## Dating system

Most sources for Roman guilds and occupation based communities are inscriptions. Dating inscriptions, however, is notoriously difficult. Some can be dated precisely, for instance to an imperial reign or even to a specific year (as in the case of consular dates). But these are the exceptions. Most are only vaguely dateable, for instance ‘early second century’, or middle of the first century’, ‘beginning of the third century’, and so on. Some have cut-off dates (mention of a *Divus *(a deceased and deified emperor), for instance, provides a hard *post quem* date). Some can be dated prosopographically when the persons mentioned are attested elsewhere. Sometimes institutions are helpful if we know when these were introduced or abolished. Some inscriptions can be dated archaeologically, some stylistically.

With the exception of inscriptions that can be dated to a specific year, all inscriptions are dated by chronological ranges that differ widely depending on the methodology underlying the dating. For chronological analysis, however, we need to establish fixed time-intervals. Two related problems need to be resolved: **resolution** and **distribution**.

The first refers to the chosen fixed time-interval, to which we then assign inscriptions. High resolution means we define short intervals (for instance one to five years) Low resolution means long time intervals (for instance centuries). For the GDRG we chose **intervals of 25 years**. Given the quality of the material we have and the vagueness with which most inscriptions are dated, this is the smallest meaningful resolution possible.

The second problem is how to distribute inscriptions over the established 25-year time ranges. The basic principle we adopted for the GDRG is a **proportional linear distribution**.

If an inscription is dated within a 25-year interval. It is counted as “1” in that interval. If the date range of the inscription stretches over more than one interval it is counted proportionally. For instance an inscription dated c. 191-210 is counted as “0.5” in the interval 176-200 and “0.5” in the interval 201-225. An inscription dated to the reign of Septimius Severus (193-211) is counted as 0.42 in the interval 176-200 and 0.58 in the interval 201-211.

This is straightforward in the case of inscriptions with fixed dates (for instance consular or imperial dates) or hard date ranges (for instance the reign of an emperor). In the case of vague date ranges we need to translate that vagueness into artificially hard date ranges.

For **longer** **date estimates not based on hard ranges** we use (multiples of) quarter centuries that coincide with the defined time-intervals. For instance ‘second century’ becomes 101-200 CE. When taking over date ranges from other databases or literature that use thirty- or twenty-year periods we have changed the estimate accordingly. For instance 130-170 or ‘second third of the second century’ becomes 126-175 in the GDRG.

For **fuzzy estimates around mid-century points or end/beginning-century points** we use a 20 year range. This creates an equal distribution in the two 25-year intervals surrounding the date-point. For instance c. 100 becomes 91-110. Mid second century becomes 141-160. Late second to early third century becomes 191-210.

For** fuzzy ‘late’ or ‘early’ estimates before or after an end/beginning-century point** we use the 25-year interval preceding or following the estimate year. For instance, ‘late second century’ becomes 176-200.

For **fuzzy ‘end of’ or ‘beginning of’ estimates before or after an end/beginning-century point** we use a 10 year interval preceding or following the end/begin point. For instance, ‘end of the first century’ becomes 91-100.

For **estimates around other specific years** we use a 10-year interval, with the estimate year falling in the second half. For instance c. 77 becomes 72-81. If there are indications that in specific cases this is too broad the interval is narrowed to 5 years, with the estimated year lying exactly in the middle, for instance c. 77 would then become 75-79.

**Guild_documents** have a single date range (*post quem* to *ante quem*) which usually corresponds to the date range of the inscription that physically constitutes the document. **Guild records**, however have a double date-range, consisting of resp. the earliest *post quem *date to the earliest *ante quem date*, and the latest *post quem *to the latest *ante quem *date. For chronological analyses the date range used is ‘early *post quem*, to late *ante quem*’, because this is the closest approximation we have for the lifespan of the group.

The **linear distribution **we chose to assign** **inscriptions to the chronological intervals, inevitably creates a distortion.[1] Mathematically the choice assumes that there is an equal probability of the dated object (in our case a ‘guild_document’ record or a ‘guild’ record) belonging in any year of the chosen interval. This is demonstrably true in some but false in many other cases. To illustrate this, we offer the following examples:

__Date based on imperial reign__: there is an equal probability for the document dating to any of the regnal years. For instance, an inscription dated to the reign of Hadrian has an equal probability of dating to 117, 118, 119, … 136, 137, 138 CE; the linear distribution is mathematically the most suitable.

In other cases, however, the linear distribution is demonstrably wrong, for instance:

__Date based on reference to an imperial freedman__:

- Referring to the emperor as still alive: if we have no further information on the date when the freedman was set free or on when he died, this would be similar to a date based on imperial reign.
- Referring to the emperor as a
*Divus*: there is a decreasing probability for the document belonging to the number of years after the death of the emperor. The slope depends on the life expectancy of the freedman at the death of the emperor. Theoretically we can model this by using model life tables, but this is only a theoretical possibility because we rarely (if ever) know the age of the freedman when his emperor/patron died. - Without a clear reference to whether the emperor is still alive or not: we should combine a linear distribution for the reign period, followed by a sloped distribution for the years after the death of the emperor

__Date based on formulae used in the document (for instance D(is) M(anibus)) or stylistic criteria__: the distribution should be sloped upwards as the formula or style used for dating becomes more popular and sloped downwards as the formula or style gets out of fashion. We cannot, however, assume a normal Gaussian distribution. For instance, in the city of Rome the funerary formula *Dis Manibus *first appears in the 40s CE, at first unabbreviated, then from the 60s onward abbreviated to D.M. While the unabbreviated version seems to conform to Gaussian distribution,[2] the abbreviated form does not. It peaks in the 130s when 90% of all funerary (dated) inscriptions use DM, then remains at that high level until the 180s when it drops to about 80% but then remains at that level until the number of inscriptions becomes statistically irrelevant.

So while some of these fuzzy criteria conform to normal distributions, others to do not. Complicating this problem further is that trends in using certain formulae and styles differ geographically. Theoretically we should develop regional criterion-specific distributions. In practice, however, that is not possible because it would require statistically relevant numbers of securely dated documents and/or monuments in/on which the criterion in question occurs. These are simply not available.

Complicating matters even more is the __general epigraphic ‘background’ distribution__. Epigraphic culture itself is not uniform through time or space. In central Italy it peaks in the first century BCE to first century CE. In most other provinces only in the second. It peters out during the third century, but not uniformly at the same pace everywhere.

Since it is methodologically impossible, therefore, in most cases to calculate the ‘real’ probabilities of an inscription belonging in any specific year of its date range, we opted for **linear distributions **as the least bad approximation. In the case of vaguely open-ended dates (for instance ‘second or third century’) we use 250, 275 or 300 CE as fuzzy end dates, depending on each individual case.

[1] For a similar solution used for papyri see Van Beek, B. and Depauw, M. (2013). ‘Quantifying Imprecisely Dated Sources. A New Inclusive Method for Charting Diachronic Change in Graeco-Roman Egypt’, *Ancient Society* 43: 101–114; Broux, Y. (2019). 'An Improved Weighed Dates Method for Ancient People', *Ancient Society *49:103-121. doi: 10.2143/AS.49.0.3286882

[2] Cf Andreau, J. (1987). *La vie financière dans le monde romainâ€Ż: les métiers de manieurs d’argent (IVe siècle av. J.-C.-IIIe siècle ap. J.-C.) *(Bibliothèque des Ecoles Françaises d’Athènes et de Rome 265). Rome.