Next manager odds - strange occurance

[canarybubbles 1,915]

I''m not in any way a statistician, so I don''t understand all this talk of ''regression to the mean''. Surely, if regression to the mean always happened, nothing would ever change? Lambert would not have taken us from L1 to PL, for example, because we would have regressed to the mean.Can anyone who knows what s/he is talking about on this topic, like to explain to this non-statistician, please?

[PurpleCanary 5,557]

[quote user="canarybubbles"]I''m not in any way a statistician, so I don''t understand all this talk of ''regression to the mean''. Surely, if regression to the mean always happened, nothing would ever change? Lambert would not have taken us from L1 to PL, for example, because we would have regressed to the mean.Can anyone who knows what s/he is talking about on this topic, like to explain to this non-statistician, please?[/quote]The problem is that this phrase gets used, sometimes rather carelessly, in two different ways.The first way refers to clubs that have a short bad run of form. This is mainly based on a Dutch survey of clubs that were performing at a certain and acceptable level (their "mean") which then suffered a four-game run of bad results and sacked the manager. The survey showed that these clubs very quickly reverted under the new manager to the previous and accceptable level of form. To their "mean". But that the clubs that suffered a similar run of bad results and kept faith with the manager also similarly returned to their "mean".This led to the now pretty much discredited mantra that "sacking the manager never works because clubs always revert to their mean." Discredited because a look at why clubs in the Premier League have sacked their manager this season shows that in not one case was it because of some four-game dip. There were always deeper-seated and/or longer-term problems.The much more relevant "regression to the mean" refers to the link between finance and performnace. There is no doubt the single biggest factor in where a club sits in the football pyramid is money. Essentially the wealthier you are the higher up you will be. More specifically the more you spend on wages. The link between wage spending and performance is undeniable, and when posters such a T talk about regressing to the mean that is what they have in mind.There is a valid argument about how strictly one should regard this rule, how much context to apply, how much influence a manager can have to buck the trend, for example, and about timescale. But not about the general principle.So in the here and now one view is that what has happened with Norwich City this season is that we are probably in the bottom three  in terms of wage spending and so, after two seasons of over-performing, have simply regressed to our financial mean.

[The Butler 0]

As Nanny Whip would say "I prefer standard deviations to means"[6]

[T 190]

The standard example is tossing an unbiased coin. You may toss the coin a few times and it just comes up heads everytime but if you keep tossing the coin enough times it will come up heads 50pc of the time. Same for a football club. Most people don''t understand statistics because it is a very dry but very important subject as probability governs our lives. Where people say you can prove anything with statistics what they really mean is they don''t understand statistics because you can''t prove something with statistics if the preposition is false.

Related is decision theory so for any stance because people misunderstand probability because it is not intuitive they think we should progress from last season when in reality the probability is we will be relegated. People also tend to blame one person when in reality it is more complicated and they tend to look at near and recent events rather than the long term big picture. If you don''t believe that people have a poor understanding of statistics, probability and reality then this message board statistical proves that theory.

[The Butler 0]

[quote user="T"]The standard example is tossing an unbiased coin. You may toss the coin a few times and it just comes up heads everytime but if you keep tossing the coin enough times it will come up heads 50pc of the time. Same for a football club. Most people don''t understand statistics because it is a very dry but very important subject as probability governs our lives. Where people say you can prove anything with statistics what they really mean is they don''t understand statistics because you can''t prove something with statistics if the preposition is false. Related is decision theory so for any stance because people misunderstand probability because it is not intuitive they think we should progress from last season when in reality the probability is we will be relegated. People also tend to blame one person when in reality it is more complicated and they tend to look at near and recent events rather than the long term big picture. If you don''t believe that people have a poor understanding of statistics, probability and reality then this message board statistical proves that theory.[/quote]

That''s fine and dandy but for true analysis you need to factor in many more variables than you are using, if not you end with a skewed result

The more variables used the truer the final picture becomes.

You can''t prove a false premise but you can ,if you limit the factors to what you require then the results will skew in the direction you want to prove.

At the moment you are citing wages as the main criteria therefore your results will skew in that direction.

Add in, player competence, manger ability, weather factors, influence of support, injuries........and so on, then you are going to get a truer result.

Then of course add in the X factor of chance/luck which you must with anything humans are involved in.(unlike machines they do not always function as predicted)

You might end up with the same result or it might just be slightly different by a place or three.

 

[CiderkiddCanary 0]

[quote user="The Butler"]

[quote user="T"]The standard example is tossing an unbiased coin. You may toss the coin a few times and it just comes up heads everytime but if you keep tossing the coin enough times it will come up heads 50pc of the time. Same for a football club. Most people don''t understand statistics because it is a very dry but very important subject as probability governs our lives. Where people say you can prove anything with statistics what they really mean is they don''t understand statistics because you can''t prove something with statistics if the preposition is false. Related is decision theory so for any stance because people misunderstand probability because it is not intuitive they think we should progress from last season when in reality the probability is we will be relegated. People also tend to blame one person when in reality it is more complicated and they tend to look at near and recent events rather than the long term big picture. If you don''t believe that people have a poor understanding of statistics, probability and reality then this message board statistical proves that theory.[/quote]

That''s fine and dandy but for true analysis you need to factor in many more variables than you are using, if not you end with a skewed result

The more variables used the truer the final picture becomes.

You can''t prove a false premise but you can ,if you limit the factors to what you require then the results will skew in the direction you want to prove.

At the moment you are citing wages as the main criteria therefore your results will skew in that direction.

Add in, player competence, manger ability, weather factors, influence of support, injuries........and so on, then you are going to get a truer result.

Then of course add in the X factor of chance/luck which you must with anything humans are involved in.(unlike machines they do not always function as predicted)

You might end up with the same result or it might just be slightly different by a place or three.

 

[/quote]Whilst this is broadly true, adding too many variables to a statistical investigation or analysis can have just as much of a damaging and unwanted effect as not having enough variables. I think there is always a need to keep a holistic and broader view on things, whilst of course analysis certain issues in detail.I completely understand and accept the reverting back to the mean theory/hypothesis - however surely the ambition of the club should be on changing the mean? The current mean is, I''m assuming, based on the last 10 - 50 years of league positions, points, finance etc? But there''s no reason why in 50 years time we can''t all look back and see that Norwich''s mean has progressed so that the club is a stable top-division side, particularly given the wide geographical monopoly that the club holds.

[PurpleCanary 5,557]

[quote user="T"]The standard example is tossing an unbiased coin. You may toss the coin a few times and it just comes up heads everytime but if you keep tossing the coin enough times it will come up heads 50pc of the time. Same for a football club.[/quote]This is a perfect example of the dangers of regarding probability as an iron law when it comes to football. Running a football club is simply not the same as tossing a coin.If you toss a coin in the air it will roughly, over time, land heads half the time and tails the other half. Because the coin is unbiased and there is no skill in coin-tossing. You cannot influence how the coin will land.But there is skill in running a football club. Not just at the managerial level but in the boardroom too. Some people are markedly better at it than others. They can beneficially influence how their club performs compared with the theoretical probabilities.