Is "average luck" a good concept in Premium Bonds

AnotherJoe

Zanderman wrote: »

The OP hasn't logged in for a year, and has only posted one post (this thread) 2 years ago, so it's probably pointless correcting him/her now.

Grr. Who the heck woke this thread up then?... ah, sharkstar.

sharkstar

There's precious little explication of 'average luck' on the internet, so I was brought here by a search whilst thinking about luck in general. I wasn't trying to criticise the MSE approach, just offering a view on the use of the phrase in this context of outcomes over time. The MSE approach, using the median, is consistent with my example, with the associated probabilities of winning appropriately adjusted.

eskbanker

sharkstar wrote: »

In the context of Premium Bonds, in order to say something meaningful about your chances of winning a prize over 12 draws for a given holding, you need to anchor the answer with reference to average luck.

But to go back to this comment, I still don't think the use of 'average luck' is particularly informative and personally find the detailed breakdown of probabilities much more illuminating. Taking the example of a maximum £50K PB holding over a year, the MSE calculator highlights reasonably granular probabilities of outcomes as (ignoring the outliers outside 1-99%):

At least £400 97.7%
At least £450 93.9%
At least £500 87%
At least £750 24.7%
At least £1,000 5.64%
At least £1,500 1.45%

However, it's still far from perfect because the median outcome here will actually be about £625, so the conclusion that the 'average luck' result would be £500 (solely on the basis that this is the last of the chosen data points with a probability of over 50%) is obviously flawed. Therefore looking at the table of probabilities is a more accurate indication of the likelihood of various outcomes rather than swallowing the oversimplified conclusion that "With £50,000 in Premium Bonds, if you have average luck you would expect to win roughly £500 over 1 year"!

And then back at post #5 a couple of years ago I gave a more extreme example of the dangers of using averages....

sharkstar

I agree that, for the statistically minded, the question 'What is the probability of my winning at least X with a holding of Y over a period of Z months' is a much better way to go. I guess NS&I were trying to present something for the less statistically minded. The problem, however, is that the concept that they are using in this attempt - 'average luck' - isn't one that is widely used - indeed it may be that they invented it. My interest here was just to try to figure out what they might have meant, which is where I was going with the idea of 'winning as often as might be expected, given the odds', but the fact that I had to try to figure it out demonstrates the problem. Anyway, thanks for your engagement on this, it has been helpful, and apologies for resurrecting an old thread. I'm more used to engagement on Twitter, and I did feel a bit like I'd barged into someone's front room.

eskbanker

sharkstar wrote: »

I guess NS&I were trying to present something for the less statistically minded. The problem, however, is that the concept that they are using in this attempt - 'average luck' - isn't one that is widely used - indeed it may be that they invented it.

Just to be clear, the whole 'average luck' thing is entirely MSE's work and nothing to do with NS&I, who, being a government agency, present information is a reasonably neutral and factual manner, whereas MSE, with their inherent desire to please via a jauntily dumbed-down house style, choose to try to encapsulate the luck-based principle of PBs by dressing up the median average in terms they believed would help.

To be fair, the median is a much better measure than the mean, in that the circa 1.2-1.25% typical winnings (with a large enough holding) are a more useful and accurate indicator of expected return than the 1.4% quoted by NS&I as the "Annual prize fund interest rate".

sharkstar

Exactly. The vast majority people won't be exposed to the bigger prizes. Life is too short. The other source I've found useful in thinking about this idea of average luck is Maboussin's 'The Success Equation', which you might have read, although he's more concerned with untangling the effects of luck and skill on success. Obviously, there's no skill in investing in Premium Bonds.