The maths of calculating “new manager bounce”: A statistician chimes in

Chris Martin examines the theory after Neil Harris got one over County at the weekend on his return to the Cambridge dugout

Feb 26, 2025

Wednesday 26 February 2025

If you’d like to write an article for The Scarf My Father Wore, share a few snippets or photos, or advertise your business, please email thescarfmyfatherwore@substack.com.

NEXT HOME GAME: Blackpool – Saturday 1 March, 3pm

NEXT AWAY GAME: Northampton Town – Tuesday 4 March, 7.45pm

Evening all!

A slightly later email dropping in your inbox today. I’ve spent most of this afternoon planning a new monthly stand-up comedy night I’m hosting in Stockport. The first one’s taking place on Friday 28 March at The Fingerpost in Offerton, and obviously I’d love to have some of you lot in the audience. Tickets are £15 for a fantastic line-up of four comedians, and the headliner will be someone off the telly! I’d really appreciate it if you’re able to support my first night. Drop me a message if you fancy it.

We’ve got something a little bit different for you to read this evening. County fan Chris Martin - who runs his own market research business called Genie Research - has written an interesting article for us concerning the theory of the “new manager bounce”, after it certainly seemed to play a part in Saturday’s proceedings at the Abbey Stadium. As you can see from the article, though, there’s a lot more to it.

Today’s edition is sponsored by Lynx Taxis. A big thank you to Ehsan.

Finally, I’m currently walking every street in Stockport to raise money for mental health charity Mentell. If you’d like to make a donation to help me reach my target, please click here.

Total distance so far: 216.74 miles

Total steps so far: 353,516

Total raised so far: £2,270

Total completed streets so far: 474 (Click here for the full list, which includes reports and photos from every day of the walk.)

Further information on the walk can be found by clicking here.

Des Junior

Photo credit: Cambridge United FC

How could we calculate if there really is such a thing as “new manager bounce”? The most obvious way would be to look at the run of games immediately after a manager change and see if it was better than the run of games immediately before the manager change. And if you do this across all clubs and seasons, it does show some improvement most times it happens. But it’s probably not mostly down to the new manager.

As County fans we all know painfully well that clubs go through random spells of above - and below - average results. There’s no logic to them necessarily. Usually there are reasons you can point to after the fact, but other times those same reasons can show up without having such an effect. What we also all know is that those runs eventually come to an end.

Every week for decades, the American magazine Sports Illustrated put on its cover a picture of a sportsman on a hot streak. But more often than not, that sportsman would very soon end their streak and start a run of bad performances. Superstitious sportsmen know this as “the Curse of Sports Illustrated”. Statisticians know it instead as an example of “reversion to the mean”.

Imagine you’re rolling a fair six-sided die. You happen to have rolled several 1s in a row. You might think, “Oh no, this die only rolls 1s now!” But it’s still a fair die, you just got unlucky. So your next several rolls are still likely to average out at 3.5, which is the average (what statisticians call “the mean”) of (1+2+3+4+5+6)/6. And likewise if you’d rolled several 6s, your next several results will probably go back down to 3.5. In the long-run, your die rolls will always go back (revert) to this average (mean): reversion to the mean.

The Curse of Sports Illustrated is obviously an example of mean reversion after rolling a string of 6s. But it might be less obvious that changing a manager is an example of mean reversion after a string of 1s. The important fact is that a manger is generally only changed deep into a very bad run. The bad run will usually have had some reason for it - for example in the Premier League this season Southampton have clearly not merely been unlucky, they’re simply a lot worse than the other teams - but there will also have been an element of bad luck. Sport has a lot of chance in it: it’s not rigidly predictable. The team has probably been rolling a long series of 1s. So its next few games are likely to be at least somewhat better whether they change the manager or not.

This isn’t to say the new manager makes no difference. There are important psychological effects when a new manager takes over, like the players wanting to impress the new gaffer or feeling inspired with new hope. But at best these probably only kickstart the process of mean reversion, of randomly rolling better than 1s at last.

If we wanted to really test whether a new manager made a difference above the effects of mean reversion, we could compare the improvement in teams that changed their manager with the improvement in teams that had similarly bad runs but stuck with their manager. This would be closer to a fair comparison, and might show some small new manager bounce above the effects of normal mean reversion. Even then though, there would be other factors that stop the comparison from being perfectly like-for-like. Take it from a statistician: stats are not an exact science!

Download the app for Lynx Taxis

Lynx Taxis is South Manchester and Cheshire’s largest private hire and taxi operator, with over 600 drivers completing over 2 million trips a year.

With a bumper crowd of 10,000 expected at Edgeley Park this Saturday, avoid any hassle trying to get a taxi, and download the Lynx Taxis app now.

➡️ Visit lynxtaxis.co.uk for further details.

Photo(s) of the day

Blackpool, Lancashire

Regular readers will know I always share a random photo each day, whether that’s from the past or the present. With Blackpool coming up this weekend, I thought I’d share a snap or two from last August, when County won 3-0 at the seaside in front of 3,911 jubilant away fans. However, upon noticing that I took 55 photos that day - and realising that number very neatly divides by 5 - I’ve decided to share the whole lot over the course of this week! Here’s the third lot, with some extremely pissed County fans in The Manchester (it’s not even 2pm at this point!), before the short walk to Bloomfield Road.

Today in SK

🍺 Food and drink

The Nelson Tavern (SK1) have a great range of offers throughout the week, including £5.50 for drinks off the Doubles Bar, a comprehensive range of shots for £1.50, and 3 for £7 on Jägerbombs. Also, double up for £2 on premium spirits.

Bitter £2.30 a pint all day at The Cross Keys (SK8).

A number of venues are featured on The Scarf My Father Wore such as The Crown (SK2), The Dog & Partridge (SK2), The Alexandra (SK3), The Crown Inn (SK6), The Steelworks (SK6), The Three Tunnes (SK7) and The Ram’s Head (SK12). Support them this month by popping in for a few drinks and a bite to eat.

Random snippets from old County programmes

#3 - County v Lowestoft, 2 April 2016

Richard Park shares an important update in his programme notes.

We have also had some very pleasing news off the pitch as you will have heard through the media. We are extremely grateful for the support we have received by our former Director and shareholder Spencer Fearn with whom we have reached agreement in relation to his outstanding loan.

Spencer put money into this club when it was badly needed and it is clear that he still has strong feelings for the club.

We still have work to do but over the last two years we have made huge strides in making this club sustainable and as we continue to progress matters off the field will also become much more attractive to potential investors. That said, we will only ever welcome investment on the basis that it does not undo any of the great work that has been done by so many people in the last couple of years.

We believe that we have a strong dedicated team committed to building our business off the field and we also have a strong, experienced and visionary team managing our on field affairs.

Together we WILL get this club back where we feel we belong. Enjoy the game and the rest of your weekend.