The vicar didn't record the baptised child's name! Now what?

Question

In my in-laws tree, there is an ancestor Robert Judson, son of James Judson who was baptised in Haworth, Yorkshire, 11 July 1736.

I haven't found an obvious candidate for James yet, but I did find a couple of unnamed sons of a Timothy Judson born in the late 1600s in Haworth. (in 1692 and 1698)

When I went to the original scans of the parish records, available on Ancestry.com, it shows that the names of the children were simply not recorded. In most (but not all) cases, it just says "a son of" or "a daughter of".

I think it might be reasonable to conclude that the 1698 one is our James Judson.

• Other James Judsons born in Yorkshire in the plausible age range (here and here) seem to have died as children.
• Robert was baptised in Haworth, and so were his children, so I have no reason to believe they were a family from a long way away.
• The father's name Timothy is relatively rare in this period. Douglas Galbi's data set of given names in Northumberland for 1530-1830 contains nearly 40,000 males and their names and dates of birth, contains only 38 Timothys (i.e. 0.1%). I think this is a reasonable comparator set for Yorkshire in the late 17th and early 18th centuries. (This sort of analysis is easy to do in R or Mathematica, less so in Excel because of the size of the data set.)
• So the fact that James had a son Timothy, leads me to think it might have been a family name. (This sort of pattern is the reason I suggested in my answer to an earlier question that one can't assume that the distribution of first names is independent of the distribution of family names. There are a few other Timothys born to other Judsons later in the 18th century.)

So my questions are:

• Are these sorts of no-name dead ends common? How do people handle them?
• Is this level of evidence considered sufficient for a tentative conclusion by more experienced researchers? I suspect I won't be able to find wills or other documents to triangulate my conclusion, as I believe these were farmworkers or similar without significant property to leave.

Answer 1

I have not previously come across a Parish Register (and this is a Parish Register, according to West Yorkshire Archives, who hold the original) with so few personal names for baptisms. The most usual explanation is an infant baptised very shortly before death and never named, but there are so many of these (and not enough corresponding burials), that doesn't seem the right explanation here.

In your situation, as a minimum, I would look to trace the two unnamed children forward and match them (or not) with later Judson marriages or burials. I would also look to understand the naming practices in the extended family -- was the eldest son always named after the paternal grandfather in the relevant period?

Even though your ancestors may not have left wills, I would still look for other sorts of records, such as settlement removal and bastardy orders, deeds and manorial records, all of which could mention your ancestors no matter how lowly they were, and provide more evidence to support or counter your hypothesis. The West Yorkshire Archives catalogue is online at http://www.catalogue.wyjs.org.uk but their documents are not, unfortunately.