# Someone better at maths than me should have a look at this

FTSE 100 firms including Tui, British Airways owner IAG and the London Stock Exchange Group have been accused of dragging their feet on diversity targets ahead of a looming 2021 deadline.

Only 53 of Britain’s largest listed firms on the London Stock Exchange have at least one director from an ethnic minority, according to figures compiled for the second annual update on the Parker review. That is a small increase from the 49 companies that had met the target since the review was launched in 2017.

So, perhaps someone would like to do the numbers here.

The average large company board is 10 people or so.

The not white portion of the population is about 14%. Lower for the working population, lower again for that in the median age for directors, around 60.

From this we should be able to work out a statistical distribution. Mebbe?

How many diverse directors would we expect there to be given this? What’s the over and under if it is just a pure statistical distribution? So, if allocation were purely random from the population, we’d expect x% of firms to have more than 1 diverse, y% to have none etc.

Lordy, it’s a long time since A Level stats class.

In the end the question is, well, how much is this demand insisting upon greater than stats based representation?

## 27 thoughts on “Someone better at maths than me should have a look at this”

1. Pretty sure this is a straightforward binomial distribution problem. A level was a while ago for me too, but probably not as long as it was for you!

Quick and dirty (but also correct, I think) says that if 14% is the correct percentage of “diverse people” in the sample population then a 10 person board selected at random has only a 22% chance of being completely non-diverse.

For 10% and 5% diverse people in the sample population, the chances are 35% and 60% respectively.

Would require more brainpower to work out the probability of having more than 1 diverse person.

2. Ethnic composition of the population may well be around 14% but I would hazard a guess that is heavily influenced by urban areas

Are company directors drawn only from urban areas or from the wider country?

What happens then? Forced nationalisation? Automatic de-listing? The usual wankers have a bit of a moan?

4. “A level was a while ago for me too, but probably not as long as it was for you!”

Yes, thank you for that. I’ll take it as a sign that I’ve matured into wisdom, shall I?

5. British Airways needs to exclusively hire black Muslim lesbian quadriplegic Hellen Keller pilots or they’re racist.

6. Qualifications and age cohorts mean that the non-white bit is probably more like 2-3% in the UK. Which means that the FTSE 100 has more ethnic minority directors than the wider UK eligible population – but since the FTSE 100 includes business that do business overseas it’s kind of moot. I do wish they’d not do this kind of crap.

7. Since it’s Directors we’re discussing, should we assume that people with criminal records should be excluded? People with IQ less than, say, 100? People who can’t speak English? People who are illiterate?

Do we count furriners as “effnik minority”? Surely we ought to. Won’t there be boards with Frogs, Krauts, Eyeties, Cloggies etc on them? Yanks, even?

People who think women are a different species may also like to make a case for their being effectively an ethnic minority.

8. “I have a dream that my four little children will one day live in a nation where they will not be judged by the colour of their skin but by the content of their character”: no wonder somebody murdered the reactionary bastard, eh?

9. Given Ken’s point, then possibly not entirely unreasonable to assume that “diversity” should include age, or that the “ethnic” requirement can only currently be met by appointing younger bodies. So some directors should be under 50, possibly even under 40.

A couple of possible responses spring to mind; the current crop of diverse board members take on multiple appointments across multiple firms, or the size of boards increases to accommodate younger directors, who will have less experience. Board committees will re-form to minimise deleterious effects arising from that inexperience.

Either way, the next round of whingeing and whining is tediously predictable.

I assume that the whole thing is down to Theresa May pulling an idea out of her arse. Again.

10. Its not the ethic composition now that we should be looking but roughly 40 years ago. That’s when people started working and gaining the experience needed to get on a FTSE100 board. And, as dearieme points out, its the proportion entering university or other professions directly that counts.

Furthermore, it not diversity of colour or sex (OK, gender if you must) but diversity of experience and success. Its no use having a multi racial, multi ethnic, multi sex board if they’ve all come from the same universities and gone through the same life experience.

11. May I just say that I now identify as BAME so please may I have a seat on a board? Or two if you twist my arm.

12. Chester T’s numbers are right. To put it the other way, if the relevant qualified sub-population is about 7.5% of the qualified population, then the number (53) is exactly the expected number/average of boards with non-zero representation.

If we followed BiND’s suggestion for that qualified population I’m guessing significant over-representation.

For 53 to be significantly low at the 5% level we would need a representation on the relevant group of 9.1% or more.

13. BiND is correct but we can go further than that by limiting the pool to those who have been working full time continuously long enough to earn successive promotions to board level. The 30% Club was formed by some intelligent women so I’ll take their target as being a reasonable one, probably somewhat higher than the fair proportion as you need to aim a bit higher in order to get to the right number..
What proportion of graduates in the 1970s and 1980s were male from ethnic minorities? Find that number and feed it into Charlie T’s formula.
What’s the betting that Jews are not included as “diverse” in the analysis of Boards of Directors but are in the calculation of minority %age in the population?

14. Radical idea: why not just hire directors – and other staff – on the basis of their suitability & competence for doing the job required?
Would make the whole thing much easier and less discriminatory – except for stupidity.
Boeing is a good topical example.

On the upside, I look forward to the job advert circumlocutions for “No blacks, jews or Irish, because we’ve filled those quotas already and need to top up on: “

15. my liitle quip deleted by HTML rules. Bother.

“…need to top up on: (insert member)”

And Boeing is of course a counter example, of what NOT to do.

16. I don’t know what the ‘Parker review’ is. Sounds insidious.

“Radical idea: why not just hire directors – and other staff – on the basis of their suitability & competence for doing the job required?”

NO!

Hire for whatever damn reason you want. It’s no one else’s business.

In a just world, anyone from the ‘Parker review’ sneaking around would be disappeared.

Additionally, corporations are individuals. They have no GROUP responsibility. What other companies are doing has no bearing on them.

‘improve diversity’

‘Diversity’ is totalist language.

Totalitarian government in UK.

17. Generally these laws do say that you should compare your workforce or directorships to the qualified proportion of minorities in the relevant population. Commonly, this might mean that there is a small number qualified to serve on these boards so they serve on lots of boards, are very well compensated for doing so, and also expected to donate liberally to the politicians who created these opportunities for them. There’s actually a lot of money to be made in being a professional minority.

18. Gamecock; “Parker review” is probably about pens. I imagine Which? runs one every twelve months or so.

19. If you are going to look at alleged under representation on the FTSE100 (which there doesn’t appear to be in any case), shouldn’t one then logically look at possible over representation in parts of the public sector.

And no, I’m not suggesting that obviously, simply a quid pro quo response, I’m with all those that say best person / attributes of those that want to and do apply and be done.

20. It’s a Bernoulli distribution with parameter p = whatever fraction of the class of people that become company directors that are of the applicable hue.

21. Someone on this site (?Jussi) pointed out a week or two ago that when Norway required every Norwegian board of directors to include at least one woman, a tiny group of professional women got about 20 directorships each. Ker-ching!

22. @dearieme February 5, 2020 at 11:48 am

“should we assume that people who” don’t want to be directors should be excluded from pool?

My favourite on this is Khan’s TfL moaning about “not enough non-whites walking and cycling, we must do something” – yep, do shut up

Black boarding bus.
Driver: Sorry mate, nine bus trips per week is max, you’ll have to walk

@Ducky

Yes, Traitor May’s continuation and gold plating of Harridan “Pedo” Harman’s mad-cap ideas

@Justin

Only if you wear that kilt again

23. dearieme,

it’s kind of moot”: only in the barbaric American sense of “moot