Consecutive pairs of units

[Peter Mugridge]

Noted 377 131 and 132 are paired up running together at London Bridge this morning. Checked RTT to make sure.

Is it a coincidence or is that getting them ready to send to SouthEastern?

They're currently in ordinary passenger service, so I think it's a coincidence.

I'm seeing a far higher volume of consecutive pairs everywhere these days than I would expect by chance, so I do wonder if people in control rooms across the country like to unofficially try to play around to do it on purpose?

Last week, for example, I saw 444 025 + 444 026 paired up. I've seen consecutive pairs of 220s paired up. I've seen consecutive pairs of 450s paired up...

Would the more mathematically minded members here be able to calculate, from the fleet sizes and number of diagrams, how often it should be happening if it is purely by chance without anyone anywhere trying to influence it?

Does it just seem like it's happening more often than it is? Does a consecutive pair stick in the mind more causing this feeling? ...or is it really happening more than pure chance would suggest it should?

 

[tumbledown]

From a group of n units numbered consecutively, 2 taken at random should have consecutive numbers 2/n of the time.

 

[Peter Mugridge]

From a group of n units numbered consecutively, 2 taken at random should have consecutive numbers 2/n of the time.

So in the case of the 444s, for example, we should expect it 4.4% of the time, so roughly once in every 25 pairings, meaning there should be at least one instance a day - the chance being slightly increased by the Bournemouth / Weymouth splitting and joining?

 

[MatthewE707]

Would the more mathematically minded members here be able to calculate, from the fleet sizes and number of diagrams, how often it should be happening if it is purely by chance without anyone anywhere trying to influence it?

Obviously more complicated when units attach and detach during the day, but for a simple example, such as Heathrow Express:

12 units (387130-141), 5 pairs diagrammed per day (assuming the pair that go to Reading depot as 3R45 are the same units that return as 3T60)

12 choose 10 = 66 ways of selecting 10 units to be in service, 11 pairs of consecutive units

For each pair of consecutive units: Probability of both being in service = 10/12 x 9/11 = 15/22. Probabiity of them being paired given both are in service = 1/9. So overall probability of them being paired on any given day = 15/22 x 1/9 = 5/66, or around 7.5%

5/66 x 11 = 5/6, so an 83% chance of having a pair of consecutive units on the Heathrow Express on any given day

 

[Peter Mugridge]

Thank you; hmm... I think my calculation for the 444s might, then, be a bit over-simplified...?

 

[MatthewE707]

so an 83% chance of having a pair of consecutive units on the Heathrow Express on any given day

Obviously this also assumes the pairs of units change each day. There is currently one consecutive pair on the Heathrow Express (which have been together for around 2 weeks now) - so this example seems to work out

Thank you; hmm... I think my calculation for the 444s might, then, be a bit over-simplified...?

The 444s are difficult to work out due to all the splitting and attaching, but if you assumed 42 out of 45 were in service per day (approximately correct), and they were in 21 pairs which didn't change during the day, there would be a 93% chance of having a pair of consecutive units on any given day

Taking into account that there are approximately 43 different pairs of 444s which exist during one day, you would expect around 2 of these 43 to be consecutive units. This still isn't quite accurate as it assumes all of the units in service have an equal chance of being in each pair - when in fact some of the 444s on Portsmouth diagrams stay in one pair all day. However, looking at the 4th September (which I happen to have the 444 diagrams from), there were indeed 2 consecutive pairs, suggesting there probably isn't anything strange going on

== Doublepost prevention - post automatically merged: 14 Nov 2025 ==

I've done one more example, of the 707s, which comes out at 0.9 per day, and on the 24th September, there was 1 - another example fitting the maths

 

[tumbledown]

5/66 x 11 = 5/6, so an 83% chance of having a pair of consecutive units on the Heathrow Express on any given day

I like your workings but have doubts about this last step.
Probability of no pairs being in service = 61/66^11≈42%, so probability of at least one pair being in service ≈ 58%.
Multiple pairs become complicated as e.g 4,5 being paired precludes pairs 3,4 or 5,6.

 

[brad465]

In December 2017 I saw 465934 and 235 in service together for a few days between Christmas and New Year (neither unit exists now); technically these are consecutive units as the former used to be 234. Also, while technically not a passenger service, 465238 and 465239 were both dragged to Newport together for scrap earlier this year, so rather poetically, they were born together, and died together.

 

[Flange Squeal]

I know a shunter who, when noticing they had some sequential numbered units come in on separate arrivals that evening, would plan some overnight shunting that would just so happen to "coincidentally" see sequentially numbered units leave together in the morning. Not sure the depot drivers found it quite as amusing though

 

[pokemonsuper9]

In over 400 non-commute journeys, 3 have been consecutive pairs (158786+158787, 156418+156419 and 331025+331026).

And in over 900 commuting journeys, 8 have been consecutive pairs (150136+150135, 150135+150136, 150114+150115, 158870+158871, 158844+158843, 158844+158843, 150110+150109, 150126+150127)

 

[NSEWonderer]

455 wise the Wimbo boys still have this running about: https://www.realtimetrains.co.uk/service/gb-nr:L51375/2025-11-14/detailed

 

[stadler]

About ten years ago i had 377301 + 377302 + 377303 + 377304 as a 12 car in that order on an East Grinstead service. I bet that was arranged by some shunters overnight who were bored and noticed four consecutive units in the depot. It is the only time i have ever seen four consecutive units coupled.

 

[bb21]

Thank you; hmm... I think my calculation for the 444s might, then, be a bit over-simplified...?

Bear in mind there is only 41 required each day of the 45, and the missing four could have different composition to affect the number of available pairs in service.

Quick look suggests 1W25 was 444016+444017 today, 1W12 was 444025+444026 yesterday, nothing consecutive on 12th or 11th however 1D34 was 220019+220020 on both days, 1B14 was 444019+444020 on 10th. So not a very high strike rate on the 444s but a 100% success rate at Bournemouth station. 221119+221120 was on 5M26 on 10th however that got split into two separate passenger services.

 

[NSEWonderer]

Rare is ever seeing a consecutive hybrid Desiro pairing. Closest I've ever seen is 444026 + 450029.

 

[MatthewE707]

I like your workings but have doubts about this last step.
Probability of no pairs being in service = 61/66^11≈42%, so probability of at least one pair being in service ≈ 58%.
Multiple pairs become complicated as e.g 4,5 being paired precludes pairs 3,4 or 5,6.

I've written some code to select 10 random numbers from 1-12 and assign them randomly into 5 pairs 10000 times, then output the results. It seems we're both right, although I think I worded my result wrong before: On average, there should be 0.83 consecutive pairs per day, and the chance of having at least one is 59%

 

[172007]

Tyseley depot reguarly send units out deliberately in consequetive number order all the time. Some of the staff like the challenge to get them shunted into pairs like that. You can tell its deliberate as some days they are all random then other days multiple units are consequetive numbers.

 

[bb21]

Tyseley depot reguarly send units out deliberately in consequetive number order all the time. Some of the staff like the challenge to get them shunted into pairs like that. You can tell its deliberate as some days they are all random then other days multiple units are consequetive numbers.

May be interesting to see whether that had any correlation to which production manager was on duty.

 

[pokemonsuper9]

If WMR's 139s ever rescue each other they'll be paired consecutively.

 

[Chiltern006]

Had 450101+102+103 last year. Must be quite rare to have 3 consecutive in a class so big

 

[Peter Mugridge]

This is more interesting than I thought; in summary it seems that in some cases it is being done on purpose but most of the time it really is just a coincidence?

 

[NSEWonderer]

Had 450101+102+103 last year. Must be quite rare to have 3 consecutive in a class so big

Now that is rare. I thought I had also seen 3 450s consecutive but couldn't remember the numbers

 

[xotGD]

331015 and 331016 were paired up yesterday (I was on them) and looks like they still are today.

Meanwhile on this side of the Pennines 331002 and 331003 are together this morning.

 

[ThePeakNed]

I know a shunter who, when noticing they had some sequential numbered units come in on separate arrivals that evening, would plan some overnight shunting that would just so happen to "coincidentally" see sequentially numbered units leave together in the morning. Not sure the depot drivers found it quite as amusing though

Was a Team Leader at Newton Heath would do the same after I made him aware of the concept

 

[brad465]

465166 and 465167 were together last night:

Realtime Trains | 2M64 2357 London Victoria to Orpington | 14/11/2025

Real-time train running information for 2M64 2357 departure from London Victoria to Orpington on 14/11/2025. From Realtime Trains, an independent source of train running info for Great Britain.

www.realtimetrains.co.uk

 

[Peter Sarf]

With 730/2s at Euston I noticed last night a few pairings where the last digit is the same. But I think I have worked out the probability is 3/10 for numbers ending 1 to 6 and 2/10 for numbers ending 7 to 0. So not really unlikely !.
I guess those become slightly lower probablilities if we include the possibility of a short form happening !.

 

[1D53]

There's a Facebook group dedicated to these 'Nice Pairs'!

 

[172007]

Tyseley have banged out a couple today.

 

[xotGD]

One from the archives

28th May 1988

I had 37682 + 37683 Shrewsbury - Wolves on 1A44

 

[31160]

There's a Facebook group dedicated to these 'Nice Pairs'!

Ooh err

 

[Thornaby 37]

One from the archives

28th May 1988

I had 37682 + 37683 Shrewsbury - Wolves on 1A44

25th May 1988
37427 + 37428 1J24 Shrewsbury to Aberystwyth (but with Cardiff Canton only having six 37/4s, 426 to 431, a consecutive pair would nave been regular on this working)

Also 31146 + 31147 were a regular pairing on the Cambrian in summer 1992