PAYE adjustment for personal pension relief does not match my contributions

Hi, I just received a new PAYE coding notice, I made some lump sum contributions to my personal pension last year which HMRC has helpfully added to this years PAYE code (so that I can obtain the higher rate relief), even though I might not have the intention of making any lump sum payments this year. I am trying to adjust the figure on the personal tax section of the web site, but before doing so I am a little confused about the amount HMRC has added to my coding notice. I paid a total sum of £8,500 (gross) last year into my personal pension but HMRC has added £4,250 personal pension relief to my PAYE code - why didn't HMRC add the full amount of £8,500 to my PAYE code? Are trying to "guess" how much I will pay this year? I note that £4,250 is exactly half of £8,500, but I don't understand where this 50% figure comes from? Can someone elaborate how HMRC arrived at this figure?

I have a similar issue so will be interested to know if this is correct.

Hi
Half of the amount goes into the tax code as 20% tax relief will be given by the pension provider.
You will need to contact our helpline to amend the figure in your code.
They will also be able to take you through the calculation.
Thankyou.
Regards.