Falke serial numbers - an analysis by a statistician

Six months on from the start of this forum, a total of almost 80 serial numbers of Falke 80s and 90s has been reached. So far nothing concrete has come up to disprove the current best guess of the numbers of rifles made; 400 of the model 80 and 200 of the model 90.

But the prevalence of lower serial numbers within this range seems strange. Curious to know what an expert might make of it, I asked for help on the Airgunbbs from a statistician. Fortunately a very able gentleman by the name of Vin came forward and he agreed to cast an eye over the numbers gathered to date.

His comments are interesting, not least his question as to why, if the above totals were in fact produced, so few of the higher serial numbers appear to have survived when logic might suggest the opposite should be true?

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Vin's comments:

There's no real statistical analysis that I'm aware of that would resolve your problem directly, but a few commonsense suggestions leap to mind.

If you graph the serial numbers of the 80s on a scatter graph there's something odd that may not be apparent from the raw list. Namely, there's a pretty steady fill of the number below 150, then an odd pocket at the 180s then a handful widely spread.

I'd suggest the reason might be that if you had 150 already made, and you were a quicker craftsman, you might have used up a bundle of serial numbers, asked for a new set and been told "Start again at number 175"(or whatever). Look at the graph and you'll see it looks a bit odd above 150. That would suggest to me that only 150-200 (and probably nearer 150 than 200) were ever made. As for the weird numbers, could they have been numbers for one-offs; the craftsman, the foreman, the boss, the investor who needs convincing you’re making more than you are? Definitely unusual.

The second odd thing (common sense, not statistical analysis) is that you would expect, if anything, the later serial numbers to be the ones turning up the most. If they are newer, less time and opportunity for them to go out of circulation (assuming a long time for the whole production run). If, on the other hand, they all came out over a short period, then the distribution mentioned above suggests even more strongly that something strange was going on in the issuing of numbers. Either way, something’s up.

A final way of looking at it is that you appear to have 44/150 of the serial numbers up to 150 surviving. You have 3 in the range 200-350. I’ve done a quick calculation; If the normal survival rate is 44/150, then I reckon it’s about 1 in twenty six thousand million million that there’d only be three left with the serial numbers 200-350, so you really do need to find an explanation other than chance.

On to the 90s. The distribution in the graph again suggests that individual craftsmen may have been given a starting point for serial numbers and told to number sequentially in those groups. Again, though, the sparseness higher up the graph looks odd; why are newer ones the ones out of circulation? You might be able to add knowledge here; did quality decline? That applies to 80s as well as 90s, obviously. I’d suggest 150-160 as the absolute maximum.

Sorry I can't be of more help - it's not a standard problem and I suspect that applying real-world knowledge makes more sense. Statistical analysis relies more on the knowledge that, say, all the sequential serial numbers WERE used.

In order to test my "one craftsman given a sequence of numbers he could use" theory, you might take a look at those different punches that appear to have been used by different craftsmen. Is there a pattern of use in blocks of numbers?

Vin

Barryeye responded:

Vin, Garvin. Thank you both so much. The plot thickens and this is all very interesting.
It is starting to look like we 80 and 90 owners are in a club that is even more exclusive then we first thought. Garvins’s Falke data base has expanded a lot in the last 6 months but one can not ignore the obvious trends.
I suspect but don’t know for sure that the majority of Falke owners and collectors that have been exposed to Garvin’s Falke site have English as their first language. I have to ask if the data base exposes any obvious blank spots when geography is taken into consideration. We know that a fair number of 80/90s went to the colonies (Australia. South Africa and New Zealand). A few made it to the U.K. but what about the closer to home market? Did the Dutch, French or even the Germans them selves buy their share of Falkes and if so are their current owners aware of our survey?
As it is the late numbers that are the least common, let me play the devils advocate and suggest that when the good people at Falke were aware that the company was going under they could have flogged off the remaining stock and hence the higher numbers on to the local market. No point in adding the cost of freight to send them to the other side of the planet. Get what you can local.
Frankly I prefer Vin’s logic but until we honestly believe that we have located the bulk of 80/90s the jury must stay out. Are we looking in the right places now and if not how can we?

Garvin responded:

All excellent points Barry and well made.

Whether this being an English language forum is a factor is another unknown, I agree. It's hard to be sure we're not missing a big chunk of the overall production, with the possibility that there's a 'reservoir' of high serial number Falke underlevers still in Germany owned by people put off from coming forward either by the language barrier, ignorance of the forum's existence, or lack of interest in the subject.

But a good number of the serial numbers in our database have been supplied from guns that either lived in mainland Europe until very recently or still do. This includes the rifles that Swedish, Dutch, and German owners have told us about and a number that have been put up for sale in Germany and imported to the UK by collectors in the last few years.

I haven't worked out exactly how many these add up to yet but I'd estimate it's a third or more of the total. I suspect that's a big enough sample to suggest a pool of rifles with higher end serial numbers probably doesn't in fact exist tucked away somewhere in Germany or nearby.

Maybe we haven't located enough of the total production to draw any firm conclusions, but the spread of numbers that has come out so far supports the idea that fewer were made than previously thought. Hopefully we'll continue to get a steady trickle of additions to the database and get a better picture in time.