Category Archives: Sports Scheduling

Explainer: how are football fixtures set?

Graham Kendall, University of Nottingham

When the English football fixtures were announced in June, many fans would have studied them from their own perspective. Are the fixtures fair to their team? Why do they have to travel the full length of the country on a Wednesday evening in the middle of February when, no doubt, it will be cold and raining?

Some people might consider fixtures to be biased. But the truth is that scheduling any sporting event is an incredibly complex job. Let’s stick with the example of English football to understand why.

The basics

English football is divided into four main divisions, with the English Premier League (EPL) being the jewel in the crown, receiving world-wide attention. Each division has to play a double round-robin tournament – that is, each team has to play every other team in the division twice, once at home and once away.

For the EPL, this means 380 games have to be played. The other divisions play 552 games each, making it a total of 2,036 games to be played and scheduled over the football season.


Teams from one division do not play teams in other divisions, so you might think that we can simply schedule each division independently. This is not the case. The football league operates a pairing system. Paired teams cannot play at home on the same day, or even the same weekend. This is done for reasons such as:

Crowd control: The police do not want paired teams such as Manchester United and Manchester City playing at home on the same day. This is because it will mean four sets of supporters will be in the centre of Manchester, making policing difficult.

Revenue maximisation: Some clubs would prefer other clubs not to be playing at home over the same weekend as they believe that it has an effect on their revenue.

Shared resources: Some clubs may share resources such as stewards and if they are playing at the same time, there may not be enough stewards for both fixtures.

Transport: The transport police would like to minimise the places where travelling fans are likely to meet and restrict the number of opposing fans that are passing through main transport hubs at any given time.

It is not always possible to respect every pairing, but the high priority pairings, such as Manchester City and Manchester United, will be given special attention.

Taking the fans into account

Over the busy Christmas and New Year period, the overall travel distances are kept to a minimum to save the fans having to travel long distances.

The fixtures are arranged so that a team does not have too many home (or away) fixtures in a row. This is to spread the costs for the home fans and to give pitches time to recover. In an ideal world teams would have alternate home/away fixtures, but it is impossible to do this for every team, for the entire season.

Even if we only had to consider the factors above it would still be a complex task to produce a schedule that is considered fair by everybody. But these factors just scratch the surface, and many others need to be taken into account.

Clubs will have special requests for a variety of reasons. These could include that their stadium is being used for a music concert on a certain date, it is a public holiday weekend and the town would prefer not to have football supporters visiting the town at that time, or there is another major event taking place in the town which should not be held at the same time as a large sporting event.

The police will have additional conditions, such as not wanting too many teams playing in the area under their control. For example, the number of fixtures that can take place in the London and Manchester areas are restricted. The police will also look at what other events they have to police, such as demonstrations, that are taking place at the same time.

Other football competitions – for example, the FA cup, international fixtures, other European fixtures – also need to be borne in mind.

Some sensitive fixtures may have to be given special consideration due to the previous history of particular clubs, which might not just mean them playing one another but also where particular groups of supporters might meet before and after a match. You don’t, for example, want lots of supporters all travelling through London at the same time, even though the fixtures might be taking place outside of London.

It may be preferential to play some derby fixtures at certain times. Some clubs might prefer to play a high-profile local derby on a midweek evening. They are likely to get a capacity crowd, whereas if the fixture was against a team where the fans had to travel a long way, they might not be inclined to travel on a midweek evening, so the clubs might prefer these fixtures to take place at the weekend.

How are fixtures scheduled?

Before the start of the season the Football League – the overarching management body – sends out a questionnaire to all the clubs asking for any special requests, although they are not guaranteed to be respected.

Once all the data has been collected, the initial schedules are produced. There follows a period of discussion with the key stakeholders – the clubs, the Football League, the Premier League and the police.

The schedule is gradually refined until everybody agrees that they have workable solution. But even with that, some games may have to be rescheduled during the season, because of cancellation, for whatever reason.

How could it be done?

Scheduling sporting events is a popular topic among researchers.

The scheduling of games is not so different from the problem supermarkets face when they need to deliver groceries (or even Santa delivering presents). For any scheduling problem the usual procedure is to develop a mathematical model and then attempt to optimise that model using one of the many tools that are available.

If the problem you are trying to solve is small enough, you may be able to use an exact method. But, as the problems get larger, exact methods tend to take too long, perhaps even millions of years of computation.

If we cannot use exact methods, then we have to resort to other methodologies such as meta-heuristics and hyper-heuristics. These algorithms tend to be reasonably fast and, although they cannot guarantee to return the optimal solution, they tend to give good solutions to the problem at hand.

Amongst the most popular methods for sports scheduling is simulated annealing, which draws its inspiration from the way metals are cooled to ensure that they have a uniform crystal structure. Like many approaches the method is based on a natural phenomena – with perhaps the most well known being genetic algorithms, which are based on Darwin’s theory of the survival of the fittest.

When simulated annealing is used for sports scheduling it starts with an initial schedule – which is probably terrible, but it gives us something to work with. It tries to improve the schedule by making small changes. This might be swapping a home and away team, changing the date of a fixture, switching two home (or away) teams etc. The important thing is that small changes are made in the hope we gradually improve the overall schedule. There are some algorithmic details that we need to control but simulated annealing is easy to understand, easy to implement and tends to run quite fast. This makes it the algorithm of choice for many researchers, and not just for sports scheduling problems, but for a wide variety of optimisation problems – such as delivering groceries.

It works – so why the fuss?

Without doubt, the Football League does a fantastic job in creating the schedules. But there is room for improvement.

We might be able to take more stakeholders into account. At the moment, supporters have little direct input. Perhaps it may be possible to take the weather into account. Or the fixtures could be arranged so that the chances of every team having something to play for are maximised. Or it may allow players to finally take that winter break they have been talking about for a while.

These are all questions not just for English football. Better algorithms are bound to improve scheduling.

Graham Kendall, Professor of Operations Research and Vice-Provost, University of Nottingham

This article was originally published on The Conversation. Read the original article.

Footballers can’t stand the heat? No sweat – just fix the fixtures

Ric Lovell, Western Sydney University

Athletes are paid for pushing their bodies to the limit, but at what stage do we acknowledge that baking hot afternoons might not be the safest time for our sportspeople to ply their trade?

Certainly, Perth Glory coach Alistair Edwards thought the line was crossed in last Saturday’s searing West Australian heat, and duly vented his frustration in the direction of Football Federation Australia (FFA) after the match against Adelaide United.

Edwards raged that the afternoon scheduling of the game compromised the welfare of both sets of players, given the high environmental temperatures in Perth’s NIB stadium (32C).

Unfortunately, this is not an isolated incident and follows calls for revision of heat policies from coaches of both AFL and NRL teams during the 2013 season.

The current climate

The governing bodies of football codes have developed guidelines for matches that are played in particularly hot conditions, in an attempt to reduce the risk of athletes developing heat-related illnesses such as heat exhaustion, exertional heatstroke and heat cramps.

A common feature of these heat policies is the inclusion of additional drinks breaks lasting approximately one or two minutes, the efficacy of which is questionable in my opinion.

The Gold Coast Titans’ Beau Fallon in the NRL match against the Canberra Raiders.

In the AFL’s pre-season NAB Cup, and in the early rounds of the NRL season, additional water carriers and/or subtle alterations to rotation regulations are permitted, should the chief medical officers of the opposing teams agree.

Perhaps a more useful condition of the NRL and AFL heat policy is the potential to increase the relief intervals between match periods, but the FFA and FIFA do not permit extended half-time breaks.

A hot topic

Judging by coach reactions to recent scenarios where matches have been played in challenging conditions, it seems that there is a growing consensus that either heat policies are not being applied appropriately, or that their clauses are insufficient to protect the players health.

However, it’s important to note that the incidence rate of heat injury is very low during training and competition in team sports.

Not long ago, sports scientists and medicos sought to avoid training during the hottest parts of the day in a bid to protect players, whereas pre-season training camps in the Middle East are now commonplace, as players fitness levels are thought to benefit from training in these hot environments.

Greater Western Sydney’s Jeremy Cameron during the Round 20 AFL match against the Gold Coast Suns.

Players in this country are also somewhat acclimatised to performing or training in hot climates so are generally well prepared to tolerate these conditions.

Recent research in AFL, for example, has shown that when matches were scheduled in hot conditions, some players’ body temperatures increased to critical levels, but these were well tolerated by players and heat injuries were not reported.

While players may be able to tolerate these conditions, playing in the heat is likely to exacerbate fatiguing symptoms, with players’ decision-making and reflexes impaired.

This might result in a greater susceptibility to other types of injuries, and it often takes players a little longer to recover from the effects of a game.

Smart fixture scheduling is the key

Whether the increased risk of heat injury when playing in the heat is significant, and whether current heat policies are adequate, are certainly matters for further debate. But these issues can be avoided if TV networks and governing bodies take extra caution when scheduling the fixtures.

The Glory had been lobbying the FFA all week to reschedule the kick-off time, but why did it not occur to anyone when the fixtures were being compiled – that arranging an afternoon fixture in Perth in late Spring could expose players to adverse conditions?

Perhaps it was considered, but the fact that fans on Eastern Daylight Time could watch the match at a more convenient viewing time (5.30pm) might be a more important consideration.

Increasing viewing figures (and advertising revenue) might also explain why the NRL scheduled a game between the Gold Coast Titans and the Canberra Raiders at 1pm in the sweltering Queensland heat during the early rounds of last year’s competition. Or why the Saints, Crows and Power contested in the AFL NAB Cup on an Adelaide afternoon of 38C in February this year.

Certainly, governing bodies and players associations should reexamine heat policies. But we can reduce the need for their implementation if fixtures are scheduled with appropriate considerations for the time of year, and the local weather patterns – not only for the welfare of the players, but also for those fans who watch the game. And by that I’m not exclusively referring to those sweating in the stadium, but the millions of others watching at home on TV.

Because let’s face it: these games played in hot conditions have a reduced intensity, more skill errors, and are generally dull affairs. That’s not really a good advert for either the football code or the broadcaster.

Ric Lovell, Sports Physiologist, Western Sydney University

This article was originally published on The Conversation. Read the original article.

Sports Scheduling: Recent Publications

This forum is part of the MISTA conference series web site.

Looking at the the latest issue of the Journal of Scheduling (Volume 15, Issue 5, Oct 2012), it is good to see that sports scheduling gets two mentions.

David C. Uthus, Patricia J. Riddle and HansW. Guesgen publish a paper entitled Solving the traveling tournament problem with iterative-deepening A* (doi). The paper tackles a problem that was introduced a few years ago by Mike Trick and Kelly Easton. I doubt that anybody realised how difficult the problem would be to solve. It still remains a challenge, even for moderately sized instances.

It will be interesting to see how the community progresses over the next few years.

The other paper in this issue is a review of the various ways that soccer schedules are used in Europe. The details of the paper are:

Dries R. Goossens and Frits C.R. Spieksma, Soccer schedules in Europe: an overview (doi).

This looks like an excellent paper for anybody who is new to the area or, indeed, to those who work in the area and needs an up to date reference of the various competition formats.

I hope more sports scheduling papers will appear in future issues of the Journal of Scheduling, as well as in other journals.


Badminton, match fixing and the problem of scheduling

Anthony Bedford, RMIT University

After a week of ups and down for our Australian Badminton players, we face an unbelievable scenario where players from China and Korea (countries in our group) in the women’s doubles have been disqualified, pending an appeal, from the doubles contest.

In a farcical display, the pairs in four matches were “playing to lose”, with the aim of improving their position in latter stages of the competition. While the result is still pending the outcome of an appeal, we should see our girls, Renuga and Leanne, play in the quarter finals.

Many are to blame here. The Badminton World Federation (BWF) draw does not help minimise the incentive of such occurrences. The scheduling of the top teams in a lop-sided round-robin often leads to a higher likelihood of match-fixing scenarios and dynamic scheduling can avoid this.

The players clearly, and importantly, were not trying to win. The sport deserves better than what we saw – deliberate faults, and ridiculous long shots.

But the players, and coaches, could reason that winning was a dis-incentive, as tougher opponents, or the players’ compatriots, would face them in the next round if they topped or finished second in their group.

Let’s hope our girls capitalise, and as we tag madly for the next matches, that success comes Australia’s way.

For the last five years, Anthony and a team of RMIT University researchers have been analysing video to develop statistical models for training and tactics used with Australian badminton Olympians. RMIT researchers are also developing Olympic ratings and rankings to help in the evaluation of opponents, and likelihood of Olympic qualification.

Anthony Bedford, Professor of Math and Geospatial Sciences, RMIT University

This article was originally published on The Conversation. Read the original article.