After my activation of G/WB-004 today I have moved onto the same activator points total as Jack GM4COX… nothing that noteworthy… however I happened to notice that this is made up of exactly 1960 points plus 387 bonus points… FOR BOTH OF US!
Now Gerald, give me a few days to get my SOTA Chasings and Activations loaded up to the SOTA Database to bring me into ‘sync’ with it, but unfortunately it takes us out of ‘sync’ - unless we agree to stay in ‘time-warp’
The odds cannot be calculated unless you are a lot more specific about the assumptions you are making about the activation pattern. But they may be shorter than you might think.
With a total score of 1960 we know that the number of bonus activations must be between 0 and 392. If we assume each possibility as equally likely then the odds against a coincidence are 393:1. Not a good bet but hardly in lottery territory.
In practice with real activators the values towards the middle of the range seem more likely, and any bias can only shorten the odds. Of course if the activators in question are known to behave very differently then a coincidence becomes very unlikely.
Your model loses credibility with that assumption Martyn. The probabilities of the possible numbers of bonus activations are more likely to follow a decay curve along the lines of Benford’s Law.
In general though, I tend to agree with the themes in your post.
Now, what about my 076 vs 076 “coincidence”? Is it, in fact, “to be expected”, as both QSO partners will have been contesting in the same event for an equal amount of time? Or would the argument be that you would still be more likely to receive 001 even when giving out 076?
I can’t stop the rain but as there isn’t anything else to do here is my slant on the great co-incidence. Bear in mind any statistical analysis will have an outcome that depends on the initial conditions, definitions and constraints. Nevertheless the simpler the analysis the better in most cases.
Lets limit the analysis to a period of time, say the last 12 months. You can change this if you wish.
I don’t know how many activations took place but for the exercise lets say it was 4,321. In that year two stations finished up wit the same number of activator points and the same number of bonus points. Again for the exercise lets assume that there were no more.
Clearly the probability is 2 in 4,321, for that year.
Considering the original question, what are the odds of that happening, all we need to know is the number of possible alternative combinations. if there are 500 alternatives, the odds are 1/500. But the variables affecting the number of possible alternatives are many.
The number of alternatives is debatable indefinitely so I submit that there is no specific numerical answer to the question, it must be treated as rhetorical. My answer is therefore: “slim”.
[following analysis is just plain wrong - retained for historical purposes only] I did consider it interesting that the two activators in question have the same callsign prefix, indicating a home location in Wales [edit: wrong: one is Wales, the other Scotland]. The common availability of summits at various points values, some with winter bonus and others not, would suggest the profile of available summits for the two operators would be similar. I did not research the number of years or the number of activations by each operator. But if the number of years was identical or nearly so, I think these factors all reduce the odds of their scores being widely different. So my secondary answer is “slim, but not as improbable as it would be for activators in different parts of the UK, or indeed in different countries”.
In the case of bonus points, the common 129 activations could be divided by the number of years of activations and it may well be that the dividend would be close to the number of relatively close summits attracting bonuses, so each operator activated each of those summits during every bonus period. Another narrowing of odds.