The Regression Principle to the Average Value in Sports Betting

Football – a very complex game that can hardly be reduced to simple numerical parameters, and for its meaningful analysis, some new methods are needed.  Old ways (including common sense and expert opinion), however, can also have some sort of scientific basis. Today we will discuss a simple statistical phenomenon that explains several manifestations of this very common sense in sports, including some annoying clichés.  It is called statistical regression to the mean, and is formulated so simply that it looks almost obvious.

This phenomenon can be explained in such a popular example. Imagine that the school conducted a control test in mathematics on a hundred-point system.  Having selected 10% of the best students according to the test results (the average score was, say, 90), the commission after two days is conducting a new testing on the same topic.  According to its results, it turns out that these best students on average scored only 85 points – as if they instead of learning something from their mistakes, suddenly become stupid.  A scandal begins, teachers are accused of fraud, and students are accused of cheating.

In fact, no one is to blame for anything if we take into account that the test result depends not only on knowledge, but also has some random component.  Oecs and omissions of something inattentiveness, guessing the right answer in an incomprehensible task, poor health and mood, in the end – all this together turns into an unpredictable random amount, which can be called “good luck. ” In the top 10% were, first, the average students who were very lucky, and secondly, very good at the usual luck.  The second time all these average is unlikely to be as fortunate, and some of the very good can’t be very lucky.  This leads to regression of the results.

Another example from school life.  At one time in the state of Massachusetts were made plans for which each school was to steadily improve their results on centralized testing.  As a result, the following year it became clear that many of the lagging schools had achieved this goal, but some of the best educational institutions had failed.  Both those and others, perhaps, did not change anything in the process of preparation – simply the result of the measurement turned out to be closer to the average value.  As a result, the state abandoned this way of assessing the work of schools.

The inability to distinguish statistical regression from real cause-effect relationships often leads to inefficient decisions.  At one time in England, set the speed measuring chambers on those sections of the highway, where recently there were many accidents.  Immediately after installation, the number of accidents, as a rule, was reduced.  The traffic police lauded the effectiveness of their method until the statistics interfered.  Having studied the problem, they did not find any significant influence of the cameras on the overall accident statistics and suggested that taxpayer money could be used in more useful ways.

It will be quite natural to assume that the performance of an athlete in a particular match of the tournament also depends on the level of his skill and good luck.  You can argue that there are a lot of other factors that affect each specific game: refereeing, weather, falling in love, partner trauma, anything – but precisely because there are a lot of these factors, they are directed in different directions, not connected and not formalized, they can be taken for a random value.  In principle, there is even folk wisdom, which confirms the validity of such a model.  “It’s football,” they say, when something unpredictable happens.

So, here is a small list of sports phenomena, expressions and common places that can be explained by the manifestations of statistical regression.

Syndrome of the second season

It has long been noted that the budding young player often spends the second season worse than the first, although it seemed that he should get used to the level of rivals and learn something in passing. The secret of this phenomenon, of course, is that attention is paid not to those players who in the first season only appeared for a few minutes at the base, but about those whose first season was outstanding.  Even if the player’s class has grown, the impact of the random component may be too great – and the next season there is a return to more realistic values.

Approximately the same explanation for the term rookie wall, denoting the moment when the shocked beginner is suddenly blown away in the middle of the season.  Beginners, beginners do not shock, in American leagues often sent back to the lower leagues, and those who remain, sooner or later, may regress to the middle.

“Star disease” and the effectiveness of a “hard hand”

If enough time to praise the brilliantly revealing player, he begins to play worse (apparently, being conceited).  If it’s enough to scold a player who does not play well, he starts to play better (apparently, after realizing everything).

The main words in the previous paragraph are “long enough”, and the explanations in parentheses are an attempt to oddsnalize the incomprehensible, soulless statistics (something like those monsters that we saw in childhood in a dark room and which turned out to be just a sweatshirt hanging on a chair).  It may very well be that the player will start playing worse (or better), even if nothing is done at all.

This phenomenon of governance, in particular, was studied by the Nobel Prize in Economics Kahneman – indeed, teachers, managers, parents, instructors get the impression that punishment brings results, and praise affects negatively, even when the effectiveness of the ward does not depend on the method of influence.  Before you trust your experience, remember the law of regression to the average.

Change of coach helps to shake the team

Heads of clubs at some point dismiss coaches – usually after a long series of defeats or one particularly shameful.  With a new coach, as a rule, the team begins to play better.  Leaders are reinforced in the opinion that they are well versed in the problem.  When the team of the new coach after a while suddenly starts to lose more than everyone else to normal, the managers again dismiss the coach – and pretty soon it helps again.  So the sport is arranged.

You already understand: a series of defeats or a loud defeat from an outsider, most likely, are associated with a random component.  The team will most likely start playing better than at the bottom of the form, even if nothing is done – but the leader, who does nothing and waits for the favor of the event, is unlikely to find understanding from the owner (unless he, of course, understands the statistics).

Stability is a sign of skill

This worldly wisdom is also known in the formulation “young – hence unstable”.  Or, if we rephrase it a little: regression to the average is not so terrible, if the average is large enough, and the variance is small enough.  If the player plays several seasons at the same level – most likely, this is really his level.  The more “instability”, the farther the average (that is, the real class) from the best games, let them be remembered in the first place.

The level of the coach becomes clear after the first full preseason

By now you must understand what this means.  This phrase is usually pronounced about the coaches who took the team in the middle of the season (see the paragraph “Change of coach. . . “).  In fact, the coach’s class simply becomes more understandable the longer he trains.  Moreover, if he was lucky at first, then at some point, most likely, he will stop taking it like this.

There is a study, the author of which argues that in the Premier League, luck does not have a significant impact in about 30 games of the season.  In the article, first of all, the percentage of realization of the heads and hits of the target is considered, but as a rough approximation the number 30 is quite suitable in other cases.  This gives, in particular, the additional meaning of the phrase “points for the fall are considered”, which was made to pronounce, when the Russian Football Championship was held on the system “spring-autumn”.

Defending the title is more difficult than winning

Example of regression to the average in pure form: in a fairly competitive tournament it is almost impossible to win the championship without a share of luck.

Curse of Sports Illustrated Cover

One of the most famous sports superstitions: with a player who got on the cover of Sports Illustrated, something bad is happening soon – a trauma, an accident, or simply a sudden recession.  In 2002, SI had a special project, dedicated to the impact of the cover on the fate of athletes.

I think you already know to what conclusions the statistician William Briggs came, having learned that 37% of the 2,456 hits on the covers led to any trouble.  Players get on the cover exactly when they perform best – most often when they perform much better than their average.  And at some point they return to their average (note – it’s to the middle, do not make the mistake of the player who thinks that after 20 eagles the chance for tails falling out increases).  Sometimes they are injured, sometimes they get into accidents – simply because the players are sometimes injured and fall into accidents, and when it happens to a bright star, it’s better remembered.

In general, remember: there is a lie, there is a blatant lie, there are superstitions – and there are statistics that should not be thoughtlessly trusted, but which can be understood.