# A statistical analysis of longsword lengths

One of the questions that frequently arises is “did longswords get longer in the 16th century”. This question is often asked on forums, and similarly the assumption that this is the case is also often stated. It is often easy to think of some particularly large 16th century swords, however it is worth to remembering that lots of swords from the 16th century were also relatively short, and even if some swords were longer in the 16th century, this does not mean that all swords were longer. On the other hand, it was also possible that the assertion that longswords were on average in the 16th century than earlier longswords was accurate. As I was not really sure about this myself, something that I thought would be worth doing would be carrying out basic statistical analysis on sword lengths from the 14th, 15th, and 16th centuries, and seeing to what degree sword lengths changed.

Alen Lovric has a rather helpful list of antique longswords with known lengths and weights on HEMA Reviews. Alen’s criteria were that:

“a) they have at least the weight, length and total length listed

b) they are not so corroded as to change their handling properties

c) they do not seem to have been tampered with in the 19th/20th century

d) they are pre-17th century

e) they are shorter than 145cm (taking into account manuscripts that say a sword should be up to a man’s armpits – 145 would be an appropriate longsword for a big man)

f) they are not federschwerter”

The criteria that the swords should be shorter than 145 cm could skew results, and if swords larger than this were included in the sample, then the average length of 16th century swords might have increased. However, if we want to distinguish between longswords and true two handed swords, in order to focus on longswords that are perhaps more typical and more commonly seen in the Fechtbücher, then a line must be drawn somewhere about what swords will and won’t be included within the sample.

This gives us a sample of 70 longswords, 15 of which were dated to the 14th century or earlier, 18 of which to the 15th century, 33 to the 16th century, and 4 could not be dated. I ignored the 4 that could not be dated, leaving us with a sample of 66 longswords.

If you would like to see the original data on these swords then please see the appropriate pages on HEMA Reviews.

14th century (and earlier) original longswords database

15th century original longswords database

16th century original longswords database

Original longswords database – undated longswords

Noteworthy examples from the data

For an initial impression of the data, the sword with the longest total length was the no.12706 (5014) from Livrustkammaren Stockholm, a 15th century sword with a total length of 1437 mm or 56.6 inches, while the shortest total length belonged to the A479 from the Wallace Collection, a 16th century with a total length of only 795 mm or 31.3 inches.

The sword with the greatest blade length was the ZEF 8 measured by Zornhau, a 16th century sword with a blade length of 1105 mm or 43.5 inches, and the shortest blade length was that again of the Wallace Collection’s A479 at 619 mm or 24.4 inches.

The heaviest sword overall was the no.12706 (5014) from Livrustkammaren Stockholm, which as we saw above also had the greatest total length, at 2720 grams, or 6 pounds. The lightest was the ZEF 12 measured by Zornhau, a 15th century sword with a weight of 1015 grams or 2.24 pounds.

From this, we can’t really see much of a clear pattern, though it is worth noting how much variance there was between different swords, and that which century a sword is from cannot be easily used to predict if it will be the longest, shortest, heaviest or lightest sword out a sample.

Averages

I then calculated the mean averages of all these swords.

Mean total length of 14th century and earlier swords: 1141.5 mm/44.9 inches

Mean total length of 15th century swords: 1220.5 mm/48.1 inches

Mean total length of 16th century swords: 1178 mm/ 46.6 inches

Mean blade length of 14th century and earlier swords: 898.9 mm/35.4 inches

Mean blade length of 15th century swords: 943.5 mm/37.1 inches

Mean blade length of 16th century swords: 916.5 mm/ 36.2 inches

So if we look at length, we can see that while the total and blade lengths of the longswords was greater in the 16th century swords than in the swords from the 14th century and earlier, the highest mean average for both total length and blade length belonged to the 15th century swords.

The mean weight however tells a different story, with the average weight being highest for 16th century swords and lowest for swords from the 14th century and earlier. So it would seem that out of the swords within this sample, swords were on average longest in the 15th century and heaviest in the 16th century.

Mean weight of 14th century and earlier swords: 1473.4 gr / 3.25 lbs

Mean weight of 15th century swords: 1647.6 gr / 3.63 lbs

Mean weight of 16th century swords: 1700.1 gr / 3.72 lbs

Graphs

Next I generated boxplots for the three measurements. Boxplots show how values are distributed, so you can easily see where the majority of data falls.

So here we can see that the 14th century and earlier swords are on average a little shorter and have a little less variance than the swords from either the 15th or 16th centuries, which are more comparable. Note the two outliers, shown on the graph by asterisks. These two swords are so far removed from the other swords we can say that they do not represent typical longswords, and are anomalies.

In this box plot we can see that the 16th century has the greatest variance in blade length, and that again, the blades from the 14th century and earlier are on average shorter than those from either the 15th or 16th centuries. Note that not all blades from the 14th century or earlier are shorter, as we can see an outlier from the 14th century or earlier with a relatively long blade. However, this blade is an outlier in a 14th century or earlier context, whereas a blade of that same length in a 16th century context would not be considered to be an outlier.

Here we can see that with an exception of one outlier from the 15th century, 16th century swords do indeed seem to be on average heavier than earlier swords.

So far it seems as if 14th century and earlier swords on average seem to be shorter, and 16th century swords on average seem to be heavier. 16th century swords seem to have a greater variance in blade length compared to 15th century swords, but the average for both total length and blade length seems to be roughly comparable for the 15th and 16th centuries.

The final step is to carry out formal statistical analysis, but before this can be done, hypotheses need to be made.

Hypotheses and statistical analysis

**Hypothesis A:** That there will be a significant difference in total length between the 14th century and earlier swords and the 15th century swords

**Hypothesis B:** That there will be a significant difference in total length between the 15th century and 16th century swords

**Hypothesis C:** That there will be a significant difference in total length between the 14th century and earlier swords and the 16th century swords

**Hypothesis D:** That there will be a significant difference in blade length between the 14th century and earlier swords and the 15th century swords

**Hypothesis E:** That there will be a significant difference in blade length between the 15th century and 16th century swords

**Hypothesis F:** That there will be a significant difference in blade length between the 14th century and earlier swords and the 16th century swords

**Hypothesis G:** That there will be a significant difference in weight between the 14th century and earlier swords and the 15th century swords

**Hypothesis H:** That there will be a significant difference in weight between the 15th century and 16th century swords

**Hypothesis I:** That there will be a significant difference in weight between the 14th century and earlier swords and the 16th century swords

I used a two sample t-test, which tests if the difference in means between two groups is statistically significant. Statistically significant in this context simply means that we can say that there is a 95% probability that the difference in means of the two groups is not just because of chance.

For the sake of readability, I won’t report the results of all the tests, however the only hypotheses that were supported were hypotheses A and I. That is to say that based on this sample, the only differences between swords from different periods that we can say are statistically significant, is the difference in total length between longswords from the 14th century and earlier, and longswords from the 15th century; and the difference in weight between longswords from the 14th century and earlier, and longswords from the 16th century.

A p-value of 0.05 is needed to state that the results are statistically significant, and the p-value for the difference between total length in swords from the 14th century and earlier, and swords from the 16th century was 0.084, so if we were being charitable, we could say this result was approaching significance, so hypothesis C was somewhat close to being supported, however the data was not clear enough to be statistically significant. No other test produced a p-value below 0.1.

So this means we can say with 95% confidence that longswords from the 15th century were on average longer than earlier longswords, and that 16th century longswords were on average heavier than longswords from the 14th century or earlier. Based on the descriptive data above, I would also say that it seems that variability in longsword length increased in the 16th century compared to earlier longswords. This may because longswords were not made as uniformly in the 16th century as before, or this may simply appear to be the case because more swords have survived from the 16th century. Judging by the boxplots above, it also seems that the total lengths of longswords was very comparable between the 15th and 16th centuries, so I think it is correct to say that longswords became longer in the 15th century, but I do not think it is correct to say that the average longsword became longer in the 16th century.

Of course, the sample used in this study is still smaller than it could be, with many swords not having published lengths and weights, and if the future data becomes available on more longswords, these results may need to be revised.

Hi Alex,

Very interesting to see the different stats of longswords across the centuries; it’s a great way to put a number on their evolution. However, as much as I applaud your effort to conduct statistical tests, the results are completely unreliable due to the limitations of t-tests and the intricacies of your data. At his point, I would stick to eyeballing the data based on the descriptives and boxplots; that’s still a good way to get an idea of how swords developed over time.

Regards,

Patrick