The really embarrassing thing about Labour's police plans is not Diane Abbott's gaffe. It's that they simply don't add up

The news coverage about Labour’s plans, announced today, to recruit an extra 10,000 police officers, has been dominated by the agonising interview given by Diane Abbott to LBC’s Nick Ferrari, in which the shadow Home Secretary seemed to forget how much the policy would cost.

Ms Abbott has since said that she simply misspoke this morning (she said the new officers would cost £300k, and then £80m). The actual costing for these extra police officers would be around £300m, she and Jeremy Corbyn said.

And indeed, the Labour press office has released a table explaining how they got their numbers, which do indeed result in a figure of £300m a year by 2021/22 (actually £299m).

And at first glance, the numbers add up: 2250 new officers on the lowest pay rank (£25,400) in year one, a further 250 in London (which pays a little more). There’s a line accounting for the fact that the new recruits will go up one point on the pay scale each year.

Here’s an alternative way of looking at it, but with each column showing you the grand total each category of officers would cost on this basis. Note the £299m in the bottom right cell, which is the key thing:

Tot it all up and by 2021/22 there you have it: 10,000 new police officers, 1,000 of them in London, costing a grand total, by then, of £299m. Now, one could ask why Labour is putting so few new officers in London – currently about 26% of all England/Wales police officers are in London.

Are Labour planning to underfund London in relation to the rest of the country? Is this part of their regional strategy? Or is it simply done to keep the costs down (London officers cost more than elsewhere)? We do not know. But leaving that aside, the numbers look, initially, quite plausible.

Except for one, very important omission. Whichever wonk in the Labour party put them together seems to have forgotten about inflation and pay increases.

Despite austerity, police salaries are planned to increase by up to 1% a year in the next few years. But the Labour costings assume that a new police officer in 2021/22 will earn precisely the same as a newly-recruited officer this year (£25,400). Were police starting salaries to increase by a mere 1% each year starting this year (2017/18), the starting salary by 2021/22 would actually be £26,431.

That might not sound like much of a difference, but the upshot is that by 2021/22 the policy would actually end up costing £310m, not £300m. See the workings here, and, again, note the bottom right cell:

So either Labour is indeed planning even tougher pay cuts than the Conservatives or they have got their numbers wrong.

In fact, a glance through the cuttings shows that Mr Corbyn has said on numerous occasions that he intends to remove the 1% pay cap for public sector workers such as the police. If he is indeed planning to raise police salaries in line with inflation, or indeed broader wage growth around the economy, that would imply them increasing by 2% or 4% a year respectively.

Those pay increases would imply that the policy would be even more expensive. If wages went up in line with CPI inflation of 2% a year, then the extra officers would cost £323m a year by 2021/22. If they went up in line with earnings of 4%, that would mean a cost of £350m a year by 2021/22.

Here’s a table for the cost of each year’s new spending assuming 4% inflation, for those who like such things:

And all this is before one considers the fact that the salaries used in the Labour party workings do not take account of extra allowances and overtime, which can be as high as £4,338 in London. Then there’s the cost of national insurance and pension contributions, which would raise the average cost of a police officer even further. The salary is just the beginning, so the workings above are likely quite generous to Labour. [UPDATE: actually the costings do include NI/pensions, as per this source]

Now, in the grand scheme of fiscal plans, £50m is hardly enormous (though it is considerably more than Ms Abbott briefly thought the entire policy would cost). And if Labour does indeed fund this policy by reversing the Tory plans to cut capital gains tax from 28% to 20%, that would bring in more than enough cash to pay for this (£760m, possibly more, by 2021/22) – though the party has already promised to pay for two other policies – a pupil arts premium and assistance for the steel industry with the CGT spoils.

But such things do matter. Small mistakes like this add up. And they underline something we often see in election campaigns – the party manifestos are often predicated on sloppy, rushed economic analysis that does not add up. Labour is not the only guilty party here: the 2015 Conservative manifesto was notorious for its enormous, open-ended fiscal promises. But this is not an encouraging start.

I have asked Labour for some comment on the numbers above, but they have yet to respond.