Never on a Tuesday?

Where, when and from whom should you buy your fuel?

Fuel costs are significant for Australian households.  To many motorists, apparently random fluctuations in prices and the differences between outlets have made it difficult to find the best price.  In 2001 the Western Australian government was concerned about impacts on households and set up a website (Fuel Watch) requiring all fuel retailers to submit their proposed prices by 2pm each day for the next day starting 6am.  The aim was to provide an informed marketplace where motorists were less likely to feel misled on prices.

Fuel Watch now contains a large set of data of millions of records.  While this is historical, it is natural to ask how this might inform future fuel purchases.  This article uses 2017 data from Fuel Watch in providing insights. 

The main product types contained in the data include unleaded petrol (ULP), premium unleaded petrol (PULP), unleaded research octane number of 98 (98 RON) and Diesel.  Prices for these fuel types aggregated at a daily level for 2017 are displayed in Figure 1. 

Figure 1. Average fuel price by day (2017) by fuel type.
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What does this tell us?

The average prices of unleaded petrol (ULP, PULP, 98 RON) fluctuate together by around 10 cents each week in WA. 

Diesel prices are much more stable and not impacted by day of week.

But is this telling the whole story?

Figure 2. Average ULP Price – 2017 WA.
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Figure 2 looks closer at the most commonly used fuel, Unleaded Petrol or ULP, indicating that, in 2017 at least, average fuel prices are cheaper on Mondays, increasing by an average of 10% from Monday to Tuesday.

However this still does not provide the whole story.  Averaging can smooth over important variation and details.  Statisticians look to understand variation so they can use it to their advantage rather than simply regarding it as a nuisance.

For example, Figure 2 doesn’t capture the variation in fuel price over location, brand or time of year.  Understanding the effect of such factors can lead to a better understanding of where, when and from who you should buy your fuel to obtain the cheapest price. 

The rest of this article focuses on more in-depth analysis of ULP prices by the use of clustering and segmentation techniques, but the same techniques could be applied to the other fuel types.

Figure 3. Average daily price of fuel stations in clusters. CLICK IMAGE TO ENLARGE

Clustering Fuel Stations by their ULP Prices

A start to answering the question of where to buy fuel from can come from letting the data itself form groups of stations based simply on their daily price behaviour.  Here we have used a statistical approach called cluster analysis.  From these clusters, factors that have greatest influence on prices can become evident.  Using “k means” clustering to group individual fuel stations based on price into four clusters shows that not all fuel stations exhibit the same price patterns.  Figure 3 illustrates the four clusters’ distinct price attributes.

While this tells us there are differences, it doesn’t tell us anything about which fuel stations follow which of these patterns.  We need to use these clusters to investigate further.

Geographic Regions and Brand – Which Ones Cluster Together?

There are known differences in fuel prices between regions and brands.  But what may be less well known is which regions and brands follow each of the cluster price patterns demonstrated in Figure 3.  Mosaic plots of geographic region and brand by cluster show:

  • Cluster 1 (fuel stations with medium-high stable prices – see Figure 4) is predominantly regional and south west locations with both large and small brands;
  • Cluster 2 (fuel stations with high stable prices) is predominantly locations in the far north of WA with both large and small brands;
  • Cluster 3 (fuel stations with prices subtly fluctuating on a weekly basis) is largely metropolitan and south of WA with smaller and independent brands* being most common; and
  • Cluster 4 (fuel stations with prices vividly fluctuating on a weekly cycle) is dominated by the Perth metropolitan area and five large brands 7-Eleven, BP, Caltex, Coles Express and Puma.

* Independent includes brands with fewer than 10 stores in this analysis

Figure 4. Mosaic plots give a visual display of the number of fuel stations in each cluster, based on the fuel station’s characteristics (e.g. region and brand). In these plots, the column widths are proportional to the number of fuel stations in each cluster. In this type of plot, each category has the same colour in each column. For example, in the region plot, South-West is always the bright green colour (3rd from the bottom), even though it appears higher in cluster 3 (due to Metro having many more stations in cluster 3 than cluster 1), and South West only appearing as a black line in cluster 2, as there were so few in that cluster.
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Defining Segments from Clusters

Figure 5. Average daily price of fuel stations in segments. CLICK IMAGE TO ENLARGE

To be useful in making decisions, segments should ideally be well-defined, meaningful and interpretable groups.  Cluster analysis on its own doesn’t do this, but being such a great statistical tool for exploring the data they can be used to provide key insights into how usable segments might be defined.

Examining which fuel stations are contained within each cluster leads into the following possible segmentation:

  1. South-West or Regional;
  2. Remote;
  3. Metropolitan Small Brands; and
  4. Metropolitan Large Brands.

Of course, this is only one possible grouping or segmentation.  Depending on the analysis needs, more detailed segments may be appropriate, which may mean choosing and analysing more clusters, giving a finer level of detailed breakdown.  It’s an iterative process!

Figure 5 is similar to Figure 3 but this time it displays the average unleaded petrol price over time after grouping stations into these four segments, rather than the cluster they were assigned to based on their fuel prices alone.  As can be seen, this gives similar shapes to the four clusters, but they are not identical.

It would be naïve to think that within a segment all stations have the same price patterns, and it may be interesting, or necessary, to examine their variation further. 

Within each segment, the variation in prices can be illustrated by what statisticians call “heatmaps” that display average prices against the day of the week and the brand, with darker colours indicating higher prices and lighter colours indicating lower prices.  To make the graphs clearer, the brands themselves have been clustered within each segment, so that the more similar brands display adjacent to each other on the graphs.  This clustering is displayed next to each heatmap as a dendrogram or tree diagram.  The heatmap shows, for example, that in the South West some of the big brands do have higher prices on Tuesdays, although this pattern is generally not as extreme as in the metropolitan area.

Figure 6. Heatmaps displaying average prices against the day of the week and the brand for each segment.
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Insights from the segmentation:

  • Regional and South West – Cheaper average prices were seen by Shell, Better Choice, United, Vibe and Gull across all days of the week.
  • Remote – Puma had the cheapest prices averaging under 140 cents per litre, vastly different to Shell and Independent fuel stations, which averaged over 150 cents per litre.
  • For a consumer who requires unleaded petrol in the Perth Metropolitan Area, purchasing fuel from a large brand on a Monday may provide the cheapest option with average fuel price under 120 cents per litre in 2017.
  • However, it would likely be cheaper to visit a smaller brand fuel station if purchasing fuel on a Tuesday or mid-week as larger brands spiked their prices substantially more than smaller brand fuel stations.

Figure 7 displays similar results for other common fuel types within the Perth metropolitan area.  Higher octane rating unleaded petrol show similar results to the metropolitan standard ULP prices and segments.  For Diesel, larger brands are usually more expensive than the smaller and independent brands. 

Figure 7. Heatmaps displaying average prices against the day of the week and the brand for PULP, 98 RON and Diesel in the Perth Metropolitan area.
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What can we take from this?

The insights in this article demonstrate the real value that can be obtained from applying statistical techniques to any dataset and any application. 

In terms of what it means for you, this analysis of the WA Fuel Watch data advises that to get cheaper fuel:

  • If you require Diesel, any day of week is likely to give a similar price, though you are likely to see cheaper prices at smaller brand stations in the Metropolitan area;
  • If in regional areas, it doesn’t matter what day you buy fuel as prices do not fluctuate as dramatically;
  • If you are buying from a large brand name in the Perth Metropolitan area, you should be conscious of the day of week, avoiding Tuesday and mid-week;
  • If you have to buy on a Tuesday in the Perth Metropolitan area, it is generally cheaper to go to a smaller brand store; and
  • If you have a choice on where and when you buy fuel in the Perth Metropolitan, it is generally cheaper to go on a Monday to a big brand.

These are broad guidelines and some individual stations will not fit in to the general advice.  The logic behind the pricing behaviour is not clear and historically has changed over the years.  Our results reflect the 2017 prices, but how long they will hold is not clear.  As always, buyer beware, but also buyer be informed!