329 days

[Wouter D]

I'm not a statistician chaps, so alas that all means about as much to me as if you'd asked me to provide you with the figures through the form of interpretative dance.

Well, actually...

[Wouter D]

And Wouter - that is rather worrying. Some examples to really boggle their minds are here, in a practical setting where the differences between the various types of average (including different sorts of mean) matter:- https://www.slideshare.net/HORIBA/un...alyzer-results

Excellent, thanks much, Janik!

[Janik]

A genuine question, can we use mean and average interchangeably or is there a difference?

You can, and in most cases in both general and mathematical conversations your interlocutor will probably (but not certainly) assume you are referring to the arithmetic mean so will extract the correct meaning. But it is an ambiguous formulation and it may lead to confusion. Wikipedia currently phrases the situation nicely: "the arithmetic mean..., or simply the mean or average when the context is clear...".
It's not that there is a difference as such, rather that 'average' refers to a whole class of possible calculations of which the arithmetic mean is just the most used example. It's not never even the only form of mean, as I say and Wikipedia implies. For example, the arithmetic mean is the sum (i.e. addition) of all elements divided by the number of elements. However another mean is the geometric one - this is the product (i.e. multiplication) of all elements, divided by the nth root (the root raised to the power of the number of elements). Or in more mathematical notation:-


In VA's example (21, 5, 3, 2, 2, 1, 1), the AM = 5 and the GM = 2.77 to 2dp

Which mean is the right one for expressing the average of the data set depends on context of that set and what you are trying to express about it. Neither is inherently more representative, even if they give notably different results.

[Antepli Ejderha]

You can, and in most cases in both general and mathematical conversations your interlocutor will probably (but not certainly) assume you are referring to the arithmetic mean so will extract the correct meaning. But it is an ambiguous formulation and it may lead to confusion. Wikipedia currently phrases the situation nicely: "the arithmetic mean..., or simply the mean or average when the context is clear...".
It's not that there is a difference as such, rather that 'average' refers to a whole class of possible calculations of which the arithmetic mean is just the most used example. It's not never even the only form of mean, as I say and Wikipedia implies. For example, the arithmetic mean is the sum (i.e. addition) of all elements divided by the number of elements. However another mean is the geometric one - this is the product (i.e. multiplication) of all elements, divided by the nth root (the root raised to the power of the number of elements). Or in more mathematical notation:-


In VA's example (21, 5, 3, 2, 2, 1, 1), the AM = 5 and the GM = 2.77 to 2dp

Which mean is the right one for expressing the average of the data set depends on context of that set and what you are trying to express about it. Neither is inherently more representative, even if they give notably different results.

Clear as mud to me but I sort of get it. Cheers

[Satchmo Distel]

Thanks, most useful!

[Janik]

Clear as mud to me but I sort of get it. Cheers

An argument by analogy - the match last Saturday at Old Trafford was United vs Newcastle. Clear in context, and most people will still know exactly what you mean even somewhat out of context, but slightly sloppy language nevertheless.

[Sporting]

An argument by analogy - the match last Saturday at Old Trafford was United vs Newcastle. Clear in context, and most people will still know exactly what you mean even somewhat out of context, but slightly sloppy language nevertheless.

This would be perfectly understood by readers of the Spanish football press, who have in recent years taken to calling Manchester United just "United" and their neighbours "City" without any previous reference or context, nor any explanation that the clubs concerned might not be Leeds or Cardiff, for example.

[Various Artist]

Just about recovered from the insane statting I did in this thread two weeks ago, and have looked up the current situation and realised the median has moved by one more slot to sit between Jos Luhukay at Wednesday and Aitor Karanka! at Forest.

It's currently between Tony Pulis at Middlesbrough and Jos Luhukay at Sheffield Wednesday – though [...] where precisely it falls is up for debate since both are subject to annotations on the Wikipedia list:

Pulis' appointment was announced on 26 December 2017, but caretaker manager Craig Liddle remained in charge for a match that same day.
Luhukay was appointed as manager on 5 January 2018, but caretaker manager Lee Bullen remained in charge until 7 January.

Simply taking the midpoint of their listed appointment dates, though, rather neatly drops us on New Year's Eve. Since today (Monday) is day 281 of 2018, that makes the present figure roughly 282 days. Going back in this thread, in late September last year it was hovering around 461, so it's taken a very substantial swing back down towards the modern-day 'norm' (?!) in that time. We're barely into October, yet the next AMS of any kind will drag the median date into this calendar year.

The Wikipedia page actually lists both Luhukay and Karanka with the same tally of 286 days, despite also listing the former as having been appointed on Jan 5th and the latter on the 8th: it's seemingly only counting Luhukay's days from the 8th onwards, as mentioned in the annotation above.

Since I factored in the above 'asterisk' against him last time though I'd better do so again for the sake of consistency, so that does give us an 'official' three-day gap between their appointments. Hence the median moves back by a day and a half to 287.5 days ago. A net gain on two weeks back, but the median appointment date for the league's 92 managers has now moved into 2018 – it's now the 6th-and-a-half of January this year.

[pebblethefish]

Possibly could go in the minor pluses of Covid thread, but the median is currently 372 days, which is higher than at any point mentioned above.

Brighton's Graham Potter is the current median (in the rather shorter "minor pluses of Bury's demise" thread, working out the median is really easy when there's an odd number of teams)

[Patrick Thistle]

Oh I remember this thread!!

[Various Artist]

Gosh, I'd forgotten about that mad statting I went off on the last time this thread was active. Must remember not to do that again, I might put it back into stasis for another year and a half. Statistically, about two-thirds of the managers who were in post then should've been sacked by now. Have sackings actually ceased over the last couple of months, as would seem likely?

[Various Artist]

Statistically, about two-thirds of the managers who were in post then should've been sacked by now.

Heh, just looked and it's conformed to that almost precisely. My previous posts were in early October 2018, and there's 31 managers still in post who were at the same clubs then.

That's very saddening though to realise that the demise of Bury means there's currently an odd number of clubs so the median figure at present falls neatly on a single person rather than between two.

On the bright side, there's a truly arrestingly strange and random picture at the top of the page of current longest-serving league manager Gareth Ainsworth though:
https://en.wikipedia.org/wiki/List_o...eague_managers

[Patrick Thistle]

The word (right) in brackets makes that caption though

[lambers]

It's an especially weird one, as the commanche was only really a "thing" when Sanchez was manager (assisted by Terry Gibson), some kind of hangover of Crazy Gang "spirit". I didn't realise it was still hanging around, even when Gareth joined the club as a player.

[Wouter D]

The word (right) in brackets makes that caption though

[Various Artist]

Dammit, beat me to it Wouter!! That penguin one is simply priceless.

[Patrick Thistle]

Hey, anyone else remember this?

Weirdly, Steve Cotterill, the Shrewsbury Town manager is the 45th manager on the list at 342 days. He is just above the median of the 91 managers, just above Lee Johnson (Sunderland) who has been in post 334 days and is 46th on the list.

[Patrick Thistle]

Gareth Ainsworth has dropped from longest-serving manager on the list to second-longest serving manager because Simon Weaver has been in charge of Harrogate for over 12 years. Most of that wasn't as a league manager but I don't have time to work out his position on the list taking his non-league tenure out of the equation.

[Discordant Resonance]

If you date it from Harrogate's league debut (12th September 2020), he has thereby had an EFL tenure of 418 days, so stick that into your table.

[Patrick Thistle]

That won't change the average then as he stays above the median.

[Sunderporinostesta]

Hey, anyone else remember this?

Weirdly, Steve Cotterill, the Shrewsbury Town manager is the 45th manager on the list at 342 days. He is just above the median of the 91 managers, just above Lee Johnson (Sunderland) who has been in post 334 days and is 46th on the list.

The natives are getting restless regarding Johnson. If it wasn’t for the entertainment being provided up the road I think there’d be a lot more pressure on him. He won’t make 400 if results continue in the manner of the last months.

[Patrick Thistle]

After the very recent bloodletting the 46th manager on the list is Thomas Tuchel, whose current tally of days in charge is 284.

So 284 is now the median number of days.

[Discordant Resonance]

How long more can OGS defy the average?

[ursus arctos]

Woodward doesn't want firing him to be his last notable action in charge

[Patrick Thistle]

The 46th manager on the list is now Simon Grayson, manager of Fleetwood Town*, who has been in post 288 days

*as I'm sure you knew...