Popularity and diversity: The negative relationship in baby names in the United Kingdom

While I remain broadly in favour of this work and its utility in facilitating further research, as far as I can tell, the revised version of this article differs only minimally from the original. Specifically, the inclusion of two clarifying footnotes and a ‘limitations’ statement regarding the original data not distinguishing between boys’ and girls’ names.
While I appreciate these additions, many of the points raised in the original reviews with regard to alternative or supporting analyses have not been addressed in the text – although could conceivably have strengthened the work further.

This is a short report which reanalyses previously published UK name data to demonstrate an inverse relationship between name popularity and name diversity, such that one variable could be used predict the other. This could provide a useful platform for future name research as many name datasets are restricted to either the top X names per year or otherwise redact rare names (about which, more below); that is, it is only practically possible to derive the first variable from them (‘popularity’). In this respect, these results may facilitate the wider interpretation of smaller, and potentially overlooked, name datasets (e.g. ‘top 10’ lists).

Nevertheless, the result remains a single, simple, correlation analysis. Beyond the suggestions made by the first reviewer (with which I concur), the conclusion may be strengthened by some corroboratory analyses, for instance using an independent dataset sampling the same population, and/or using name datasets that do not redact rarer names (which would otherwise affect the calculations).

It is important to note that the raw data used for the analysis (Table S15 of Bush et al. 2018) ultimately derives from birth registration counts compiled by the UK Office for National Statistics (ONS); specifically, https://www.ons.gov.uk/file?uri=/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/datasets/babynamesenglandandwalesbabynamesstatisticsboys/2016/adhocallbabynames1996to2016.xls, and strictly speaking covering only England and Wales rather than the entire UK. As with many name datasets, the long tail of the name distribution is redacted: in this case, names registered to < 3 people per year are excluded. As such, for any given year, the “diversity indicator” (the ratio of the no. of unique forenames to the total number of birth records per year) will be under-estimated. In addition, because the total no. of birth records will be lower than the total number of births, the “popularity indicator” (% of birth records registered with a top 1/top 10 name) will be over-estimated.

For instance, we can see from Table S15 that in 2016, the total number of birth records was 639,126 (this number being used to calculate both the popularity and diversity indicators). However, the total number of births in 2016 was 696,271, an approx. 9% difference (this value is also made available by the ONS but in a separate file; see the link to ‘download figure 1 data’ in https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/livebirths/bulletins/birthsummarytablesenglandandwales/2023#live-births).

It would bolster the overall conclusion – that popularity and diversity are negatively correlated – if it could be demonstrated that refinements to these values make negligible difference. A simple way of doing so would be to calculate them using birth registration datasets that do not redact rare names in the first place. Examples present themselves in the form of data from the Government of Alberta, Canada, specifically for the years 1980-2020 (see https://open.alberta.ca/opendata/frequency-and-ranking-of-baby-names-by-year-and-gender; specific file: https://open.alberta.ca/dataset/11245675-b047-49fc-8bd1-cc2ce8314a6d/resource/e8aac308-c754-484c-b446-0c57ed0e8d37/download/baby-names-frequency_1980_2020.xlsx) and, to draw the focus back to the UK, data from the National Records of Scotland, covering the years 1974-2023 (https://www.nrscotland.gov.uk/media/mbmjzs2q/full-list-1974-2023.csv).

In addition, two points foundational to the overall argument – that “names have become less popular over time” and that “raw data on names is restricted from being openly shared, making it common for only the ranking of popular names” are supported by reference to the author’s not-yet-published review (Ogihara 2025 ‘Uncommon names are increasing globally’). To provide further context, it would help if a citation was provided for at least a pre-print of this manuscript. I am particularly drawn to the point that names have become less popular over time as, in the UK, this most strongly manifests as the 20^th century progresses, i.e. during the time period covered by the ONS data. It would therefore be useful to know to what extent the relationship of popularity and diversity holds over a longer time period, and in that respect whether the conclusion can be generalised. That in mind, Bush et al. 2018 contains two different datasets sampling birth records from the English and Welsh population, of which the present work uses only one of them (from Table S15; the ONS dataset, which is much greater in depth but narrower in temporal scope). The second dataset – which has the same popularity and diversity indicators – is available in Table S6, and may be viewed as a representative population sample from 1838-2014, albeit of varying coverage depths per year. Nevertheless, a cursory examination of this data suggests that, as with the ONS data, there is a strongly negative correlation of popularity and diversity for the years 1996-2010 (this time period chosen because within it there are > 10,000 birth records per year). If we accept this as independent support of the conclusion drawn using the ONS data (and thereby the utility of this dataset), then it may be worth looking at how popularity and diversity correlate throughout history, too. This is of particular relevance as the conclusion drawn in the abstract (“we can predict one indicator from the other indicator”) implies a general relationship between the concepts that may not be universally true and that instead they may only “consistently measure the same concept” for a limited period of time.

I have expanded the Table S6 dataset substantially since the original publication; see Bush 2024 (https://doi.org/10.5195/names.2024.2543) and its raw data, specifically https://github.com/sjbush/uk_bmd/blob/main/dataset_B/summary_of_records_per_year.txt, which is essentially equivalent to Table S15 and contains the columns “most popular forename (% of records)” and “forename diversity (i.e., ratio of the no. of different forenames to the total no. of records per year)”. It should be clear from this data that before (approx.) the second half of the 20^th century, and compared to contemporary records, forename diversity was not only persistently lower but that popular names were given to a higher proportion of people and remained popular for longer, e.g. John and Mary were consistently the most popular male and female names, respectively, for a century (see https://demos.flourish.studio/namehistory/?names=John,Mary, which visualises data from Bush et al. 2018). So, although the present work (using late-20th century data) finds that one indicator predicts the other, it also appears the case that (earlier in the 20th century) popularity could vary without discernible change to diversity. Consequently, the two variables do not necessarily change simultaneously. This may be the subject of a more in-depth analysis but could be usefully commented upon here.

Finally, could some comment also be made on the gender of names, and the effect this may have on the conclusions? In contemporary UK name data, there is typically a larger pool of female than male names (discussed in Bush 2020, https://doi.org/10.1080/00277738.2020.1775471): that is, one would expect female names to have a higher “diversity indicator” and lower “popularity indicator” than male names. Accordingly, a direct correlation of popularity with diversity may not quite be comparing like with like: diversity being affected more strongly by female names, but popularity by male (such that in Table S15, the top 1 names, across the whole population, are all male).