DS ranked Top 150 for Tommies, Marling and Crypt, but 235 for Pates, so I've been looking to see how many children shared their results with each school:

Pates: more than 1800
Crypt: just over 2000
Tommies: 1031
Marling: 912.

Given that Pates qualified the top 230, this means that at least the top 230 reached the minimum standard in all parts of the test (as Pates are the only one who require this). At 235, it's highly likely that DS did too. He's in the Top 150 for Crypt, which as another mixed school is the only one we can compare to. Crypt had more children sharing, which if anything would have made it harder for DS to get in the Top 150 - but it's the other way round. So I can only conclude that there were children who shared with Pates but not Crypt, who ranked more highly than DS. Maybe some of the brighter out of county children are only interested in Pates?

Not that any of it matters at this point but I'm just trying to get my head around it all! You would think with a score of Top 150 in Crypt but not Pates, he must have done particularly well on one part of the paper but not quite met the standard on another bit.

I'm also curious to know where in the Top 150 he came for the various schools but none of the boys schools tell you (unlike Ribston). I can only assume that he must at least be around 75 for the boys' schools if he's Top 150 for a mixed school.

Now we just need to decide which school......

Do you live closer to Crypt than Pate's? If there are equal scores then they'll be in order of distance from school. Not sure that would make that big a difference though?

Distance from the school does not affect the ranking for any of the grammar schools. It is purely on the test result.

If you have a significantly lower result for Pates than Crypt then it would suggest that your DS had a good average result but had one weaker paper which pulled him down the Pate's ranking.

"If two or more children achieve the same total score (i.e. have the same Test
ranking) their respective positions in the rank order, whether for entry in to
Year 7 or in any subsequent year, will be determined by closeness to school
(measured in a straight line from the front door of the child’s address at
registration, to the front entrance of Pate’s)."

Have I misunderstood the admission criteria? I read that to mean equal score/test rank would be put in order of distance, so they would have a different rank position despite the same score. I'm probably misinterpreting and over-thinking! Not sure how many would be affected by this anyway?

I thought the distance was just for admissions but reading that I can see it suggests it would be used when 2 children have exactly the same standardised score to provide the rank for that school.

However I don't know if other schools do the same, and I can't imagine that there are about 70 children all with exactly the same score who have been ranked by distance.

In any case, Pates is our closest grammar school so that's not going to be the case here.

I think he must have been pulled down by one section, as guineapigs suggested earlier. I can't imagine exactly how they wok out those Pates rankings though!

I've broken the news to him - his first reaction was "can we appeal?" but he's accepted that we can't and realised that actually, that was an amazing score, so he's bounced back up and is feeling proud of himself now. I think it helps that one of his friends who was expecting to get into Pates is in the same situation - he thought the friend would have done better than he did so it sort of validates his own score.

Pate's could have many just apply for them and not the others?
Pates may be the only one they would consider a long commute to, or parents may work/travel to Cheltenham, GCHQ for example.
Many may only consider Pates if Balcarras is their catchment school etc

Possibly - I believe this is under Pates "Qualifying and oversubscription policy" - it comes into effect when the school is oversubscribed at allocations, rather than affecting the test result rankings.

This is just about admissions - which, until you put your CAF in, you haven't done yet. They refer here to the "same Test ranking" - that is what you have currently, based on your child's total score. If you have the same test ranking as someone at application/admissions, you will be given separate rankings based on distance.

Sorry to hear your DS was unsuccessful for Pates. I suspect that your original thought that the cohort is different is correct, rather than DS doing badly in one section. Last year, NVR was very hard so it caused some strange anomalies in Pates rankings, but the feedback after the latest exam seems to be that it was easier than expected, so I don't think the same thing will happen this year.
Looking back to the 2018 crypt /Pates scores, there was about a 55 ranking gap between them. You clearly have a bigger gap, but it might be that girls have done particularly well this year, or more people have just applied to Pates.