## Allowing for measurement error – a principled approach to peak baggingChris Crocker
Recent debate on the latest revision of The reason why the OS declines to quote decimal places is that the measurements aren't that accurate. How accurate are they, then? When I contacted the OS, their Geodetic Advisor referred me to Chapter 11 of J B Harley's A lot of problems with lists can be resolved by changing the issue from "what hills are currently considered to be over 3000ft?", to "what hills should I climb to give a reasonable degree of assurance that I have climbed all hills over 3000ft?" The difference is that the second approach takes into account measurement error (including rounding error) while the first does not. Producing such a list requires an elementary statistical calculation, requiring only the assumption that the errors are normally distributed and that the quoted accuracy is to be interpreted as ±3 standard deviations, as elsewhere in Harley's book. The calculation for Munros is shown below. The first step is to compile a list of "near misses". Thanks to the efforts of Alan Dawson and others, details of 'subs' for most published lists are readily obtainable. In the case of Munros, the obvious candidates are Corbetts of 911m and above. (The probability of a hill mapped at 910m being above 914.4m is too remote to be worth considering). The only non-Corbetts meriting consideration are Creag na h-Eighe (913m) and Meall Gaineimh on Ben Avon (914m), both of which have c 69m of reascent. Although several Munros have less reascent than this, neither of these two peaks exerts sufficient individuality to make a strong case for inclusion - Creag an Dail Mhor to the south of Ben Avon (972m and a Top) has a similar amount of reascent to Meall Gaineimh, for example. The probability of any single hill mapped at Assuming that the errors on different hills are independent of each other, the probability that Similar calculations can be made for other lists. For example, neglecting sub-Murdos will give you only a 22% probability of having climbed all subsidiary peaks likely to merit the status of Munro Top - using the Murdo criterion of >30m of reascent. To get a probability of 99.6%, you need to climb Carn na Caim S Top in Drumochter (914m), Sgurr na Ruaidhe E Top in Strathfarrar (913m), Meall Buidhe SE Top in Glen Lyon (912m and a Munro Top until 1974), Beinn a'Chlachair E Top (977m but 29m of reascent), The Chancellor on the Aonach Eagach (924m, 28m of reascent), and Bidean a'Ghlas Thuill N Top (919m, 26m of reascent), Creag na h-Eighe (not the top in the 1891 For Corbetts, sticking to the published list gives a 51% probability of having climbed those hills meeting Corbett's criterion. "Near misses" include Grahams Beinn Talaidh, Sgurr a'Chorainn, and Cnoc Coinnich, all mapped at 761m, and Shee of Ardtalnaig, Beinn a'Chapuill, and Carn an Tionail, mapped at 759m. To these add Glas Mheall Mor (830m), Marg na Craige (834m), Beinn Gharbh (896m), and Kirriereoch Hill (786m), each with nominally 149m of reascent and an individual 1.4% probability of the actual drop being at least 152.4m (500ft). Climbing all these gives a "completion" probability of 99.98%. Miss out the three 759m hills and it's still 99%. Finally, there is a quite different source of error which I have not attempted to evaluate: the possibility that the measurement is not at the highest point. Spot heights are obtained by positioning a cursor on a computer screen and reading off the co-ordinates; there is no guarantee that the operator has spotted the highest point (or lowest in the case of a bealach), particularly if the hill is not very "peaky". This accounts for some of the differences between 1:50000 and 1:25000 maps, as they are produced by different teams. All this will doubtless seem pedantic to many - but isn't peak bagging pedantic by its very nature? If your objective is to climb Munros, or Corbetts, or some other named list, then fine; but if it is to climb all Scottish 3000ft hills, all English 2000s, or whatever, then a "probabilistic" approach will at least give you confidence of having achieved your goal. |