.

Growth Rate Years Left

Reserves 90 times 2008 production

Optimists may counter that the ABARE estimates of the available reserves might be far too conservative. Perhaps there are coal fields out there just waiting to be discovered. Surely that would give us room to have coal export growth go gangbusters, wouldn’t it? Let’s see. I’ll be generous and assume that coal reserves are in fact twice as big (EDR has not changed much over the last 30 years). Running the figures again assuming reserves total 180 times 2008 production levels still means that with 3.1% annual production growth, the coal will all be gone in 60 years and if growth is 5%, it will only last 46 years.

Growth Rate Years Left

Reserves 180 times 2008 production

Now it may be the case that climate change will trigger disasters on such as scale that in 40 years time we are not too worried about coal production, nevertheless, these basic calculations mean that some or all of the following must be true.

  • Australian coal is going to run out in around 40 years
  • The coal industry cannot continue to grow at the rate it has done over the last 50 years
  • Australian energy will be turning to coal alternatives sooner that we may expect (with or without a carbon price)
  • There is a significant expansion in EDR in the future (much greater than we’ve seen over the last 30 years)

If we are going to stretch coal supplies beyond 40 years, what can slow down the need for production? With a price on carbon not looking likely to slow Australian energy consumption in the near future, one possibility would be to reduce the share of coal production that is exported and keep more of it for our own energy needs. After all, the export share has been growing quite rapidly.

Export Share II (chart)

Share of Australian coal production exported (1961-2008)

With around 66% going offshore, there is quite a bit that could be clawed back there. But who would dare suggest slowing export growth? Maybe we will just wake up one morning and discover, with a shock, that the coal is all gone and, since it is estimated that Australia has about 6% of the world’s coal reserves, the rest of the world may face the same realisation even sooner.

Data source: ABARE (note that the 2007-08 production figures in this data set look a little lower than the 490 Mt figure quoted in the report, this is because the chart shows saleable coal which is lower than total coal extracted).

UPDATE: there was initially an error on the export share chart. Thanks to @paulwallbank for pointing it out!

Generate your own Risk Characterization Theatre

In the recent posts Visualizing Smoking Risk and Shades of grey I wrote about the use of “Risk Characterization Theatres” (RCTs) to communicate probabilities. I found the idea in the book The Illusion of Certainty, by Eric Rifkin and Edward Bouwer. Here is how they explain the RCTs:

Most of us are familiar with the crowd in a typical theater as a graphic illustration of a population grouping. It occurred to us that a theater seating chart would be useful for illustrating health benefit and risk information. With a seating capacity of 1,000, our Risk Characterization Theater (RCT) makes it easy to illustrate a number of important values: the number of individuals who would benefit from screening tests, the number of individuals contracting a disease due to a specific cause (e.g., HIV and AIDS), and the merits of published risk factors (e.g., elevated cholesterol, exposure to low levels of environmental contaminants).

As regular readers would know, most of the charts here on the blog are produced using the statistics and graphics tool called R. The RCT graphics were no exception. Writing the code involved painstakingly reproducing Rifkin and Bouwer’s theatre floor plan (as well as a few of my own design, including the stadium). For the benefit of anyone who would like to try generating their own RCTs, I have published the code on github.

RCT (Shaded theatres)

Using the code is straightforward (once you have installed R). Copy the two files plans.Rdata and RCT.R onto your computer. Fire up R and switch to the directory containing the downloaded files. Load the code using the following command:


You will then have a function available called rct which will generate the RCTs. Try the following examples:

rct(18, type="theatre")
rct(18, type="stadium")
rct(c(10, 8, 5))

The rct function has quite a few optional parameters to tweak the appearance of the theatre:

rct(cases, type=”square”, border=”grey”, fill=NULL, xlab=NULL, ylab=””, lab.cex=1, seed=NULL, label=FALSE, lab.col=”grey”, draw.plot=TRUE)

  • cases: single number or vector giving the number of seats to shade. If a vector is supplied, the values indicate how many seats of each colour to shade. The sum of this vector gives the total number of seats shaded
  • type: the floor plan to be used. Current options are “square”, “theatre” (the original Rifkin and Bouwer floor plan), “stadium” and “bigsquare”
  • border: the color for the outlines of the floor plan
  • fill: vector of colours for shading seats. If no value is supplied, the default is a sequence of shades of grey
  • xlab: text label to appear below floor plan. Default is “x cases in n”
  • lab.cex: character expansion factor (see ‘par’) to specify size of text labels (if any) on the floor plan
  • seed: specify the starting seed value for the random number generator. Setting this makes it possible to reproduce exactly the same shaded seats on successive calls of rct
  • label: if TRUE, any text labels for the specified floor plan will be displayed
  • lab.col: colour used for any text labels
  • draw.plot: if this is FALSE, the RCT is not drawn and instead a data frame is returned showing the seats that would have been shaded and the colours that would have been used

Risk Characterization Stadium

Shades of grey

The recent post on the risks of smoking looked at Rifkin and Bouwer’s “Risk Characterization Theatre” (RCT), a graphical device for communicating risks. The graphic in that post, which compared mortality rates of smokers and non-smokers taken from the pioneering British doctors smoking study, highlighted both the strengths and weaknesses of RCTs.

The charts certainly illustrate the risks of smoking in a striking way and seem to elicit a far stronger reaction than drier statistical tables or charts. I also suspect that, for many people, the charts succeed in conveying the relative risks more effectively than more traditional approaches. On the other hand, there is no doubt that RCTs are extremely inefficient. The smoking graphic required an awful lot of ink to represent a mere eight data points.

In the comments on the original post, it was suggested that a colour-coding scheme could be used to combine the charts for the different age ranges, reducing the inefficiency while still preserving the immediacy of the theatre graphic. I took that as a challenge, and here is the result. Returning to the Rifkin and Bouwer theatre floor plan, rather than the more prosaic squares, I have coded deaths in different age ranges with shades of grey: the earlier the death, the darker the grey.

RCT (Shaded theatres)

Mortality of doctors born between 1900 and 1930

The risks of smoking still come through clearly in this version of the chart, but the increased efficiency may come at the expense of a potential for confusion.

What do you think?

Natural frequencies

In my last post, I made a passing reference to Gerd Gigerenzer’s idea of using “natural frequencies” instead of probabilities to make assessing risks a little easier. My brief description of the idea did not really do justice to it, so here I will briefly outline an example from Gigerenzer’s book Reckoning With Risk.

The scenario posed is that you are conducting breast cancer screens using mammograms and you are presented with the following information and question about asymptomatic women between 40 and 50 who participate in the screening:

The probability that one of these women has breast cancer is 0.8%. If a woman has breast cancer, the probability is 90% that she will have a positive mammogram. If a woman does not have breast cancer, the probability is 7% that she will still have a positive mammogram. Imagine a woman who has a positive mammogram. What is the probability that she actually has breast cancer?

For those familiar with probability, this is a classic example of a problem that calls for the application of Bayes’ Theorem. However, for many people—not least doctors—it is not an easy question.

Gigerenzer posed exactly this problem to 24 German physicians with an average of 14 years professional experience, including radiologists, gynacologists and dermatologists. By far the most common answer was that there was a 90% chance she had breast cancer and the majority put the odds at 50% or more.

In fact, the correct answer is only 9% (rounding to the nearest %). Only two of the doctors came up with the correct answer, although two others were very close. Overall, a “success” rate of less than 20% is quite striking, particularly given that one would expect doctors to be dealing with these sorts of risk assessments on a regular basis.

Gigerenzer’s hypothesis was that an alternative formulation would make the problem more accessible. So, he posed essentially the same question to a different set of 24 physicians (from a similar range of specialties with similar experience) in the following way:

Eight out of every 1,000 women have breast cancer. Of these 8 women with breast cancer, 7 will have a positive mammogram. Of the remaining 992 women who don’t have breast cancer, some 70 will still have a positive mammogram. Imagine a sample of women who have positive mammograms in screening. How many of these women actually have breast cancer?

Gigerenzer refers to this type of formulation as using “natural frequencies” rather than probabilities. Astute observers will note that there are some rounding differences between this question and the original one (e.g. 70 out of 992 false positives is actually a rate of 7.06% not 7%), but the differences are small.

Now a bit of work has already been done here to help you on the way to the right answer. It’s not too hard to see that there will be 77 positive mammograms (7 true positives plus 70 false positives) and of these only 7 actually have breast cancer. So, the chances of someone in this sample of positive screens actually having cancer is 7/77 = 9% (rounding to the nearest %).

Needless to say, far more of the doctors who were given this formulation got the right answer. There were still some errors, but this time only 5 of the 24 picked a number over 50% (what were they thinking?).

The lesson is that probability is a powerful but confusing tool and it pays to think carefully about how to frame statements about risk if you want people to draw accurate conclusions.

Visualizing smoking risk

Risk is something many people have a hard time thinking about clearly. Why is that? In his book Risk: The Science and Politics of Fear, subtitled “why we fear the things we shouldn’t–and put ourselves in greater danger”, Dan Gardner surveyed many of the theories that have been used to explain this phenomenon. They range from simple innumeracy, to the influence of the media, or even the psychology of the short-cut “heuristics” (rules of thumb) we all use to make decisions quickly but that can also lead us astray.

In Reckoning With Risk, Gerd Gigerenzer argues that the traditional formulation of probability is particularly unhelpful, making calculations even harder than they should be. Studies have shown that even doctors struggle to handle probabilities correctly when explaining risks associated with illnesses and treatments. Gigerenzer instead proposed expressing risk in terms of “natural frequencies” (e.g. thinking in terms of 8 patients out of 1,000 rather than a 0.8% probability) and tests with general practitioners suggest that this kind of re-framing can be very effective.

The latest book on the subject that I have been reading is The Illusion of Certainty: Health Benefits and Risks by Erik Rifkin and Edward Bouwer. Rifkin and Bouwer are particularly critical of the common practice of reporting medical risks in terms of relative rather than absolute frequencies. When news breaks that a new treatment reduces the risk of dying from condition X  by 33%, should you be excited? That depends. This could mean that (absolute) risk of dying from X is currently 15% and the treatment brings this down to 10%. That would be big news. However, if the death rate from X is currently 3 in 10,000 and the treatment brings this down to 2 in 10,000 then the reduction in (relative) risk is still 33% but the news is far less exciting because the absolute risk of 3 in 10,000 is so much lower.

In an effort to facilitate the perception of risk, Rifkin and Bouwer devised an interesting graphical device. They note that it is particularly difficult to conceive and compare small risks, say a few cases in 1,000. In thinking about this problem, they came up with the idea of picturing a theatre with 1,000 seats and representing the cases as occupied seats in that theatre. They call the result a “Risk Characterization Theatre” (RCT). Here is an example to illustrate a 2% risk, or 20 cases in 1,000.

Risk Characterization Theatre

Now data visualization purists would be horrified by this picture. In The Visual Display of Quantitative Information, Edward Tufte argues that the “ink to data ratio” should be kept as low as possible, but the RCT uses a lot of ink just to display a single number! Still, I do think that the RCT can be an effective tool and perhaps this can be justified by thinking of it as a way of visualizing numbers rather than data (but maybe that’s a long bow).

Attractive though the theatre layout may be, there is probably no real need for the detail of the aisles, seating sections and labels, so here is a simpler version (again illustrating 20 in 1,000).

Simple Risk Characterization Theatre

To illustrate the use of RCTs, I’ll use one of the case studies from Rifkin and Bouwer’s book: smoking. One of the most significant studies of the health effects of smoking tracked the mortality of almost 35,000 British doctors (a mix of smokers and non-smokers). The study commenced in 1951 and the first results were published in 1954 and indicated a significantly higher incidence of lung cancer among smokers. The study ultimately continued until 2001 and and the final results were published in the 2004 paper Mortality in relation to smoking: 50 years’ observations on male British doctors.

The data clearly showed that, on average, smokers died earlier than non-smokers. The chart below would be the traditional way of visualizing this effect*.

Smoking Survival RatesSurvival of doctors born between 1900 and 1930

While it may be clear from this chart that being a smoker is riskier than being a non-smoker, thinking in terms of percentage survival rates may not be intuitive for everyone. Here is how the same data would be illustrated using RCTs. Appropriately, the black squares indicate a death (and for those who prefer the original layout, there is also a theatre version).

Smoking RCTsMortality of doctors born between 1900 and 1930

This is a rather striking chart. Particularly looking at the theatres for doctors up to 70 and 80 years old, the higher death rate of smokers is stark. However, the charts also highlight the inefficiency of the RCT. This graphic in fact only shows 8 of the 12 data points on the original charts.

So, the Risk Characterization Theatre is an interesting idea that may be a useful tool for helping to make numbers more concrete, but they are unlikely to be added to the arsenal of the serious data analyst.

As a final twist of the RCT, I have also designed a “Risk Characterization Stadium” which could be used to visualize even lower risks. Here is an illustration of 20 cases in 10,000 (0.2%).

Risk Characterization Stadium

* Note that the figures here differ slightly from those in Rifkin and Bower’s book. I have used data for doctors born between 1900 and 1930, whereas they refer to the 1900-1909 data but would in fact appear to have used the 1910-1919 data.

Getting caught in the traffic

Guest author @pfh007 returns today to the Stubborn Mule. Staying on the theme of Sydney transport, but moving from train lines to motorways, he once again pulls out his beer coaster calculator (perhaps one day I’ll get him onto R).

QUICK SUMMARY: The proposal to widen the M2 motorway in Sydney recently received government in principle agreement.  This post examines the risk that due to a provision in the original motorway deed the widening proposal may put at risk the completion a rail link to North West Sydney until after 2046!

UPDATE – 26 October 2010  – Government announces it has now signed the deal with the operators to widen the M2!

The recent post “Playing with trains” took a stab at a cost-benefit analysis for a North-West rail link in Sydney. In the comments on the post, the question arose as to whether the construction of a rail link would require compensation payments to be made to the operators of the Hills M2 motorway, since the original agreement to build the M2 included a provision that provided protection from any government action that undermined the viability of the toll road.  In this post I will dig into this “no-prejudice” provision.

Naturally, any compensation payment(s) would be an additional cost in building and/or operating the North-West rail link and thus might be a factor in decisions to build it and where to locate it.

Last week the NSW government announced that an in-principle agreement had been reached with the operators of the M2 motorway to widen certain sections of the motorway.  The ASX announcement by Transurban stated that the costs of widening the road were $550 million and provided for the extension of the original concession period by 4 years to 2046.

The announcement was, however, silent as to how the no-prejudice provision in the original M2 agreement would apply to the road-widening proposal. This was surprising as the no-prejudice provision had been very controversial when first revealed in the 1990’s and it seems relevant to the recent discussions about rail or metro links to the North West.

Time for some more Google-assisted beer coaster calculations!

First stop is to find out what the original M2 no-prejudice provision actually said.  Google could not produce the actual deed but it did produce this interesting old report from the NSW Auditor General.

The M2 Deed and the “no-prejudice” provision.

The Auditor General report sets out the no-prejudice provision. In summary, the provision provides that if the NSW government takes action relating to the servicing of the transport requirements of the North West of Sydney which prejudices the operational results of the M2, then it will negotiate with the trustees so that the investors in the M2 will get the lower of the base-case equity return or the equity return they would have received if the prejudicial event had not occurred.

Of great interest to rail fans is the content of a letter from the Chairman of the Hills Motorway that the Auditor General included in the report. This “side letter”, which pre-dated the M2 deed, stated:

The Hills Motorway acknowledges the announcement of the New South Wales Government proposing a mass transit route connecting Parramatta to Hornsby via Epping, utilising the Carlingford line alignment in part.

The Hills Motorway proposes to execute the M2 Motorway Project Deed, having taken into account the above proposal and its likely impact on the M2 Motorway. As a consequence, the development of the Parramatta to Hornsby Mass Transit Route would not constitute grounds for negotiation under the M2 Motorway Project Deed.

The Auditor-General noted that the letter appeared to mitigate claims by the operators for at least the Parramatta-Epping section of any Chatswood to Parramatta rail link.

On the face of it, the no-prejudice provision would therefore appear to be directly relevant to action by the government to

  • introduce or increase bus services to the North West
  • build a heavy rail link to the North West
  • build a metro line to the North West
  • improve other roads servicing the North West

if those actions might reduce the number of toll payers using the M2 and thereby “prejudice the operating results from the M2 motorway”.

There is nothing really remarkable about having a provision like the no-prejudice provision.  If you were an investor and had just stumped up a lot of money to build a toll road, you would not be too happy if the government then decided to undermine your business model by providing an alternative transport option to your potential toll payers.

The question is whether the current no-prejudice provision is too wide and should, for example, be limited to certain types of government action (such as selling another competing toll road concession) and whether, while negotiating to widen the M2, now is a good time to clip its wings.

Has the “no-prejudice” provision ever flapped its wings?

The 1994 letter concerning the Parramatta to Epping rail proposal suggests that both Hills Motorway and the government of the day considered the no-prejudice provision to be a serious issue, but I have been unable to locate any information that confirms whether the existence of the provision has been a significant factor in any government decision or in the resolution of any issue relating to the M2 motorway since then.

It would be interesting to know whether there was any correspondence or discussion between the government and Hills Motorway about the Chatswood to Epping rail link before it was completed as the Auditor General notes it does not appear to be covered by the 1994 side letter to the M2 deed.

I have a hazy recollection that the initial introduction of bus services on the M2 was not all plain sailing.  I think there may have been an argument at some stage between the government, the M2 operator and Hills buses about the terms of commuter bus access to the M2. As that debate occurred in the era of human history now known as the pre-Googlassic, I was unable to locate any online references.  It would be interesting to find out if, in the course of those negotiations, there were discussions about the extent to which public bus services might prejudice the operating results of the M2.

One immediate question that comes to mind is whether the public bus services that use the M2 pay a special toll or whether the government pays the M2 operator some sort of compensatory payment that reflects the fact that 17,000 public bus trips each day might be considered to result in a certain number of individual M2 car/toll trips avoided.

Presumably, there was some discussion about the provision before the Metro link was announced but as the link was initially only going as far as Rozelle perhaps not.

Missing in Action – The “no-prejudice” provision

Despite its relevance to both a proposal to widen the M2 and to building a metro line or heavy rail link to the North West of Sydney, the no-prejudice provision has been keeping a low profile lately.

I am more than happy to be directed to some information on discussion of the application of the no-prejudice provision to the M2 widening proposal, but I was unable to find any reference or discussion of it on the RTA website, the Hills Motorway website or the 277 page RTA “Submissions and Preferred Project Report (August 2010)”.

The closest I found were some submission questions on pages 123‒133 of that document, but the responses to those questions did not touch on the no-prejudice provisions in the original M2 Deed.

Does it really matter?

If you read the RTA Submissions and Preferred Project Report (August 2010), the impression given is that the North West region of Sydney is generating a swelling sea of cars and that buses and new rail links do not reduce the need to increase the capacity of the M2.  This might suggest that we can sleep easily and not worry about dusty old provisions from 1994 that require the government to guarantee the returns of investors.

But it might also suggest that there is no good reason to retain the no-prejudice provision in its present form.  At the very least, it might suggest that in coming to an in-principle agreement with the M2 operator to widen the current motorway, now is a good time to modify the provision to explicitly exclude the impact of new bus services, new rail links and other public transport options as events that may trigger the no-prejudice provision.

Finally, one last reason for caution.  Traffic forecasting appears to be a very challenging science.  The history of Sydney’s toll road projects has been remarkable in the regular disconnect between the estimates of traffic flow contained in the glossy prospectus documents and the number of toll payers who actually turn up when the red ribbon has been snipped and they have to start paying.

I am no expert in this area and the forecasts underpinning the M2 widening proposal may prove 100% accurate, but I would feel more comfortable if the tax payer was not exposed to the risk that they do not.

On page 129 of the RTA document, response (b) notes that the tolls from the increase in usage after widening would not be sufficient to fund the project and that is why the widening deal involves an increase in the toll of 8% and an extension of the concession period by 4 years.  That suggests that a failure to hit usage targets will readily prejudice the operating results of the M2.

Finally, it is also worth noting that a large chunk of the Auditor General report on the M2 that I referred to earlier was concerned with the forecasts of traffic numbers contained in the original prospectus. More on that below.

Calculating the Prejudice

Leaving to one side what a flock of lawyers and judges might decide the words of the no-prejudice provision actually mean, how might we go about calculating the prejudice?

Time to turn over the beer coaster!

According to the RTA, approximately 100,000 vehicles currently use the M2 every day. That is an interesting figure because the Auditor-General’s report in 2000 set out the original base case projection of traffic numbers by 2010 to be 94,659, but only 76,289 under the then proposed financial restructuring. Transurban’s figures report that in the Sept 2010 quarter 96,983 trips per day were made on average, or 105,068 trips on the average workday.

The vehicle figures (whichever you prefer) suggest that the M2 is currently going gang-busters and exceeding the traffic projections made when the original deed was entered in 1994. That, of course, is entirely consistent with a proposal to widen the roadway.

If the M2 is currently at or exceeding capacity, minor government action would seem unlikely to prejudice the operating results of the M2.  A few additional bus services to the North West are unlikely to trigger the no-prejudice provision.

The Transurban ASX announcement states that one of the objectives of the M2 widening project return is to achieve by 2016 an increase in average daily trips of 17,300.

Current toll revenue

Currently the toll on the M2 is $4.95 for a Class 2 vehicle (cars and motorcycles) and $14.50 for everything else (trucks, etc) for the full route, or less to Pennant Hills Road ($2.20 and $7.10 respectively).

According to Transurban figures for the Sept 2010 quarter they earned approximately $36.7 million net of GST which is about $40.37 million inclusive of GST.

That equals $161.48 million per annum including GST.

Their daily average figure of approximately 97,000 trips amounts to about about 35.4 million trips per annum.

That suggests an average toll per trip inclusive of GST of $4.56.

Toll revenue in 2016

Assuming that an 8% increase in toll is applied, the average toll per trip stays constant (plus the 8%) and the 17,300 extra trips are occurring by 2016, then the toll revenue figures will have increased substantially.

114,300 car trips per day at $4.92 (the average toll per trip $4.56 + 8%) = $562,356 per day or $205.3 million per year.

That’s a tidy revenue increase of $43.8 million per annum (inclusive of GST) per year for the remainder of the now longer concession period (2016 to 2046, 30 years) for the $550 million investment to widen the road.

Needless to say the above figures are beer coaster calculations.

Could the M2 experience train pain?

How much pain could a heavy rail link to the North West cause?

As beer coaster fanciers would recall from the “Playing with trains” post, a modestly efficient heavy rail link to the North West with 15 train stations could move approximately 30,000 passengers on 25 services (at 6 minute intervals) during the morning peak period of 6.15 am‒8.45 am, or 60,000 trips assuming every person returned to their home each night.

Assuming that only 10 of the stations proposed are likely to compete with the M2, that would mean that competing stations on the North West rail link could service 40,520 commuter trips each day (once again assuming that the stations have equal passenger loads of 2,026 people per morning peak period).

As discussed in the rail post, securing that many commuters will not be easy and may require substantial re-zoning to increase population densities and perhaps other policies to build patronage on the new rail link, such as building extensive commuter car parks and connecting bus services throughout the catchment. The actions are also likely to decrease the appeal of a daily return trip on the M2.

Let’s assume that the rail link was built (and, conveniently for this exercise, that it is done by 2016—yes, optimism is good for the soul) and succeeded in achieving only 66% of capacity—attracting only 20,000 passengers each morning peak period to its 25 comfortable air-conditioned Waratah carriage (only a few months away now, fingers crossed) equipped services.

Let’s also assume that 40% of those 20,000 passengers are car users who have been attracted by the thought of relaxing and reading their iPads on the train rather than listening to honking horns and breakfast radio on the M2.  Those 8,000 train converts represent 16,000 lost trips each day on the M2.

The value each day of those lost trips is 16,000 × $4.92 = $78,700 per day or $18.1 million per annum (assuming they work 230 = 46 × 5 days per year) .

Considering that the business case for the widening of the M2 has a target of 17,300 extra trips by 2016, there could be some unhappiness if the majority of those 17,300 exciting motorway trips vanished into a railway tunnel.

That unhappiness would only increase if the railway hit its target capacity of 30,000 passengers per peak period (60,000 trips) and 50% of them were lost trips on the M2.   A loss of 30,000 $4.92 toll payments per day would represent an annual loss of toll revenue on the M2 of $33.95 million per annum (again assuming those train commuters only turn up to work 230 days per year).


That would mean that the tidy toll revenue increase of $43.8 million per year under the widening proposal might shrink to $9.85 million if there was a North West rail link that could attract 15,000 people who would otherwise be paying a toll to travel on the M2.


As the estimated ticket revenue in my train post from approx 30,000 people paying $50 for a weekly ticket was only $70 million, it would be a nasty sting if $33.95 million of that had to be handed over to the M2 operators as compensation for loss of toll revenue.

It seems highly likely that a moderately well-patronised and well-designed new rail link to the North West (that interconnects with the Chatswood-Parramatta railway) would have the potential to prejudice, perhaps significantly, the operating results of an M2 that is widened and has a daily trip capacity increase from 97,000 trips to 114,300 trips per day. It is even possible that a well-designed and run North-West rail link could prejudice the operating results of the M2 without any widening taking place, but that is less likely as the M2 is already exceeding the capacity that formed part of the original base case for the road.


The absence of any substantial public discussion of the application of the no-prejudice provision in 1994 Deed to the M2 widening proposal and a North-West rail link and the potential for possible compensation payments to the operators of the M2 is surprising.

No doubt people with much bigger beer coasters than I have available will have performed much more sophisticated modeling of the potential impact of governments actions like a North West rail line or significantly expanded public bus services on the number of vehicles using the M2 per day. But even with my little beer coaster, it seems that there is real potential for government action servicing the transport requirements of North West Sydney to prejudice the operating results of a widened M2.

The problem is clear.

If the agreement to widen the M2 is likely to expose the government (and therefore the residents of NSW) to even greater risk of compensation should a North-West rail link go ahead, then the likelihood of a North-West rail link being approved for construction is reduced as those compensation costs would weigh heavily on the decision.  Furthermore, every action taken to improve patronage by creating bus links to train stations, or commuter parking or expanding the number of  services will only worsen the problem and understandably meet some resistance from the M2 operator.

Of course if the sophisticated modeling, that I am sure is on a laptop somewhere in Sydney, shows that future public transport by rail and bus to the North West will not prejudice the operating results of the M2, because the M2 when widened will have no trouble attracting 114,300 trips per day, then the agreement to widen the M2 should include a modification of the original no-prejudice provision to exclude future public transport services to North West Sydney as potential triggers for the operation of the provision.

At the very least there can be no harm in releasing the modeling that has been done on this issue so that the context of the in-principle agreement to widen the M2 and its potential implications on future public transport to North West Sydney can be fully understood by the community.

Bubbles to Brains

A couple of weeks ago I ranted about a bubble chart which attempted to illustrate trends in CDO issuance by large investment banks. If circles are a bad choice for depicting data, pictures of brains are even worse, but brains are what the BBC News designers settled on when it came to looking at the countries which have been most successful at winning Nobel prizes.

Nobel Brains - bad chart

There is no doubt that the idea to link Nobel prizes to brains is an appealing one, but comparing the relative sizes of these blobs of grey matter is not easy. In fact, it’s hard to avoid simply reading the numbers rather than looking at the graphics, which rather defeats the purpose of charting the data. A simple league table would have done the same job.

This would come as no surprise to William Cleveland, a statistician who took an experimental approach to understanding the effectiveness of different graphing techniques. In Graphical Perception: Theory, Experimentation, and Application to the Development of Graphical Methods, published jointly with Robert McGill in 1984, Cleveland ranked our ability to judge variation in charts in the following order:

  1. Position along a common scale
  2. Positions along nonaligned scales
  3. Length, direction, angle
  4. Area
  5. Volume, curvature
  6. Shading, color saturation

Furthermore, Cleveland’s experiments used circles rather than brains when area perception was tested and I suspect, brains would fall somewhere between four and five. This perception ranking also points at a better choice of graphic: a simple bar chart, which relies on judgement of length rather than area. Better still, since the bars have a common baseline, comparing them in fact requires judgement of position along a common scale, the easiest of the perception tasks.

Nobel Prize Bar ChartTop 5 Nobel Prize winning countries from 1901

The bar chart is much easier to read, but it may seem a little pedestrian to graphic designers excited by the idea of weaving in a brain image. While I am happy with the simple bar chart, sprucing it up with a background image does not interfere very much with the ease of reading the data. Here is an example, although I am sure those more adept at the use of Photoshop (or Gimp in this case) could come up with something better still.

Nobel Prize Bar Chart with Brain

The BBC post includes two more charts, which also have their shortcomings. The pie chart showing just how few women have won Nobel prizes is a particular waste of space. Certainly it is evident from the chart that women have not been awarded very many prizes, but simply stating in words that “the 41 of 806 prizes that went to women represent a mere 5.4%” does an even better job. Of course, the percentage could be added to the chart, but the necessity of adding a lot of numbers to a chart is a sure sign that the chart is not doing its job very well.

Forget the wisdom of crowds!

Congratulations to all you insightful Stubborn Mule readers! Despite the fact that pricing in the financial markets was indicating around a 60% probability of the Reserve Bank hiking the official interest rates, participants in a poll here on the blog put the chances of no move at 60%. Even the fact that Sportsbet punters* were tipping a rate rise did not sway Mule readers. And it turns out that they had a better read of the RBA tea-leaves than the so-called experts. Today the RBA announced they were leaving the official cash rate unchanged. Well done, all of you!

* Interestingly, Sportsbet have pulled financial bets from their website. Perhaps the Mule post on the topic had some repercussions. UPDATE: their financial bets are up and running again.

Playing with trains – a North-West rail link

Not content with scrutinising the plan for a National Broadband Network in Australia, guest contributor @pfh007 has now turned his analytical beer coaster to a network of a different sort: a railway network.

There is a Ph.D. for the taking by any researcher who is able to unlock the evolutionary origins of the propensity of young children (and many older people) to be mesmerised by trains, even the generic suburban variety. You can see the rush of endorphins on the faces of weary commuters as an express service roars past within a metre or two of their aching feet. People seem to have a railway gene.

Sydney Train

During the 1970s and early 1980s, the annual model train exhibition held in the Willoughby Town Hall in Chatswood was a highlight for the local kids. It took a full day to observe every detail of the elaborate models complete with green fuzz trees, fields of tiny cows and platforms full of frozen people and Hornby OO gauge recreations of famous rolling stock clattering around and around. Although remarkable as demonstrations of what can be achieved in a backyard shed, those models and their kin were probably responsible for turning large measures of the population into armchair rail network designers.

Consider this a contribution from one such Backyard Bradfield.

One of the striking features of the recent federal election was the ferocious response to the promise to complete the Epping to Parramatta section of the Chatswood to Parramatta line even though new (or finally completed) rail should be of immense appeal to residents of the area. It seems clear that the strength of the reaction was largely due to the failed rail promises of recent NSW political history. In short people were tired of having their railway gene tweaked for short term political advantage.

At one level it is hard to understand why building a new railway in Sydney is so difficult. Unlike the technological challenges facing the early railway builders in Sydney (see the ponies and pick axes in the photos at Museum Station) we have access to marvellous mole-like machines that can bore tunnels right through the Sydney sandstone. We also have advanced administrative systems for compensating people whose houses must give way to new surface track. Shanghai has been laying a new subway at a great rate over the last 15 years, so why can’t Sydney?

Could the problem be cost, even though modern technology and construction methods should have caused construction costs to fall over the last 100 years? Perhaps it is not so much the cost as the complexity of the financing arrangements, which have become too ‘elegant’. The Waratah train deal seems remarkably ‘elegant’ and yet, according to the press, it is poised for implosion.

I think the real problem is that these days we are spending too much time thinking about what we want rather than what a railway needs to be viable. That is we should decide to build a railway and then shape that part of the city to suit the railway. After all, if the majority of Sydney’s suburbs were designed around the car it is highly unlikely that they will be suited to a rail line without substantial modifications.

As the National Broadbank Network (NBN) has established back of the beer coaster calculations as a valid method of policy analysis, I will adopt that technique for some rough calculations of the North-West rail line viewed from the perspective of the needs of the railway.


Using Google Maps, the following route seems reasonable in terms of not going too close to existing rail lines. The precise route is not critical as the demographics and structure of the suburbs will change to suit the new rail line by way of changes to zoning requirements.

Number of Stations: 15

Balmain, Drummoyne, Gladesville, Top Ryde, Denistone East, Eastwood (interchange with Northern Line), Carlingford (interchange with Chatswood-Parramatta Line), North Rocks, West Pennant Hills, Castle Hill, Kellyville, Rousehill, Box Hill, McGrath’s Hill and ending at Windsor.

Train Capacity

Capacity of the new Waratah trains is 896 seated (8 carriages) and, say, another 320 standing (20 in each vestibule) = 1,216 people in total per train

Peak Hour Capacity

The beer coaster is not very big so I will stick with peak hour only and peak “hour” is taken to extend from 6.15 am to 8.45 am, so 2.5 hours. We want a well-signaled, well-designed speedy network that can handle trains at 6 minute intervals. This means we can run 10 trains per hour. Thus the number of peak hour trains is limited to 25 trains.

25 trains in 2.5 hours can carry between 22,400 people (all seated) and 30,400 people (40 standing in each carriage) into the CBD.

I have assumed that during peak hour everyone gets on and travels to the city and everyone comes home by train at the end of the day. I have also assumed that every train going in the opposite direction during peak hour is empty

Station Capacity at Peak Hour

With a capacity at 30,400 people between 6.15 and 8.45 am and assuming that the load is spread equally between all 15 stations, each station will process 2,026 passengers during peak hour. Assuming they all arrive evenly spaced during peak hour, there would be no more than about 80 people on the platform at any one time.

Ticket revenue generated by Peak Hour Capacity

Assuming that everyone works about 46 weeks per year and no one uses the train for any other purpose the revenue generated by the new line (at $50 per week for a weekly ticket) is 30,400 × 46 × 50 = $69,920,000 (roughly $70 million per year)

Certainly people will use the rail line outside of peak hour, but as they will often be concession fares, etc. it is probably safer to do the sums on the basis of the peak hour capacity.

Out of that $70 million you will need to remove operating costs (say $25 million) leaving you with $45 million to pay down the debt used to construct the rail line. As $45 million would only produce a 6% return on $750 million worth of bonds and building the line would cost a lot more than that, there is quite a large shortfall to be found.

To give you an idea of how much that shortfall might be, the price tag for completing the Epping–Parramatta line is estimated at $2 billion.  It seems likely that the cost for the full North-Western rail line would be well in excess of $5 billion.  How do we cover the shortfall?

Remodeling the suburbs along the route

The beer coaster calculations make it quite clear that the finances of our beloved new railway are marginal even if we squeeze 1,200 people on trains running every 6 minutes non-stop between 6.15 am and 8.45 am.

That means we need a nice steady supply of warm bodies arriving at the station.  Where will they come from?  This is what demands the remodeling of the suburbs along the route.  Unless there are  sufficient people who can use the rail line we will not even get to the stage of trying to convince them to use it.

Finding 30,400 people in a Sydney of 4 million during peak hour can’t be that hard, can it?

Well yes it can.

It is worth keeping in mind that, currently, the inner West line in Sydney only runs about 4 services per hour in peak time and you can usually get a seat at Petersham, which is one of the closer stops to the city.  That means that, even in the relatively densely-populated inner Western suburbs of Sydney, it would be a struggle to get anywhere near 30,400 people.

Walkers are unlikely to want to walk more than 15 minutes to the station. It may be that  most people will only be willing to walk a shorter distance. A 15 minute walk at a brisk pace is only 1.5 km.  That means that the walker catchment for each railway station will be a circle of radius 1.5 km.

Bus links and commuter car parks can help extend the catchment for each station, but when you are trying to get an average of 2,026 people to each station during the peak hour, that means a lot of buses or a rather large commuter car park for each station.

The only practical solution is to permit or, better still, encourage medium-high density housing for a 1.5 km radius around each of the 15 stations. Ideally this would be mixed office/housing/retail construction so that the inhabitants of the 1.5 km zone might get away without having a car at all.

On the assumption that only 20% of the people living in the 1.5 km radius will be daily commuters, we will need about 10,000 inhabitants in each 1.5 km radius to generate the 2026 passengers. That is quite a lot of houses or, more likely, apartments (say 5,000–2 people per dwelling).

The re-modeling will not require an army of town planners.  Simply change the zoning rules for the 1.5 km radius around each station to allow medium-to-high density construction of approximately 5,000 dwellings and let the builders and developers of Sydney do the rest.

If this approach was applied to the other rail lines in Sydney we may find that we can deliver an enormous supply of new dwellings (apartments) over the years ahead without any increase in the area occupied by Sydney.  This would allow the preservation of the market gardens on the outskirts, which currently supply much of Sydney’s vegetables.

Needless to say, an increased supply of dwellings where people want to live will go a long way to making housing more affordable in Sydney.

What about the shortfall between construction costs and ticket revenue?

It might be possible to increase the weekly ticket price, but I think $50 is probably a price that will not cause too much “sticker shock”.

It is hard to justify making people outside the railway catchment pay the cost as they will probably have their own rail link developments to fund. It seems reasonable that the shortfall between ticket revenue and paying the construction cost should be recovered from all the property owners in the railway catchment as the rail line will increase the value of their properties.

This could be done by imposing an annual State “infrastructure” tax on houses in the catchment for as long as it takes to retire the bonds issued to raise the construction capital (perhaps 20 years). The rate of the tax could vary depending on the benefit to the taxed property of the rail line.

For example:  the 75,000 dwellings (15 × 5,000) within the 1.5 km radius of each of the 15 stations might pay $3,000 per year for 20 years and the 300,000 dwellings (I have no idea how many there are!) outside the 1.5km radius but still within the railway catchment might pay $750 per year for 20 years.   This ‘infrastructure’ tax would raise $450 million per year.  Add in the $45 million from ticket sales and the annual total of $495 million would pay 6% interest on about $8.2 billion worth of government bonds (or less for a non-government borrower). Taking into account repayment of principal as well over, say, a 20 year period, the debt $450 million could support would be closer to $5 billion.

Not quite there, as the construction cost is probably a lot more than $5 billion but at least in the ball park!

Is it all too hard?

The numbers above are all beer coaster figures, but they do suggest that better public transport has a real cost and involves changes that cannot be imagined away.

Survey after survey reports that Sydney is sick of congestion and wants better public transport, and yet I cannot recall too many attempts by our politicians (of any shades of the political rainbow) to lead the debate as to what better public transport may require of us in terms of contributing to its cost and accepting some changes to the car-flavoured landscape of Sydney.

Perhaps that is the real obstacle to improving public transport in Sydney.


  • If we want new rail lines, we need to think more about what they require of us rather than what we require of them.
  • If we are serious about better public transport, we need to be serious about increasing the density of Sydney’s population (although not necessarily increasing the total population).
  • The main obstacle to building new rail lines in Sydney is low population density.
  • Building a new rail line will require substantial remodelling/re-zoning of the areas within a 1.5 km radius of each station, preferably a mix of medium-high density housing/offices and retail.
  • One way of funding the cost of better public transport is a state infrastructure tax on the properties that benefit from better public transport services.
  • The next time you catch a train in Sydney, take along a beer coaster and count the people on the platform, the density of housing around the station, the frequency of services and the price of the ticket and then start designing your own preferred extension to the City Rail network
  • Some suggestions—Bondi Junction to Cronulla via Kurnell (tunnel under the mouth of Botany Bay), Northern Beaches, Parramatta to Hurstville, Chatswood to Dee Why, Hornsby to Mona Vale.
  • It the context of the above discussion, it is perhaps unsurprising that people are raising questions about the rationale for an expenditure of $43 billion on the NBN.

Photo credit: coverling (copyright Creative Commons)

Will the Reserve Bank hike rates next week?

Over the last few months, the Reserve Bank of Australia (RBA) board meetings have not provided any real surprises, but coming up next week is the most interesting meeting in a while. The cash rate is currently 4.5%, but there have been enough noises from the bank’s governor and other RBA board members about the strength of the Australian economy, that consensus is leaning towards a rate hike next week. Financial market pricing is currently indicating a 62% probability of a 0.25% rate rise. Interestingly, the online betting agency Sportsbet offers bets on possible RBA actions (somewhat controversially) and its odds are indicating an even higher chance of a rate hike.

Reserve Bank move Payout Probability
Rise Between 0.01 and 0.25% 1.33 75%
Stay The Same 3.40 29%
Rise Between 0.26 and 0.5% 4.50 22%
Rise 0.51% or More 21.00 5%
Any Decrease 101.00 1%
Sportsbet Odds (as at 1 October 2010)

My own contacts in the markets (you know who you are) tell me that the HSBC economist Paul Bloxham, who recently joined the firm after 12 years at the RBA, is calling for no move until November. So, perhaps a hike is not as sure a thing as Sportsbet punters believe.

What do you think? Here is another chance to pit the collective wisdom of Stubborn Mule readers against both the financial markets and online gamblers!

If you need more information to help you make up your mind, you could read Christopher Joye’s arguments as to why the RBA should just be getting a move on in the fight against inflation. It might help tame property prices in the process. Then again, perhaps not.

UPDATE: there was an error with the calculation of probabilities, which has been corrected. By the way, the fact that the probabilities add up to well over 100% gives an insight into Sportzbet’s profit margin, which looks to be around 25%.

FURTHER UPDATE: Sportsbet’s pages of financial markets bets are down…I wonder if ASIC are on to them now.