Poor return on Premium Bonds

polymaff

eskbanker said:

polymaff said:

Whenever MSE discusses Premium Bonds, the posts become so dogmatic / extreme, e.g.

" ... premium bonds are for people who want to join a club where you give your money to another member on a random basis."

Premium Bonds make sense for some and not for others. The issues are easily understood.

Trouble is, the issues are easily misunderstood too - more than one thread has been bogged down in attritional attempts to pigeonhole them into one of the conventional categories, when the truth is that they don't have any particularly convenient label, but yes, the concept is simple!

Yes, but that's an everday story of MSE Forum posts!  I suppose that PBs are a bit like Regular Savers.  The same issues become combat zones again and again.  For PBs, I blame MSE for its "nutty professor" approach.  I think that, even you accept my "fit-for-purpose" but far less mysterious approach to understanding how non-gamblers can relate PBs to other saving products.

eskbanker

polymaff said:
For PBs, I blame MSE for its "nutty professor" approach.  I think that, even you accept my "fit-for-purpose" but far less mysterious approach to understanding how non-gamblers can relate PBs to other saving products.

I don't have a problem with the principle of publishing a tool to illustrate the highly variable nature of returns, which helps quantify the prospects of receiving nothing like the 'average return', but as ever with stats, they can confuse and need to be interpreted with care, which is evidently beyond many.  The guff about the "post-doctoral cosmology statistician" is unhelpful though, and the calculator is flawed in the way it presents its results, but it can be difficult to get the balance right between oversimplifying and overcomplicating!

Zanderman

WaywardDriver said:

Probability of no wins with £1000 over 27 years is about 1 in 700,000. But you say some early wins so not quite as bad as that. With your holding today you'd expect 1 win every 2 years.

No one should expect any particular number of wins with premium bonds.
It's a game of chance.
You can calculate likelihood of a win.
But that shouldn't be interpreted as expectation of a win.

bowlhead99

Zanderman said:

WaywardDriver said:

Probability of no wins with £1000 over 27 years is about 1 in 700,000. But you say some early wins so not quite as bad as that. With your holding today you'd expect 1 win every 2 years.

No one should expect any particular number of wins with premium bonds.
It's a game of chance.
You can calculate likelihood of a win.
But that shouldn't be interpreted as expectation of a win.

As with all gambles or games of chance, you shouldn't base anything important on what you 'expect' to get out of it. You can't bank it until it happens.

However, it's quite normal for people to set an expectation based on probability of something happening. The term 'expected value' (https://en.wikipedia.org/wiki/Expected_value) is a key part of probability and statistical theory, and is covered in A-level maths, so is generally fine for adults to use it when discussing the expected returns from an investment or other account. 

If you have the max allowed amount of premium bonds, you'd 'expect' to win 23 prizes in a year (based on 600,000 entries at 26,000:1 chance). If that happened, it's most likely that they'd all be the minimum £25 prize, but some years you might be lucky and get something better (statistically, you'd expect that they wouldn't all be £25 prizes if you were doing it year in year out). When I had the max amount of premium bonds I did end up with roughly what I expected, but I have less in there now so the prizes are less frequent which can make it seem less likely that I'll get what I 'expect'...

Zanderman

bowlhead99 said:

Zanderman said:

WaywardDriver said:

Probability of no wins with £1000 over 27 years is about 1 in 700,000. But you say some early wins so not quite as bad as that. With your holding today you'd expect 1 win every 2 years.

No one should expect any particular number of wins with premium bonds.
It's a game of chance.
You can calculate likelihood of a win.
But that shouldn't be interpreted as expectation of a win.

As with all gambles or games of chance, you shouldn't base anything important on what you 'expect' to get out of it. You can't bank it until it happens.

However, it's quite normal for people to set an expectation based on probability of something happening. The term 'expected value' (https://en.wikipedia.org/wiki/Expected_value) is a key part of probability and statistical theory, and is covered in A-level maths, so is generally fine for adults to use it when discussing the expected returns from an investment or other account. 

If you have the max allowed amount of premium bonds, you'd 'expect' to win 23 prizes in a year (based on 600,000 entries at 26,000:1 chance). If that happened, it's most likely that they'd all be the minimum £25 prize, but some years you might be lucky and get something better (statistically, you'd expect that they wouldn't all be £25 prizes if you were doing it year in year out). When I had the max amount of premium bonds I did end up with roughly what I expected, but I have less in there now so the prizes are less frequent which can make it seem less likely that I'll get what I 'expect'...

I accept that the word 'expect' is widely used in stats.  But that's mathematical thinking.  And should be understood as such.

In this context - general chat (particularly in the context of the original OP's post!) about premium bond likelihoods - it shouldn't be used so freely, as many people using it are not thinking mathematically, and they seem, often, to equate it in their heads to certainty.  Which it isn't, obviously.  

People don't - in general - use the term 'expect' for bad things - for instance likelihood of getting run over by a bus.

If you told people the likelihood of them getting run over by a bus was, say, 1 in 1000, they wouldn't then 'expect' to be run over once every 1000 road crossings. They'd be really surprised if they were.

But if you told them the likelihood of winning on the premium bonds was 1 in 1000 many of them would then 'expect' to win every 1000th time. They'd be really surprised when they don't.

People (when not thinking mathematically - and most don't) optimistically misinterpret the mathematical term 'expect' without realising it.  

Gary1984

If the chance of being run over by a bus on any given day is 1 in 1000 then I'd absolutely expect to die within 3 years due to the ongoing bus related carnage. Or stay inside. 

WaywardDriver

Zanderman said:

WaywardDriver said:

Probability of no wins with £1000 over 27 years is about 1 in 700,000. But you say some early wins so not quite as bad as that. With your holding today you'd expect 1 win every 2 years.

No one should expect any particular number of wins with premium bonds.
It's a game of chance.
You can calculate likelihood of a win.
But that shouldn't be interpreted as expectation of a win.

Expectation is a statistical term referring to the average value over a large number of events. For £1000 over 2 years the probabilities of 0, 1, 2, 3, 4 wins are 0.38, 0.37, 0.18, 0.06 and 0.01 respectively. So the expected number of wins is 0*0.38 + 1*0.37 + 2*0.18 + 3*0.06 + 4*0.01 = 0.96 i.e. approx. 1 win every 2 years. 
To put this another way, if a large number of people (say 1000) had £1000 then we would expect 380 to have 0 wins over 2 years, 370 to have 1 win etc. with the average number of wins over the 1000 people being close to 0.96.
Disregarding higher prizes, this equates to prize money of 0.96*25 = £24.96 = £12.48 per year equivalent to an annual return of 1.248%. Taking account of higher prizes the annual return is actually 1.4%.

aroominyork

Thrugelmir said:

I was given a £2 of premium bonds as a christening gift. Never won a prize in more decades than I care to mention. 

Try a new religion.

polymaff

ColdIron said:

polymaff said:

EDIT: Here's the real issue - how do you make this B awful new MSE software single-space paragraphs which show as single-spaced in Preview but as double-spaced when posted - as above?

Try Shift Enter

Finally found a work-around. Don't use Preview.

Then

it looks

just like it should!

Carp Software