Welcome to the Guindex!
The Guindex is a project whose aim is to analyse the price distribution of Guinness pints across Ireland.
We are particularly interested in how the price variation is affected by geographic and social factors.
We are also interested in how the pubs themselves are distributed around Ireland and mathematical problems related to the placement of these pubs.
To examine some of these themes we have been conducting "in the field" data collection. We have collected the price of a pint in over 300 bars, pubs and nightclubs so far!
The Guindex map tab displays a user-centred map of Irish pubs and the prices of the pints at those pubs.
The statistics tab directly tracks this data collection, including the top 15 cheapest and most expensive pints thus far. This tab also offers some relevant quantifiers of the Guinness pricing.
In the analysis tab we have transformed the collected data in order to examine the aformentioned themes. In particular we examine geographic variation in the pricing of Guinness within Dublin at the level of:
1) Dublin Post routing administrative areas 2) Electoral divisions within county Dublin.
1) Dublin Post routing administrative areas
2) Electoral divisions within county Dublin.
We also examine interesting problems related to the distributions of the pubs in Dublin including:
1) What is the furthest you can be from a pub in county Dublin? 2) What is the order to visit the pubs in between the two circular roads to minimise travel time?
1) What is the furthest you can be from a pub in county Dublin?
2) What is the order to visit the pubs in between the two circular roads to minimise travel time?
Users can sign up for the site using the login link in the header. The data tab allows users to start submitting their own data to help the project. The project began with data being collected solely from Dublin but we have recently expanded to the other 25 counties!
|The Travelling Drunkard||Coming Soon|
|Correlation of Socioeconomic Factors and Guinness Pricing||Coming Soon|
|Geographic Variation of Guinness Pricing||January 2018|
|Furthest Distance to a Pub in County Dublin||January 2018|
The principal aim of the project is to exaimine whether and if so how geographical and social factors affect the price of a pint of Guinness arund Ireland. As the project began as a solely Dublin focused project all of the analysis conducted so far has looked at aspects of Dublin's pubs and the Guinness offered at those pubs.
Before looking at these questions we should first try and understand the distribution of the data itself. The statistics dashboard provides figures of merit relating to the data collected so far. These figures of merit show the extremes of the pricing distribution as well as overall quantitative descriptors of the data.
The Snug Bar on upper Stephen street is the cheapest pint thus far! It along with Eleanora's in Drimnagh are the bastions of sub four euro Guinness in Dublin. Unsurprisingly four of the top five most expensive pubs collected thus far have come from Temple Bar. Temple Bar is the scourge of all our pockets and is best avoided.
We can also look at the overall Guinness price distribution of the data collected so far, it'd be neat if the data followed the Student's t-distribution (essentially indistinguishable from a normal distribution for this number of samples) because of the historical connection between Guniness and that distribution. We look at this distribution below:
The Guinness price distribution is shown as a stacked pint histogram of the prices collected so far, the corresponding Student's t-distribution (same average, same standard deviation, degrees of freedom = number of prices collected -1 and scaled to match maximum of histogram) is displayed also in blue. We can see that, unfortunately, the Guinness distribution is quite non-normal. The Guinness distribution is considerably more centrally peaked between €5.00-€5.30 than the corresponding t-distribution.
We can now look at problems concerning how this distribution is allocated geographically. The geographical regions we have considered are:
1) Dublin post routing administrative areas
2) Electoral divisions within county Dublin.
This analysis is found here
Dublin post routing administrative areas
Dublin electoral divisions
The examination of the effect of social factors on Guinness pricing will be carried out once a more complete price distribution has been collected. This analysis will be here in the future.
A secondary theme of the project relates to the distribution of the pubs themselves. Interesting problems related to this theme are:
1) What is the furthest you can be from a pub in County Dublin? The solution of which can be found here
2) The travelling drunkard problem; what is the route that minimises travel distance and visits every pub within the two circular roads bounding Dublin city centre? The solution of this problem can be found here.
We also aim to look at other interesting mathematical problems concerning Guinness, pubs and Dublin. The next thing we plan to do is to analyse Dublin's electoral divisions as an N-colour map problem. If you have any suggestions as to what might be an interesting problem please get in contact.
The Travelling Drunkard
A write-up of the travelling drunkard problem will appear here.
Effect of Social Factors on Guinness Pricing
Analysis of the correlation between Guinness pricing and social factors in each electoral division will appear here. We are currently waiting for a more complete picture of the Guinness distribution
The correlation analysis will take the form of various bivariate choropleth maps of county Dublin's electoral divisions. For now here's a plot showing the population in each electoral division in county Dublin.
Geographic Variation of Guinness Pricing
Here we will attempt to assess and visualise geographic trends in Guinness pricing over the county Dublin area. We will look at the pricing in two separate types of sub-divisions of Dublin: An Post's Dublin post routing administrative areas and Dublin's electoral divisions.
To conduct this analysis we have obtained shape files describing the boundaries of these sub-divisions. A shape file carries geometric information about the boundaries of particular geographic regions.
There are 34 An Post routing administrative areas (22 Dublin city postcodes plus 12 county Dublin administrative areas) and 322 electoral divisions within county Dublin.
The post routing administrative areas are thus a coarse microscope through which to examine geographic variation, while the electoral divisions are a finer probe albeit at the expense of high standard deviation of intra-division average prices. First let's look at the Dublin post routing adminatrative areas:
Dublin Post Routing Adminastrative Areas.
The Dublin City postcodes are Dublin 1 through 24 excluding 19, 21 and 23 but including the controversial 6W (six west) postal area (see image below). The river Liffey which runs generally west to east and cuts through Dublin city centre offers a natural geographic partition to the city. The odd numbered city postcodes are all north of the river Liffey. The even numbered postcodes are generally south of the river Liffey. There are two exceptions to this which straddle the river: 1) Dublin 8 (which contains the Phoenix park) and 2) Dublin 20 (which contains Chapelizod).
The Dublin county postcodes are mainly from north county Dublin. There are three exceptions: Lucan (west county Dublin), Blackrock (south county Dublin) and Glenageary (south county Dublin).
Note in the image above that the Donabate/Portrane area of county Dublin belongs to the Malahide post routing adminastrative area and Lambay island belongs to the Rush post routing adminastrative area. To begin the analysis we will sort the pubs into their respective postal region. The result of which looks like this:
As you will have expected the most pubs are in the four city centre postcodes, Dublin 1, 2, 7 and 8. Dublin 2 has the most amount of pubs with 190 in that postcode alone! Other things to note are that Bull island is shared between the Dublin 3 and Dublin 5 post codes, hence the dual-tone colouring and despite Lambay island belonging to the Rush routing area I have coloured it black in an attempt to dissuade people from going pinting there. Despite Malahide (5 pubs) and Donabate (4 pubs) belonging to the same postal area I have couloured them independently as they are formed from two distinct shape files, i.e. I have colored them as having 5 (green) and 4 (green) rather than 9 (blue).
These pictures are produced from incomplete data, I know for instance that Skerries has more than 2 pubs even though there are currently only two in our database. In order for these pictures to better describe reality we need your help. If there are pubs missing in an area that you are familiar with please add them to the database by signing up to the website through the Data tab in the sidebar. On the right above we see the same image superposed on a map of Dublin. We can see the quality of the shape file describing the post routing adminastrative areas from this image. The only clear discrepancy between the shape file and the actual geographic picture is the Portmarnock spit. Let's now look at the data taken from pubs within these postcodes up to this point:
Above we plot the fraction of the pubs visited within each postal area. We can see that we have visited the highest fraction of Dublin 6s pubs - all but one of them in fact. Dublin 6 is folllowed by Dublin 2 and Dublin 4. All the other areas have quite low coverage, less than 50%. We have also been tracking the prices in the pubs visited within each postal region. This data can be visualised below:
In the figure above we have taken all the collected data in each post routing adminastrative area and averaged the prices. Some of these averages should be considered very reliable, having been calculated from many pubs within that area. Some, however, have only data from a single pub and should be taken less seriously. Unsurprisingly the most expensive area is Dublin 2 with an average of €5.37 of the data collected so far. The cheapest area is Dublin 12, this is perhaps not that definitive as there have only 4 submissions from that postcode so far. As well as looking at between postal area variation we can also look at the variation within each postal region:
The plot above shows the distribution of pricing within each postal region. Of particular note is the "Temple Bar" tail of the right skewed Dublin 2 distribution. The irregularity of the Dublin 1, Dublin 7 and Dublin 8 distributions is also very interesting and I'd contend that it is reflective of the social and cultural diversity and inhomogeneity of these postcodes. Although some of the other distributions (D6W, D9 and D12) are quite irregular this is probably due to the low level of data collected in these postcodes thus far. The Dublin 4 and Dublin 6 distributions both look reasonably normal with a slight left skew. We have conducted ANOVA analysis of the pricing over these regions. This analysis tests whether there is a statistically significant difference in the pricing across different postal regions or whether the spread seen above is the product of random variation around some overall Dublin mean. The p-value of the F-test (~1*^-12) indicates that there is at least one mean statistically distinct from the others. To assess which means are statistically different we have carried out a Tukey analysis on the data. The results of this test indicate that the following pairs of postcodes have statistically different average prices of Guinness: (1,8), (2,1), (2,6), (2,7), (2,8). As expected this test concludes that the pricing of Guinness in the city centre, particularly in Dublin 2, is more than other parts of Dublin. We expect that this dichotomy of Guinness pricing between city centre and outside will be more fully borne out as more data is collected.
Dublin Electoral Divisions.
The electoral division (ED) is the smallest legally defined adminastrative region in Ireland. They are almost the finest geographic scale at which the government distributes census data. As such they offer the possibility of comparing Guinness pricing in each ED to social factors in that ED.
The analysis of price variation with respect to social factors from census data will appear here . Let's now examine how the Dublin pubs are distributed over the EDs
The image above shows the number of pubs in each ED by colour. There are a surprising number of electoral divisions which don't have a pub at all (indicated in black in the image). The ED with the most pubs is the Royal Exchange A ED in Dublin 2, comprising Temple Bar, Dame St, Georges St etc. This ED has 72 pubs! Note that Lambay island belongs to the Donabate ED, despite being coloured orange there are no pubs on Lambay island and only 7 people live there. Similarly for Dalkey island off Dalkey (Glenageary/Dalkey-Coliemore ED) and Ireland's Eye off Howth (D13/Howth ED), although neither have any permanent inhabitants. We can now move on to assess the average price in each ED containing at least one pub
The figure above looks at the price of a pint of Guinness in each ED from the data collected, in EDs where more than one entry have been logged we have averaged the entries. The most expensive ED is Royal Exchange A which features the dreaded Temple Bar tail. This is we think likely to be the most expensive venue to go pinting. The cheapest ED is currently Walkinstown B which hosts Eleanora's pub and their €3.90 pint of Guinness, although this may change as more data is collected.
The figure on the right hand side shows the left hand figure overlaid on a road map of county Dublin in order to better appreciate where the value is and what EDs need to hang their head in shame.
Furthest Distance to a County Dublin Pub
We wish to find the furthest distance you can be away from a Dublin pub and still be breathing Dublin air. We also want to know where you are in county Dublin when this occurs. The solution to this problem is shown below:
The solution is a logarithmic heat map of the distance to the nearest pub over the county Dublin region. We can see from the map that the most remote point in Dublin is ~9300m away from the nearest pub. This point is on the Wicklow border of Dublin in the south indicated by the green circle.
The extremum occurring on a boundary is a very plausible solution, consistent with looking to maximise/minimise mathematical functions over a region. The methodology used to solve this problem is now explaned:
To solve this problem we need two sets of data: 1) the location of all the Dublin pubs (in some coordinate system) and 2) a polygon specifying the boundaries of county Dublin (in the same coordinate system)
We also require a method to calculate the physics distance, d, (in m) between any two points in the chosen coordinate system. In this work we have used (longitude,latitude) (λ, ϕ) spherical coordinates, so the Haversine formula (below) is the necessary equation for calculating distances. This formula calculates the distance between two points on a spherical surface of radius r (sorry flat Earthers).
The difficulty then lies in defining the very irregular boundary of county Dublin. At this stage we knew nothing about shape files (which are files carrying geometrical information on geographical regions). So instead we specified the boundary by manually picking 327 points using Google Earth and forming a polygon from them.
To generate the coordinates interior to this polygon we formed the square bounding the polygons extreme latitude and longitude values and defined an x-y mesh over this square with a chosen granularity. The granularity (mesh step-size) was chosen to be approximately 30m.
We then check whether each point in the mesh is inside the county Dublin polygon and retain the points that are.
This generated a set of 885,126 latitude longitude points constituting county Dublin. One then can, in principle, calculate the distance to the nearest pub at each of these points using the Haversine formula to obtain a distance scalar field.
Attempting this procedure would however take too much computer time. Instead I took 27,222 points from the 885,126 and calculated the distance to nearest pub at each of them. This represents an error inflation of approximately 5.7x so instead of having a maximum error of plus or minus 30Sqrt(2) it'll be ~ 170Sqrt(2). This isn't the biggest deal.
The picture above uses quadratic interpolation to smooth out the scalar field in between the actual calculated points. This is a procedure to allow the variation to be estimated (and visualised) at a finer scale than was considered initially. To see the effect of the interpolation consider the raw image below. We see that the interpolation smoothes out the effects of the irregularly shaped boundary. To make the scalar field drop off at the boundary I've put in an absorbing wall by appending the defined boundaries of the region with a distance value of 0 to the calculated points.
(The procedure used to find the points constituting county Dublin is analogous to finding the area of some region by integration. Since we know the area of the square we can numerically estimate the area of county Dublin by looking at the fraction of points within the polygon (Area Dublin = Fraction of points inside Polygon * Area of Square). The fraction of points falling within the polygon ~0.589 which then gives an estimate for the total area of county Dublin of 1.002904*10^9 m^2 which is 9% off the value quoted on wikipedia (9.22*10^8 m^2). Not bad considering how crudely we defined the boundary!)
The Guindex project was started in August 2017. The project is seen as a labour of love, intended to celebrate the black stuff.
The database of pubs was extracted from openstreetmaps, everything marked as a pub, bar or nightclub was taken. As such it is not-exhaustive and the analysis presented should only be considered as a good approximation to reality. Asymptotic to reality is the best we can hope for.
We have decided (completely arbitrarily) the criteria for a pub; it must serve pints, be open to the public, have regular hours and in the cases where there is a cover charge further pinting should be the primary motivation to paying that charge. So for those reasons hotel bars are in, as are sports club bars provided they don't require club memberships. Bars at concert venues are out, as are those at sporting events. We are certainly missing many pubs so if you notice one in particular be sure to add it yourself to the database.
The project began in August 2017 with just three of us but in the months since the project has grown to comprise fifteen Guinness enthusiasts.
The project members are all twenty-somethings, primarily from quantitative fields (physics, maths, chemistry and computer science) .
The project will never be complete, but to get a more complete picture of the price distributions around Ireland we need your help!
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