New junior doctor contract is a pay cut: A proof

Many people have eloquently expounded the problems with the contract from a patient safety point of view.  The government have said I won't get a pay cut, and some of my non medical friends have asked me what my problem is as I'm getting a 13.5% pay rise. So I thought I would compare my current pay with the proposed pay from the new contract. Hopefully I can prove I am getting a pay cut despite the government assertion that I'm getting  a 13.5% pay rise. #algebra

I have a 1:8 rota where I work 7 nights (8pm-8.30am) every 8 weeks and 1 Saturday and 1 Sunday day shift every 8 weeks (8am-8.30pm). I also work 5 long weekdays every 8 weeks(8am-8.30pm). Every other day is a normal working day or rest day. As far as I know our department is not planning to change the rota despite the need for 7 day services. I therefore will be working the same hours in August as I am on now. Our rota is EWTD compliant, i.e. we work no more than 48 hours per week on average. Just for the record, I've worked a very similar 1:7, 1:8 or 1:9 rota in every hospital job I have had in the UK, so I don't work a particularly unusual or busy rota, I'm not in the small minority.

Prove by contradiction that new contract will result in a pay.

I will use the assumption that I will not get a pay cut.

Current pay = Proposed pay

Current pay is a 50% banded job  = 1.5x (x = basic salary for 40h/wk normal working days)

Proposed pay: (source NHSE)
 Nights attract 50% uplift
 Sundays attract 30% uplift

 87.5 of my 384 (48hrs per week x 8weeks) hours over an 8 week period are nights. ~23% which attract 50% uplift

and 12.5 of my 384 hours over an 8 week period are long day Sundays. ~3% which attract 30% uplift

No uplift is attracted for weekday long days or Saturday long days. This means 74% of my hours attract normal rate.

New basic salary = y = 1.135x (13.5% payrise)

Proposed Pay breakdown: 0.74y + [0.23 (1.5y)] + [0.03(1.3y)]

multiplying out gives us:

0.74y + 0.34y + 0.039y = 1.119y

substituting y = 1.135x

New pay = 1.27x

1.27x =/= 1.5x

QED

I'm OK for 3 years as my  pay protection is worth the ~4.8k a year I will lose. This is an appreciable amount of money. This is stated very clearly on my NHSE pay calculator. This won't help the new doctors starting  this year or doctors coming from abroad who will be worse off than I am, despite doing the same job.

Not fair is it?