Regretfully, I have [had] to make corrections to my (open access) quantitative analysis of open-source data on metal detecting for cultural property: estimation of the scale and intensity of metal detecting and the quantity of metal-detected cultural goods. They do not undermine the findings or their significance. The miscalculation produced an underestimate that reduced the apparent significance of the results.
I notified the journal 27 weeks ago and hoped to arrange the corrections, then announce them. Yesterday, I was informed that corrections could not be made until response papers had been processed and a response was still being processed. I understand and support the journal’s due process and the rigour of that process. However, I also want to correct the public record. [It was officially corrected on 13th March 2018.]
Reproduction errors
Quotation on page 2
In the introduction to the submitted version, I provided a quotation and cited ‘Thomas, 2016, p. 141; see also Huth, 2013, p. 133’. Whether by the bibliographical program or the proofreader, in the published version, this was converted to ‘see also Huth, 2013, p. 133; Thomas, 2016, p. 141’, which detached the author from their statement.
Quotation on page 18
In the section on the Netherlands in the submitted version, I provided a quotation and cited ‘KN, 2016, Ch. 2, Art. 2.2; see also VDA, 2016’. Whether by the bibliographical program or the proofreader, in the published version, this was converted to ‘Koninkrijk der Nederlanden, 2016, Ch. 2, Art. 2.2; see also Vlaanderen is Erfgoed, 2016’, which provided the wrong corroborating source, as VDA, 2016 is Vereniging De Detector Amateur, 2016.
Terminology in correction
They were both reproduction errors in the publication process. However, Cogent Social Sciences described the first as “incorrectly reproduced” and the second as “incorrectly acknowledged”, in order to distinguish between the switching of the cited sources and the misidentification of a cited source.
Denmark
It is difficult to follow the minutiae of the categorisations of danefæ (treasure trove) in Denmark through local academic sources. The National Museum of Denmark (2016a) excludes ‘other [andre]’, ‘[non-]extraordinary [ekstraordinære]’, ancient and medieval iron weapons and tools. A Danish archaeologist who researches metal detecting, Andres Dobat (2013, p. 708), includes ‘bronze and lead, as well as iron[,] weapons or tools from prehistoric periods or the Middle Ages’.
I drew my examples from a list on a page of the National Museum of Denmark, which answered the question, “What can be danefæ?” Danish detectorist Arne Hertz kindly pointed out that the bullet-points were actually pluses for “can be (or is)” and minuses for “cannot be (or is not)”. Some of my examples were mistakenly drawn from the negative answers to the question.
So, danefæ does not include ‘smelted lumps of lead (and, alongside them, shards of glass, sherds of pottery and [implicitly, all] tools that have been made out of stone, bone, tooth and antler)…. includ[ing] musket balls (musketkugler)’, even though it does include some such tools.
This does not undermine the analysis of the reporting of finds in Denmark or the comparison of Denmark with other territories. Indeed, this reinforces the analysis and comparison, as detectorists in Denmark still report finds at the same rate as cited in the article, yet they do so from a more restricted range than was suggested.
Original text
[An] association between non-reporting of danefæ and illicit activity is not an assumption that all detectorists find exceptional things, such as ancient gold jewellery or hoards of silver coins.
It is only an assumption that detectorists find ordinary things, as unexceptional as iron objects, fragments of bronze pots and smelted lumps of lead (and, alongside them, shards of glass, sherds of pottery and tools that have been made out of stone, bone, tooth and antler, cf. Nationalmuseet Danmark, 2016a). Notably, danefæ include musket balls (musketkugler). As discussed, they are so numerous on battlefield sites that a detectorist and an FLO in England agreed to stop recording them (cf. Ferguson, 2013, p. 142).
Proposed correction
[An] association between non-reporting of danefæ and illicit activity is not an assumption that all detectorists find exceptional things, such as ancient gold jewellery or hoards of silver coins.
It is only an assumption that detectorists find ordinary things, as unexceptional as bronze pots, weights and seal stamps; lead weights; ceramic pots; finds of multiple flint tools together (cf. Nationalmuseet Danmark, 2016a); and any coins from 1536 and before, gold and large silver coins even after 1536 yet from more than 100 years ago, and finds of multiple coins together (cf. Nationalmuseet Danmark, 2016a), ‘even… a worn, corroded fragment of a copper coin’ that is more than 100 years old (Moesgaard, 1999, p. 77).
United States
When producing an estimate of the number of detectorists in the United States, I applied the rate of consumption of detectors (0.32 detectors per detectorist per year) to the then only identified (and still most recent) sales figures of 500,000 metal detectors per year.
Unthinkingly, because it was a fraction, I multiplied instead of divided sales by consumption. So, I estimated around 160,000 active detectorists; I should have estimated around 1,562,500. Still, in the course of investigating the statistics to correct the error, less recent yet lower sales rates were identified.
In 2002, around ‘100,000 recreational metal detectors [we]re sold annually to people who [we]re engaged in the hobby’ in the United States (according to the Associate Director of Consumer Sales for Garrett Metal Detectors, Jack Lowry, on 12th February 2002, paraphrased by Walsh, 2003: 905).
Around 2001, ‘about 150,000 metal detectors [were] sold every year in the United States’; and ’99 percent of those [were] purchased by hobbyists’ (according to then Corporate Manager for White’s Electronics, Alan Holcombe, paraphrased by Stahlberg, 2002).
The various rates may be complementary. For example, at the time of the higher sales rate, the world’s largest detector distributor stated that its ‘annual sales ha[d] been growing in the double digits for the [previous] seven years’ (according to the Founder and Chief Executive of Kellyco Metal Detectors, Stuart Auerbach, cited by Wong, 2010). Over a largely overlapping, slightly more recent period of five years (in a comparison of 2010 with 2005), its sales had grown by 63 per cent (according to the Founder and Chief Executive of Kellyco Metal Detectors, Stuart Auerbach, cited by Nicas, 2011).
Since the time of the highest estimates and the reports of seven years of continuous high growth, professional reviews have identified ‘exponential growth of metal detecting in the United States… in the last four decades’ (Stine and Shumate, 2015: 291), which is still ‘growing’ (Scott et al, 2015) , particularly as ‘this activity [is] becom[ing] more popularized by the entertainment industry’ (Bradshaw, 2016: 178). Still, it is prudent to use the lower sales rates.
Even using those newly-identified, less recent, lower sales rates, the number of detectorists would still be far higher than was mistakenly inferred in the original study. Applying the consumption rate of 0.32 detectors per detectorist per year to sales of 100,000-150,000 detectors per year would suggest an active detecting community of 312,500-468,750.
I was mortified when I identified the error. I felt ill for a day and a night. Nonetheless, the method of estimating the rate of consumption, the data for estimating the rate of consumption and the estimated rate of consumption remain valid. The analysis remains valid, too, as the error seriously underestimated the number of detectorists and thus seriously underplayed the significance of the findings.
I have offered either to correct the calculation for the originally identified sales rate of 500,000 (which would [have] produce[d] the least worst estimate from then available data) or to augment the data with the later identified sales rates of 150,000 and 100,000 (which would [have] provide[d] the least worst estimate from now available data). [Cogent Social Sciences judged that it would be best to restrict the correction to the data that was available at the time of publication.]
Extract from a work-in-progress
The method(s) and data for the consumption rate (and for ownership numbers) did pass the peer review of the submitted version of the published article. However, it was suggested that those data were not essential to the article, and I did not want to publish the method(s) without the data, so those pieces were withheld.
In the interests of (re)checking and sharing those methods and data, they are now the foundations of a paper on methods that is currently under review. Below, the first section presents the method for the consumption rate. This follows the presentation of the method for ownership numbers (which has a significant sample size). That follows a detailed discussion of estimation of the detectorist population from the detector market. The second section discusses data from the United States.
Method
hedgehog‘s (2009) consumption survey in Detecting Wales is augmented with usable evidence from commenters on polls and respondents to surveys by Judy (2007) in Canadian Metal Detecting, Steve in PR (2009) in TreasureQuest, timesearch (2011) in the UK and European Metal Detecting Forum, Viking (2011) in American Detectorist and teamroper (2014) in TreasureQuest, so the sources span Europe and North America.
The sample is insignificant in size, but there is no reason to assume that it is unrepresentative in content, as the sources were general forums with wide ranges of participants, from poor to more affluent in a range of countries. Plus, of those detectorists who specified the duration of their activity, 76 per cent had been active for at least a decade; 60 per cent had been active for at least two decades.
Such long-term counts should cancel out any peaks and troughs in detector consumption. Also, the compilation of surveys on possession of detectors, which was significant in size, established the consumption of at least 3.18 detectors per detectorist.
A total of 94 respondents indicated that they had consumed 474 detectors over the course of their engagement in detecting, 5.04 detectors per detectorist (table 2). With regard to the respondents who did not specify the duration of their detecting, 307 detectors were consumed by 69 detectorists, 4.45 detectors per detectorist.
With regard to those who did specify, 167 detectors were consumed by 25 detectorists over 530 person-years of detecting, 6.68 detectors per detectorist over 21.2 years. This very tentatively suggests around 3.17 years between acquisitions or the consumption of 0.32 detectors per detectorist per year.
It is difficult to account for beginners, some of whom will give up the hobby as insufficiently enjoyable and/or insufficiently rewarding. Some of the disused detectors will remain unused, while some will be sold onto the second-hand market. Nonetheless, excluding beginners, there is an average of 7.52 detectors per detectorist over 25.05 years, 3.33 years between acquisitions of detectors, or 0.30 detectors per detectorist per year (table 2).
The wastage of disused yet unresold detectors is inestimable; the difference is negligible; and market data include consumption by consumers who give up the hobby, anyway, so the difference between the two averages is even smaller than it appears. In order to contribute to a secure estimation of the detecting population, this study uses the higher consumption rate of 0.32 detectors per detectorist per year.
Table 2(A): netnographic survey of the average consumption of metal detectors (derived from Judy, 2007; Steve in PR, 2009; teamroper, 2014; timesearch, 2011; Viking, 2011)
Table 2(B): netnographic survey of the average consumption of metal detectors (derived from Judy, 2007; Steve in PR, 2009; teamroper, 2014; timesearch, 2011; Viking, 2011)
Table 2(C): netnographic survey of the average consumption of metal detectors (derived from Judy, 2007; Steve in PR, 2009; teamroper, 2014; timesearch, 2011; Viking, 2011)
Data
In the interests of affirming or querying the open-source method’s potential to generate proxy data for community statistics, a range of market operators were requested to officially or unofficially corroborate or discount the open-source market statistics. Seven manufacturers did not answer or refused repeated requests for information to confirm or disqualify the open-source data, even in the most generic terms or in the form of private guidance. Nevertheless, some statistics and inferences have been published.
When the hobby was establishing itself across the country, one detector manufacturer alone, White’s Electronics, which was then at least the USA’s largest manufacturer, was selling at least 40,000 detectors per year (Franklin, 1975, p. 31). According to the established rate of consumption, those sales would imply that this brand alone had a long-term customer base of at least 125,000.
Soon after, in total, it was estimated that around 600,000 detectors were consumed by around 1,000,000 hunters of ‘coins, jewelry and artifacts’ per year (UPI, 1979, p. 71), at a rate of 0.6 detectors per detectorist per year. However, at the time of those statistics, hobbyist metal detecting was still becoming established across the USA (according to the spokesperson for detector manufacturer Wilson-Neuman, Pat Bryan, interviewed by the Cincinnati Enquirer, 1984, p. 45).
Hence, there would have been disproportionately many novice detectorists who were equipping themselves immediately and disproportionately few experienced detectorists who were merely maintaining their toolkit when necessary, so the apparent consumption rate would have been unrepresentatively close to one detector per detectorist per year.
Moreover, that statistic is far out-of-date; it may not reflect either the practices and disposable incomes of detectorists or the quality and variety of detectors anymore.
According to the Associate Director of Consumer Sales for Garrett Metal Detectors, in the early 2000s, around ‘100,000 recreational metal detectors [we]re sold annually to people who [we]re engaged in the hobby’ in the USA (on 12th February 2002, paraphrased by Walsh, 2003, p. 905).
During the same period, according to then Corporate Manager for White’s Electronics, Alan Holcombe, ‘about 150,000 metal detectors [were] sold every year in the United States’; and ’99 percent of those [were] purchased by hobbyists’ (paraphrased by Stahlberg, 2002. Likewise, a decade earlier, it had been stated that ‘[m]ost [were] in the hands of amateurs’, according to the founder of detector distributor Warner Distributing, Scott Warner, cited by Golin, 1992).
According to former National Accounts Manager for First Texas Products, Debra Barton, in the late 2000s, around 500,000 devices were sold per year (‘a half-million a year’, paraphrased by Yoffe, 2009). There is piecemeal evidence that these numbers could be complementary, as the world’s largest detector distributor stated that its ‘annual sales ha[d] been growing in the double digits for [those intervening] seven years’ (according to the Founder and Chief Executive of Kellyco Metal Detectors, Stuart Auerbach, cited by Wong, 2010).
Applying the average consumption rate of 0.32 detectors per detectorist per year (table 2), sales from 100,000 to 150,000 to 500,000 detectors per year would suggest an active detecting community from 312,500 to 468,750 to 1,562,500.
As suggested by the growth between the early 2000s and the late 2000s, it is prudent to assume that the highest rate is a peak in the market. As when the hobby was establishing itself, the growth indicates that the highest apparent consumption rate will have been distorted by the disproportionately many novice detectorists who are assembling toolkits and the disproportionately few experienced detectorists who are merely maintaining toolkits.
Thus, it is prudent to assume that there is a long-term customer base of around 312,500 active detectorists. Among a population of then around 287,625,193, this would suggest that the scale of detecting is around 1 in 920.
conflict antiquities 
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