More than R – how we underestimate the impact of Covid-19 infection

We have got so used to seeing R numbers quoted. However, taking this at its immediate value means we underestimate the impact of our individual and corporate actions.

Even with a lockdown R value of 0.9 when the disease is ‘under control’, a house party that leads to 10 initial infections will ultimately give rise to a further 90 cases, so is actually likely to lead to an additional Covid-19 death, probably totally unrelated to anyone at the original house party.

This multiplication factor is far bigger than the apparent 0.9 figure suggests and is at first counter-intuitive. This difference between the apparent figure and the real figure can easily lead to complacency.

If you have been following the explanations in the media you’ll know that R is the average number of further people to whom an infected person passes the disease. If R is greater than one, the disease increases exponentially – an epidemic – if R is less than one the disease gradually decays. In most countries the R-value before lockdown was between 2 and 3 (out of control), and during lockdown in the UK it reduced to a figure between 0.7 and 0.9 (slow decay).

However, note that this R value is about the average number of people directly infected by a carrier.

First it is an average – in reality most people infect fewer than the R number, but a few people infect a lot more, especially if the person has a large social network and is asymptomatic or slow to develop symptoms. This is why some news articles are picking up discussions of the ‘k’ factor1, a measure of the extent to which there is variability.

Secondly, this is about direct infections. But of course if you infect someone, they may infect another person, and so on. So if you infect 3 people, and they each infect 3 more, that is 9 second order contacts.

Thirdly, the timescale of this infection cycle is 3–4 days, about half a week. This means that an R of 3 leads to approximately 9 times as many cases two weeks later, or doubling about every 2½ days, just what we saw in the early days of Covid-19 in the UK.

Let’s look at the effect of these indirect infections for an R below 1, when the disease is under control.

As a first example let’s take R=0.5, which is far smaller than almost anywhere has achieved even under lockdown, as an extreme example to begin with. Let’s start off with 64 cases (chosen to make the numbers add up easily!). These 64 infect 32 others, these infect 16 more, each time halving. The diagram shows this happening with two cycles of infection each week and the cases peter out after about 4 weeks. However, in that time a further 63 people have been infected.

If we do the same exercise with R = 0.9 and start off with 100 cases, we get 90 people infected from these initial 100, then a further 81 second order infections, 72 after the next cycle, and then in the following cycles (rounding down each time) 64, 57, 51, 45, 40, 36, 32, 28, 25, 22, 19, 17, 15, 13, 11, 9, 8, 7, 6, 5, 4, 3, 2, 1. That is, after 15 weeks we have a further 763 cases. On average (rather than rounding down), it is a little higher, 900 additional cases.

In general the number of additional cases for each seed infection is R/(1-R): 9 for R=0.9; 2.3 for R=0.7.  This is very basic and well-known arithmetic series summation, but the large sizes can still be surprising even when one knows the underlying maths well.

Things get worse once R becomes greater than 1. If R is exactly 1 there is on average 1 new case for each infected person case.  So if there is one ‘seed’ case, then in each succeeding week there will be two new cases for ever. In reality there will not be an infinite number of cases as eventually there will be a vaccine, further lockdown, or something to clamp down on new cases, but there is no natural limit when the new cases peter out.

Mid-range estimates in the UK suggest that during the winter we may see an R of 1.52. This is assuming that social distancing measures and effective track-and-trace are in place, but where winter weather means that people are indoors more often and transmission is harder to control. The lower bound figure being used is 1.2.

If we look over just a 5-week window, with R=1.2 each seed case leads to nearly 25 additional cases during the period; with R=1.5 this rises to over 100 new cases.  Over a 10-week period (a university term), these figures are around two hundred new cases with R=1.2 or six and half thousand for R=1.5.

So next time you see R=0.7 think two and half, when you see R=0.9 think ten, and when you see R=1.5 think thousands.

The last of these is crucial: taking into account a mortality rate of around 1%, each avoided infection this coming winter will save around ten lives.


  1. For example, BBC News: Coronavirus: What is the k number and can superspreading be stopped? Rebecca Morelle, 6 June 2020[back]
  2. The Academy of Medical Sciences. Preparing for a challenging winter 2020-21. 14th July 2020 [back]

Free AI book and a new one coming …

Yes a new AI book is coming … but until then you can download the first edition for FREE 🙂

Many years ago Janet Finlay and I wrote a small introduction to artificial intelligence.  At the time there were several Bible-sized tomes … some of which are still the standard textbooks today.  However, Janet was teaching a masters conversion course and found that none of these books were suitable for taking the first steps on an AI journey, especially for those coming from non-computing disciplines.

Over the years it faded to the back of our memories, with the brief exception of the time when, after we’d nearly forgotten it, CRC Press issued a Japanese translation.  Once or twice the thought of doing an update arose, but quickly passed.  This was partly because our main foci were elsewhere, but also, at the danger of insulting all my core-AI friends, not much changed in core AI for many years!

Coming soon … Second Edition

Of course over recent years things have changed dramatically, hence my decision, nearly 25 years on, to create a new edition maintaining the aim to give a rich but accessible introduction, but capturing some of the recent trends and giving these a practical and human edge.  Following the T-model of teaching, I’d like to help both newcomer and expert gain a broad perspective of the issues and landscape, whilst giving enough detail for those that want to delve into a more specific area.

A Free Book and New Resources

In the mean time the publisher, Taylor & Francis/CRC has agreed to make the PDF of the first edition available free of charge  I have updated some of the code examples from the first edition and will be incrementally adding new material to the second edition micro-site including slides, cases studies, video and interactive materials.  If you’d like to teach using this please let me know your views on the topics and also if there are areas where you’d like me to create preliminary material with greater urgency.  I won’t promise to be able to satisfy everyone, but can use this to adjust my priorities.

Why now?

The first phase of change in AI was driven by the rise of big data and the increasing use of forms of machine learning to drive adverts, search results and social media.  Within user interface design, many of the fine details of colour choices and screen layout are now performed using A–B testing …sight variants of interfaces delivered to millions of people – shallow, without understanding and arguably little more than bean counting, but in numerous areas vast data volume has been found to be ‘unreasonably effective‘ at solving problems that were previously seen to be the remit of deep AI.

In the last few years deep learning has taken over as the driver of AI research and often also media hype.  Here it has been the sheer power of computation, partly due to Moores’ Law with computation nearly a million times faster than it was when that first edition was written nearly 25 years ago.  However, it has also been enabled by cloud computing allowing large numbers of computers ti efficiently attack a single problem.  Algorithms that might have been conceived of but dismissed as impractical in the past have become commonplace.

Alongside this has been a dark side of AI, from automated weapons and mass surveillance, to election rigging and the insidious knowledge that large corporations have gathered through our day-to-day web interactions.  In the early 1990s I warned of the potential danger of ethnic and gender bias in black-box machine learning and I’ve returned to this issue more recently as those early predictions have come to pass.

Across the world there are new courses running or being planned and people who want to know more.  In Swansea we have a PhD programme on people-first AI/big data, and there is currently a SIGCHIItaly workshop call out for Teaching HCI for AI: Co-design of a Syllabus. There are several substantial textbooks that offer copious technical detail, but can be inaccessible for the newcomer or those coming from other disciplines.  There are also a number of excellent books that deal with the social and human impact of AI, but without talking about how it works.

I hope to be able to build upon the foundations that Janet and I established all those years ago to create something that fills a crucial gap: giving a human-edge to those learning artificial intelligence from a computing background and offering an accessible technical introduction for those approaching the topic from other disciplines.



Software for 2050

New Year’s resolutions are for a year ahead, but with the start of a new decade it is worth looking a bit further.
How many of the software systems we use today will be around in 2050 — or even 2030?
Story 1.  This morning the BBC reported that NHS staff need up to 15 different logins to manage ‘outdated’ IT systems and I have seen exactly this in a video produced by a local hospital consultant. Another major health organisation I talked to mentioned that their key systems are written in FoxBase Pro, which has not been supported by Microsoft for 10 years.
Story 2.  Nearly all worldwide ATM transactions are routed through systems that include COBOL code (‘natural language’ programming of the 1960s) … happily IBM still do support CICS, but there is concern that COBOL expertise is literally dying out.
Story 3.  Good millennial tech typically involves an assemblage of cloud-based services: why try to deal with images when you have Flickr … except Flickr is struggling to survive financially; why have your own version control system when you can use Google Code, except Google Code shut down in 2016 after 10 years.
Story 3a.  Google have a particularly bad history of starting or buying services and then dropping them: Freebase (sigh), Revolv Hub home automation, too many to list. They are doing their best with AngularJS, which has a massive uptake in hi-tech, and is being put into long-term maintenance mode — however, ‘long-term’ here will not mean COBOL long-term, just a few years of critical security updates.
Story 4.  Success at last. Berners-Lee did NOT build the web on cutting edge technology (an edge of sadness here as hypertext research, including external linkage, pretty much died in 1994), and because of this it has survived and probably will still be functioning in 2050.
Story 5.  I’m working with David Frohlich and others who have been developing slow, meaningful social media for the elderly and their families. This could potentially contribute to very long term domestic memories, which may help as people suffer dementia and families grieve after death. However, alongside the design issues for such long-term interaction, what technical infrastructure will survive a current person’s lifetime?
You can see the challenge here.  Start-ups are about creating something that will grow rapidly in 2–5 years, but then be sold, thrown away or re-engineered from scratch.  Government and health systems need to run for 30 years or more … as do our personal lives.
What practical advice do we give to people designing now for systems that are likely to still be in use in 2050?

On the edge of chaos

Running in the early morning, the dawn sun drives a burnt orange road across the bay. The water’s margin is often the best place to tread, the sand damp and solid, sound underfoot, but unpredictable. The tide was high and at first I thought it had just turned, the damp line a full five yards beyond the edge of the current waves. Some waves pushed higher and I had to swerve and dance to avoid the frothing edge, others lower, wave following wave, but in longer cycles, some higher, some lower.

It was only later I realised the tide was still moving in, the damp line I had seen as the zenith of high tide, had merely been the high point of a cycle and I had run out during a temporary low. Cycles within cycles, the larger cycles predictable and periodic, driven by moon and sun, but the smaller ones, the waves and patterns of waves, driven by wind and distant storms thousands of miles away.

I’m reading Kate Raworth’s Doughnut Economics. She describes the way 20th century economists (and many still) were wedded to simple linear models of closed processes, hence missed the crucial complexities of an interconnected world, and so making the (predictable) crashes far worse.

I was fortunate in that even in school I recall watching the BBC documentary on chaos theory and then attending an outreach lecture at Cardiff University, targeted at children, where the speaker was an expert in Chaos and Catastrophe Theory giving a more mathematical treatment. Ideas of quasi-periodicity, non-linearity, feedback, phase change, tipping points and chaotic behaviour have been part of my understanding of the world since early in my education.

Now-a-days ideas of complexity are more common; Hollywood embraced the idea that the flutter of a butterfly wing could be the final straw that causes a hurricane. This has been helped in no small part by the high-profile of the Santa-Fe Institute and numerous popular science books. However, only recently I was with a number of academics in computing and mathematics, who had not come across ‘criticality’ as a term.

Criticality is about the way many natural phenomena self-organise to be on the edge so that small events have a large impact. The classic example is a pile of sand: initially a whole bucketful tipped on the top will just stay there, but after a point the pile gets to a particular (critical) angle, where even a single grain may cause a minor avalanche.

If we understand the world in terms of stable phenomena, where small changes cause small effects, and things that go out of kilter are brought back by counter effects, it is impossible to make sense of the wild fluctuations of global economics, political swings to extremism, and cataclysmic climate change.

One of the things ignored by some of the most zealous proponents of complexity is that many of the phenomena that we directly observe day-to-day do in fact follow the easier laws of stability and small change. Civilisation develops in parts of the world that are relatively stable and then when we modify the world and design artefacts within it, we engineer things that are understandable and controllable, where simple rules work. There are times when we have to stare chaos in the face, but where possible it is usually best to avoid it.

lovefibre – waves

However, even this is changing. The complexity of economics is due to the large-scale networks within global markets with many feedback loops, some rapid, some delayed. In modern media and more recently the internet and social media, we have amplified this further, and many of the tools of big-data analysis, not least deep neural networks, gain their power precisely because they have stepped out of the world of simple cause and effect and embrace complex and often incomprehensible interconnectivity.

The mathematical and computational analyses of these phenomena are not for the faint hearted. However, the qualitative understanding of the implications of this complexity should be part of the common vocabulary of society, essential to make sense of climate, economics and technology.

In education we often teach the things we can simply describe, that are neat and tidy, explainable, where we don’t have to say “I don’t know”. Let’s make space for piles of sand alongside pendulums in physics, screaming speaker-microphone feedback in maths, and contingency alongside teleological inevitability in historic narrative.

Paying On Time – universities are failing

Universities are not living up to Government prompt payment targets.  As many suppliers will be local SMEs this threatens the cashflow of businesses that may be teetering on the edge, and the well being of local economies.

I’ve twice in the last couple of months been hit by university finance systems that have a monthly payment run so that if a claim or invoice is not submitted by a certain date, often the first day or two of the month, then it is not paid until the end of the following month, leading to a seven week delay in payment.  This is despite Government guidelines for a normal 30 day payment period and to aim for 80% payment within 5 working days.

I’d like to say these are rare cases, but are sadly typical of university payment and expense systems.  In some cases this is because one is being treated as a casual employee, so falling into payroll systems.  However, often the same systems are clearly being used for commercial payments.  This means that if a supplier misses a monthly deadline they may wait nearly two months for payment … and of course if they are VAT registered may have already had to pay the VAT portion to HMRC before they actual receive the payment.

The idea of monthly cheque runs is a relic of the 1970s when large reels of magnetic tapes had to be mounted on refrigerator-sized machines and special paper had to be loaded into line-printers for cheque runs.  In the 21st century when the vast proportion of payments are electronic, it is an embarrassing and unethical anachronism.

As well as these cliff-edge deadline issues, I’ve seen university finance systems who bounce payments to external suppliers if data is on an out of date form, even if the form was provided in error by a member of university staff.

Even worse are universities finance systems which are organised so that when there is a problem in payment, for example, a temporary glitch in electronic bank payments, instead of retrying the payment, or informing the payee or relevant university contact, the system simply ignores it leaving it in limbo.  I’ve encountered missing payments of this kind up to a year after the original payment date.  If one were cynical one might imagine that they simply hope the supplier will never notice.

The issue of late payments became a major issue a few years ago.  Following the recession, many SMEs were constantly teetering on the edge of bankruptcy, yet larger firms were lax in paying promptly knowing that they were in a position of power (e.g. see “Getting paid on time” issued by the Department for Business, Innovation & Skills, February 2012).

Five years on this is still a problem.  In April last year The Independent estimated that British SMEs were owed 44.6 billion in late or overdue payments(see “The scourge of late payment“).  There is now mandatory reporting of payment processes for larger companies, and recent returns showed that some companies missed prompt payment up to 96% of the time, with bad performers including major names such as Deloitte (see “Ten of the UK’s big businesses that fail to pay suppliers on time get named and shamed by the Government“).

There is also a voluntary “Prompt Payment Code“, but, amongst the signatories, there are only two universities (Huddersfield and Westminster) and three colleges.

Universities are often proud of the way they support local economies and communities: being major employers and often offering advice to local businesses.  However, in respect to prompt payment they are failing those same communities.

So, well done Huddersfield and Westminster, and for the rest of the university system – up your game.

physigrams – modelling the device unplugged

Physigrams get their own micro-site!

See it now at at

Appropriate physical design can make the difference between an intuitively obvious device and one that is inscrutable.  Physigrams are a way of modelling and analysing the interactive physical characteristics of devices from TV remotes to electric kettles, filling the gap between foam prototypes and code.

Sketches or CAD allow you to model the static physical form of the device, and this can be realised in moulded blue foam, 3D printing or cardboard mock-ups.  Prototypes of the internal digital behaviour can be produced using tools such as Adobe Animate, or atomic or as hand-coded using standard web-design tools.  The digital behaviour can also be modelled using industry standard techniques such as UML.


Physigrams allow you to model the ‘device unplugged’ – the pure physical interaction potential of the device: the ways you can interact with buttons, dials and knobs, how you can open, slide or twist movable elements.  These physigrams can be attached to models of the digital behaviour to understand how well the physical and digital design compliment one another.

Physigrams were developed some years ago as part of the DEPtH project., a collaboration between product designers at Cardiff School of Art and Design and  computer scientists at Lancaster University. Physigrams have been described in various papers over the years.  However, with TouchIT ,our book on physicality and design (eventually!) reaching completion and due out next year, it felt that physigrams deserved a home of their own on the web.

The physigram micro-site, part of includes descriptions of physical interaction properties, a complete key to the physigram notation, and many examples of physigrams in action from light switches, to complete control panels and novel devices.

Timing matters!

How long is an instant? The answer, of course, is ‘it depends’, but I’ve been finding it fascinating playing on the demo page for AngularJS tooltips. and seeing what feels like ‘instant’ for a tooltip.

The demo allows you to adjust the md-delay property so you can change the delay between hovering over a button and the tooltip appearing, and then instantly see what that feels like.

Try it yourself, set a time and then either move over the button as if you were about to click t, or wondering what it does, or simply pass over it as if you were moving your pointer to another part of the page.
If the delay is too short (e.g. 0), the tooltip flickers as you simply pass over the icon.
If you want it as a backup for when someone forgets the action, then something longer about a second is fine – the aim is to be there only if the user has that moment doubt.
However, I was fascinated by how long the delay needed to be to feel ‘instant’ and yet not appear by accident.
For me about 150 ms is not noticeable as a delay, whereas 200ms I can start to notice – not an annoying delay, but a very slight sense of lack of responsiveness.

Solr Rocks!

After struggling with large FULLTEXT indexes in MySQL, Solr comes to the rescue, 16 million records ingested in 20 minutes – wow!

One small Gotcha was the security classes, which have obviously moved since the documentation was written (see fix at end of the post).

For web apps I live off MySQL, albeit now-a-days often wrapped with my own NoSQLite libraries to do Mongo-style databases over the LAMP stack. I’d also recently had a successful experience using MySQL FULLTEXT indices with a smaller database (10s of thousands of records) for the HCI Book search.  So when I wanted to index 16 million the book titles with their author names from OpenLibrary I thought I might as well have a go.

For some MySQL table types, the normal recommendation used to be to insert records without an index and add the index later.  However, in the past I have had a very bad experience with this approach as there doesn’t appear to be a way to tell MySQL to go easy with this process – I recall the disk being absolutely thrashed and Fiona having to restart the web server 🙁

Happily, Ernie Souhrada  reports that for MyISAM tables incremental inserts with an index are no worse than bulk insert followed by adding the index.  So I went ahead and set off a script adding batches of a 10,000 records at a time, with small gaps ‘just in case’.  The just in case was definitely the case and 16 hours later I’d barely managed a million records and MySQL was getting slower and slower.

I cut my losses, tried an upload without the FULLTEXT index and 20 minutes later, that was fine … but no way could I dare doing that ‘CREATE FULLTEXT’!

In my heart I knew that lucene/Solr was the right way to go.  These are designed for search engine performance, but I dreaded the pain of trying to install and come up to speed with yet a different system that might not end up any better in the end.

However, I bit the bullet, and my dread was utterly unfounded.  Fiona got the right version of Java running and then within half an hour of downloading Solr I had it up and running with one of the examples.  I then tried experimental ingests with small chunks of the data: 1000 records, 10,000 records, 100,000 records, a million records … Solr lapped it up, utterly painless.  The only fix I needed was because my tab-separated records had quote characters that needed mangling.

So,  a quick split into million record chunks (I couldn’t bring myself to do a single multi-gigabyte POST …but maybe that would have been OK!), set the ingest going and 20 minutes later – hey presto 16 million full text indexed records 🙂  I then realised I’d forgotten to give fieldnames, so the ingest had taken the first record values as a header line.  No problems, just clear the database and re-ingest … at 20 minutes for the whole thing, who cares!

As noted there was one slight gotcha.  In the Securing Solr section of the Solr Reference guide, it explains how to set up the security.json file.  This kept failing until I realised it was failing to find the classes solr.BasicAuthPlugin and solr.RuleBasedAuthorizationPlugin (solr.log is your friend!).  After a bit of listing of contents of jars, I found tat these are now in  I also found that the JSON parser struggled a little with indents … I think maybe tab characters, but after explicitly selecting and then re-typing spaces yay! – I have a fully secured Solr instance with 16 million book titles – wow 🙂

This is my final security.json file (actual credentials obscured of course!

    "blockUnknown": true,
      "tom":"blabbityblabbityblabbityblabbityblabbityblo= blabbityblabbityblabbityblabbityblabbityblo=",
      "dick":"blabbityblabbityblabbityblabbityblabbityblo= blabbityblabbityblabbityblabbityblabbityblo=",
      "harry":"blabbityblabbityblabbityblabbityblabbityblo= blabbityblabbityblabbityblabbityblabbityblo="},


End of an era

A few weeks ago, I gave a panel presentation at the ARMA conference in Liverpool — however, this was my last official duty with a Talis hat on.

Talis is a small employee-owned company, and maintaining a research strand has been far sighted, but unusual. After a period focusing more in the development of new products, Talis is shifting to a phase when every resource should be focused on delivery … and hence long-term research, and my own role in the company, has had to cease.

Talis has been a wonderful place to work over the past seven years, both the individuals there, but also, and crucially important, the company atmosphere, which combines the excitement of a start-up, with real care and sense of community.   So if you spot posts advertised there, it is a great place to be.

Talis was my principal regular income, as my academic role at Birmingham has only been 20%, so long-term I need to think about whether I should increase again my academic time, or do other things. I have been very fortunate never having previously had a time without regular income, so this is a new experience for me, although, of course, common.

Over the past few years, I have kept some time ‘unwaged’ for other projects (such as walking round Wales!) and occasional consultancy, and my to do list is far from empty, so this summer and autumn I am intending to spend more time writing (yes TouchIT will be finished, and editing the Alan Walks Wales blog into a book), picking up some of the many half-finished coding projects, and doing videoing for Interaction Design Foundation

value for money in research – excellence or diversity

Government research funding policy in many countries, including the UK, has focused on centres of excellence, putting more funding into a few institutions and research groups who are creating the most valuable outputs.

Is this the best policy, and does evidence support it?

From “Big Science vs. Little Science: How Scientific Impact Scales with Funding”

I’m prompted to write as Leonel Morgado (Facebook, web) shared a link to a 2013 PLOS ONE paper “Big Science vs. Little Science: How Scientific Impact Scales with Funding” by Jean-Michel Fortin and David Currie.  The paper analyses work funded by Natural Sciences and Engineering Research Council of Canada (NSERC), and looked at size of grant vs. research outcomes.  The paper demonstrates diminishing returns: large grants produce more research outcomes than smaller grants, but less per dollar spend.  That is concentrating research funding appears to reduce the overall research output.

Of course, those obtaining research grants have all been through a highly competitive process, so the NSERC results may simply be a factor of the fact that we are already looking at the very top level of the research projects.

However, a report many years ago reinforces this story, and suggests it holds more broadly.

Sometime in the mid-late 1990s HEFCE the UK higher education funding agency, did a study where they ranked all universities against every simple research output metrics1. One of the outputs was the number of PhD completions and another was industrial research income (arguably whether an output!), but I forget the third.

Not surprisingly Oxford and Cambridge came top of the list when ranked by aggregate research output.

However, the speadsheet also included the amount of research money HEFCE paid into the university and a value-for-money column.

When ranked against value-for-money, the table was near reversed, with Oxford and Cambridge at the very bottom and Northampton University (not typically known as the peak of the university excellence ratings) was the top. That is HEFCE got more research output for pound spent at Northampton than anywhere else in the UK.

The UK REF2014 used an extensive and time-consuming peer-review mechanism to rank the research quality of each discipline in each UK university-level institution, on a 1* to 4* scale (4* being best). Funding is heavily ramped towards 4* (in England the weighting is 10:3:0:0 for 4*:3*:2*:1*). As part of the process, comprehensive funding information was produced for each unit of assessment (typically a department), including UK government income, European projects, charity and industrial funding.

So, we have an officially accepted assessment of research outcomes (that is government funds against it!), and also of the income that generated it.

At a public meeting following the 2014 exercise, I asked a senior person at HEFCE whether they planned to take the two and create a value for money metric, for example, the cost per 4* output.

There was a distinct lack of enthusiasm for the idea!

Furthermore, my analysis of REF measures vs citation metrics suggested that this very focused official funding model was further concentrated by an almost unbelievably extreme bias towards elite institutions in the grading: apparently equal work in terms of external metrics was ranked nearly an order of magnitude higher for ‘better’ institutions, leading to funding being around 2.5 times higher for some elite universities than objective measures would suggest.


From “REF Redux 4 – institutional effects“: ‘winners’ are those with 25% or more than metrics would estimate, ‘losers’ those with 25% or more less.

In summary, the implications both from Fortin and Currie’s PLOS ONE paper and from the 1990s HEFCE report suggest spreading funding more widely would increase overall research outcomes, but both official policy and implicit review bias do the opposite.

  1. I recall reading this, but it was before the days when I rolled everything over on my computer, so can’t find the exact reference. If anyone recalls the name of the report, or has a copy, I would be very grateful.[back]