When Sports Rules Go Awry: How TheConversation led to a collaborative paper

Whilst looking through Conversation articles I came across an article entitled “When scoring an own-goal is the only way to win” by Liam Lenten.

By coincidence, I had just read another article about an analysis of sporting rules from the perspecive of Operations Research, written by a good friend of mine – Mike Wright from Lancaster.

The two articles had some similaraties and, after reading Mike Wright’s article I was already planning to write a follow up. Reading Liam’s Conversation article I posted some comments and he was kind enough to respond.

One thing led to another and we agreed to write a paper together.

I am pleased to report that this article (“When Sports Rules Go Awry“) has just been accepted in the European Journal of Operational Research.

The abstract of the paper reads:

Mike Wright (Wright, M. OR analysis of sporting rules – A survey. European Journal of Operational Research, 232(1):1–8, 2014) recently presented a survey of sporting rules from an Operational Research (OR) perspective. He surveyed 21 sports, which consider the rules of sports and tournaments and whether changes have led to unintended consequences. The paper concludes: “Overall, it would seem that this is just a taster and there may be plenty more such studies to come”. In this paper we present one such study.

This is an interdisciplinary paper, which cuts across economics, sport and operational research (OR). We recognize that the paper could have been published in any of these disciplines but for the sake of continuity with the paper that motivated this study, we wanted to publish this paper in an OR journal. We look at specific examples where the rules of sports have led to unforeseen and/or unwanted consequences. We hope that the paper will be especially useful to sports administrators, helping them to review what has not previously worked and also encouraging them to engage with the scientific community when considering making changes.

We believe that this is the first time that such a comprehensive review of sporting rules, which have led to unexpected consequences, has been published in the scientific literature.

When Sports Rules Go Awry is really a review of where sporting rules have been introduced by sports administrators, but which have led to unintended consequences. For example, when it is sensible to score an own goal. The paper has several tanking (the act of deliberately dropping points or losing a game in order to gain some other advantage) examples.

We hope that the paper will be of interest to anybody who likes sports, as well as sports administrators.

It is pleasing to note that TheConversation was instrumental in making this paper happen. If it were not for them, I would have been unaware of Liam’s work. The paper may have still be written (either by Liam or me) but it would not have been as good as the paper that has now been accepted.

If you are interested, you can see my Conversation articles here and Liams articles are here.

This post also appeared on the University of Nottngham blog pages.

The Monty Hall Problem

You’re on a game show and the host asks you to pick one of three doors. Behind one of them is the star prize: a sports car. Behind the other two are goats. Once you have Goatmade your pick, the show host opens one of the other doors – always revealing a goat. The host then asks if you are happy with your original choice, or whether would you like to switch.

Would you switch? Think about it before reading on.

The Monty Hall Problem

The Monty Hall Problem is based on a game show called Let’s Make a Deal, originally presented by Monty Hall.

This problem was posed to the mathematical community in a letter to The American Statistician in 1975, but was popularised by Marilyn Vos Savant in 1991.

Marilyn’s article suggested that the right thing to do is to switch. If you read the article – and please do – you will see that Marilyn received many very negative comments – some would say rude,  to her conclusion. Here are some examples:

  • You blew it, and you blew it big! Since you seem to have difficulty grasping the basic principle at work here, I’ll explain. After the host reveals a goat, you now have a one-in-two chance of being correct. Whether you change your selection or not, the odds are the same. There is enough mathematical illiteracy in this country, and we don’t need the world’s highest IQ propagating more. Shame!
  • Since you seem to enjoy coming straight to the point, I’ll do the same. You blew it! Let me explain. If one door is shown to be a loser, that information changes the probability of either remaining choice, neither of which has any reason to be more likely, to 1/2. As a professional mathematician, I’m very concerned with the general public’s lack of mathematical skills. Please help by confessing your error and in the future being more careful.
  • Maybe women look at math problems differently than men.
  • You are the goat!

It is incredulous that people could write such comments and – and it is now accepted that Marilyn was correct and the right thing to do is to switch doors. There would have ben some red faces and I hope they apologised.


If you are faced with three doors and choose one of those at random, I think we’d all agree that you have a one in three (1/3) chance of choosing the car.

If one of the other doors is opened, showing a goat, one argument says that switching doors now gives you a 1/2 chance of winning the car.

Another argument says that once you have chosen a door, you have a 1/3 chance of winning the car. If you could choose the other two doors instead you would have a 2/3 chance of winning the car. If you are now showed one of these doors – revealing a goat – by switching, you still have a 2/3 chance of winning the car. Of course, you will not always win a car but over many games, by switching you will win 2/3 of the time, compared with only winning a 1/3 of the time if you do not switch.

There are two ways that might persuade you that switching is the right thing to do.

  1. Increase the number of doors to 50. When you choose a door you have a 1/50 chance of winning the car. This means that there is 49/50 chance that the car is behind one of the other doors. The host now opens all the remaining doors, just leaving your original door and one other. If you stick with your original door you still have a 1/50 chance of winning the car. If you switch, you have a 49/50 chance of winning the car.
  2. We can run a simulation. In preparing this article, I wrote a Java program to do that. We ran the Monty Hall Problem 5,000 times, both switching doors and not switching. If we have three doors, by not switching, the car was won 1702 times, compared to 3310 when switching. These are close enough to the 1/3 and 2/3 win ratios that we would expect. If we now change the number of boxes to 50, if we don’t swap we win the car 99 times. If we swap, we win 4,914 times. Again, this is close enough to the theoretical figures to persuade us that switching is the correct thing to do.

Hopefully, you are now persuaded that you should switch doors when faced with a similar situation. Good luck!


This post was also published on LinkedIn.

Knight’s Tour

Knight's Tour
Knight’s Tour (screen shot from Numberphile video)

If you are interested in Chess, you may have come across Knight’s Tour problem before.

Your task is to take a knight and place it anywhere on the chess board. Then, by performing legal Knight’s moves. can you visit each square on the chess board? Moreoever, you are only allowed to visit each square once (so 64 moves)?

If you end up at the final square, and it would be possible to move to your starting square with a legal Knight’s move, this is know as a close tour. Mathematicians would also recognise this as a Hamiltonian Path.

If you end up on a square where it is not possible to get to your starting position (via a legal Knight’s move) this is know as an open tour.

When you first see this problem, you tend to think that it would be impossible to find any tour, whether open or closed.

You might be surprised to learn that there are 26,534,728,821,064 closed tours. Yes, that’s right, 26 TRILLION of these tours. So if you tried it and could not find one, then shame on you :-).

How many open tours do you think there are? At the time of writing, nobody knows!

The video below does the job of exaplaining Knight’s Tours much better than I can, and it also includes some extra information about semi-magical squares.

I have a particular interest in this video and I had some discussions with Brady Haran (the producer of this series) as I have published a couple of papers on this topic (see here and here) , where we used ants to find Knight’s tours.

The 2009 IEEE Symposium on Computational Intelligence and Games: Report

I have just spent the last week at the 2009 IEEE Symposium on Computation Intelligence and Games in Milan (see last post).

It has been an excellent week both from a scientific point of view and from a networking point of view (I have even added a few new facebook friends as a result of the symposium).

There really is some fantastic work going on around the world. The plenaries and tutorials showed just some of this. The work being done by people such as Ken Stanley, Michael Mateas, Yngvi Björnsson, David Stern (Microsoft Research), Stefano Lecchi (Milestone) and James Vaccaro is very impressive and the products they produce have the commercial sector (some of which work in this area anyway) really taking notice.

Of course, there is other excellent work being done, by a great many other people, and to list them all would mean listing most of the presentations given at the conference. So, although I have highlighted just a few presentations, it does not detract from all the other work being done in this area. Indeed, the newly established IEEE Transactions journal in this area is a testament to how bouyant the area is.

Another highlight at CIG’09 was the competitions. This year they really seem to have come of age. In previous years (at both CIG and other conference) the competitions were very popular, and well received, but it just has a slightly different feel this time around.

At this year’s conference there were four competitions:

I will try and blog about each one in the future.

We hope that the presentations from the symposium will be available to view soon. They were all recorded but there are some copyright issues to resolve.

The symposium will be run again in 2010. The venue has just about been decided but it needs to be rubber stamped so I cannot say on a public forum where it will be.

The 2009 IEEE Symposium on Computational Intelligence and Games

I have just arrived in Milan for the 2009 CIG (Computational Intelligence and Games) conference. This was a conference that Simon Lucas and I started in 2005. Simon is now editor-in-chief of the IEEE Transactions on Computational Intelligence and Artificial Intelligence in Games. The 2005 conference, I believe, was partly responsible for paving the way to enabling this journal to be established. I am fortunate enough to serve as an Associate Editor for the journal.

As I said above, the first conference (actually it’s a symposium, as the correct title is The IEEE Symposium on Computational Intelligence and Games) was held in 2005 in Essex (UK). The original plan was to hold the symposium every two years, but it was so successful that we decided to hold it again in 2006. This time, Sushil Louis and I chaired it. It was held at the University of Reno in Nevada.

In 2007 it was held in Hawaii, as part of the then newly formed Computational Intelligence Symposium Series of conferences (CISS). Simon, again chaired this symposium, along with Sung-Bae Cho and Alan Blair. Actually, at the 2007 CISS, I chaired the associated scheduling conference (Computational Intelligence in Scheduling (CISched).

In 2008, CIG was held in Perth, Australia, chaired by my good friends Luigi Barone and Phil Hingston.

The sympsium has now moved to Milan (chaired by Pier Luca Lanzi). It has certainly done the rounds (Essex, Reno, Hawaii, Perth and Milan) and, having been to all of them, I know from first hand experience that it is going from strength to strength.

Looking at this years program it promises to be a very interesting week. If you have an interest in computational intelligence or games, take a look at http://www.ieee-cig.org/.