Longevity – A New Scoring System

It’s change afoot at Rex Factor as, after many years, we have decided to change the way that we score on monarchs in the Longevity category (i.e. for how long they ruled). To find out more about our new scoring system and what impact this has had on past scores, read on.

Backgroundy Stuff

While Battleyness, Scandal and Subjectivity are given scores by us on the basis of ouropinion, the Longevity and Dynasty scores have always been absolute fact. However, the numbers given as scores has changed. Originally, we simply went with the number of years a monarch had ruled for and the number of legitimate surviving children they had when they died. However, this system seemed unfair to us as it meant that a rubbish king who stuck around for a long time (e.g. Henry VI with 39 years) would get an artificially high total score when all the factors were added up. As such, Longevity had far more weight than the other categories.

So, we put a challenge to our listeners to come up with a more mathematical approach that would retain the scoring based on the number of years but would fit in with the other factors scored out of 20. Thus we adopted the Pattiometre, whereby the monarch with the longest reign would act as the measure by which all others were measured. So, in the original series Victoria had the longest reign (this was before Elizabeth II broke the record!) and she reigned for 63.58 years. So, we divided 20 by her reign, which gave us 0.3145, so in order to give all our monarchs a score out of 20 we simply had to multiple the number of years for which they reigned by 0.3145.

For example:

  • Alfred the Great – 28.5 years multiplied by 0.3145 = 8.97
  • Henry II – 34.75 years multiplied by 0.3145 = 10.93
  • George III – 59.25 years multiplied by 0.3145 = 18.64

The Problem

We were well into the series when we adopted this new scoring system and it has served us very well. However, when we started the Scottish series, the Longevity score for the early medieval Scottish monarchs always seemed rather unfair. Scotland in the 9th to 11th centuries was remarkably violent for the monarchs, with 18 out of the first 21 that we reviewed either being killed in battle or assassinated. In such circumstances, in which killing your predecessors was pretty much the accepted method of succession, a reign of 29.67 years for someone like Malcolm II was clearly a great achievement. Similarly for Alfred the Great in England with his 28.9 years despite the Vikings having nearly conquered all of England and reducing him at one point to ruling a swamp.

And yet…when you put their reigns into the Pattiometre they come out looking rather measly: 8.97 out of 20 for Alfred the Great; 10.29 for Malcolm II. Surely these scores were not reflective of the achievement at ruling for about 30 years (a pretty decent stretch of time with or without rampaging Vikings and dynastic rivals)?

The problem was that in both series we had a handful of monarchs with exceptionally long reigns who thus rather imbalanced the scoring. The average reign in England was about 20 years but this is dwarfed by Victoria’s reign of 63.58 years. Similarly in Scotland, an average reign of 19 years looks pretty small compared to the 57.67 years for which James VI was in charge. This meant that we had a rather large number of monarchs with decent reigns getting low to middling scores while a few at the top got very high scores.

The Solution

We decided that it was time to make another change and to have a fairer system for scoring Longevity that would not be so biased towards the longest reigns. Once again, we put it to the listeners and we received some very interesting suggestions: simply turning it into a subjective judgement (i.e. what score do we think they deserve given the context) or even measuring the length of reign against the average life expectancy for the period!

However, we still wanted to have it work in such a way that the longest reign would get the highest score and the lowest reign would get the lowest. As such, we decided to go with a system suggested by one Ed Cadwallader, in which you put all the reigns in order. So, for England, at the bottom we have Sweyn Forkbeard (0.08 years) getting 0.5 and at the top (now) Elizabeth II (upwards of 64) getting 20.

Then, we start to get mathematical! We work out the median score (i.e. the one in the middle), which was Edgar the Peaceable with 15.75. As such, this length of reign gets 10 points (i.e. the half-way point). Then we did the lower quartile (i.e. the one halfway between the bottom and the middle) which was Edmund I (Edgar’s father, coincidentally) with his 6.58 years achieving 5 points. Then we took the third quartile (halfway between the middle and the top), with George V getting 15 points for his reign of 25.67 years. Finally, we worked out equal intervals for the positions between each milestone, going up by a score 0.5 at a time. Each monarch then is given the score closest to their reign (though it always rounds down unless an exact match).


The Dynasty Question

Originally, we were planning to adopt this new system for Dynasty as well as Longevity. However, the problem here is that we are (obviously) dealing with much lower numbers when talking about how many children people had as opposed to how many years they reigned. In particular, the highest number of children any monarch produced was 10.

Having 0 children would still need to have a total score of 0 but with the new scoring system, this would really be a harsh punishment in the overall scores. As so many Scots failed to have children, the median score (i.e. the one in the middle) is actually 1 child, meaning you would jump from 0 points for no children to 10 points for one child! We thought this was a bit too much, and with the Pattiometre producing a very simple case of effectively doubling the number of children to get a score (i.e. 1 child = 2 points) we decided to stick with the Pattiometre for Dynasty.

The Consequences

We’re happy with the new system as basically it means that the scores are much more evenly distributed and also we have scores more in line with the other factors (i.e. 0.5, 1.0, 1.5 rather than 1.17 etc.). But the big question is, what impact has this had on our overall scores?

As a rule, the monarchs with the very highest scores will not have changed a great deal and nor will those at the very bottom. However, a lot of monarchs have seen their scores rise, which has resulted in certain changes in the overall positions. As we’ve not completed the Scottish monarchs, we’ll just focus on the English ones to avoid any spoilers!

Here are some of the big winners in Longevity – all with reigns kind of half-way up to HMTQ’s record:

  • Alfred the Great – rocketing up from a lowly 8.97 to a rather impressive 15 (up by 6.03)
  • Henry II – rising from 10.93 to 16 (up 5.07)
  • George V – the biggest gain of all, rising from 8.08 to 15 (6.92)

The losers, in contrast, are a mix of long and short reigns:

  • Elizabeth II – 64ish years and her score is unchanged at 20
  • Harold II – only 0.75 years, his score up by just 0.26 (0.5)
  • George III – 59.25 years but his score only up by 0.36 (19)
  • Edmund Ironside – only 0.58 years and his score only up by 0.32 (0.5)

The League Table

So, when we tot up their total scores, are there any big changes? Well, yes there are – so let’s see the movers and shakers!

Here are the three monarchs to have risen the most places up the chart:

  • Edward II – up 4 places, from 33rd to 37th
  • Stephen – also up 4 places, from 48th to 44th
  • Charles I – the biggest gainer, zooming up 6 places from 49th to 43rd

Not perhaps the best advert given that these were not exactly three of the most successful monarchs in English history! But the factors are there to assess different attributes and despite not being overly successful, all three actually stuck around for a decent amount of time! And some good monarchs also benefited – Charles II moved up by 3 places; Alfred the Great by 2 places; Cnut by 1. Overall, 38 out of 57 either stayed still or had their position improve.

However, there were some losers:

  • Harold II – that arrow in the eye must hurt even more, as his short reign and limited score change means he drops 6 places (from 31st to 37th)
  • Elizabeth II – because she already had 20, she’s just seen those behind her gain on her score and she also drops by 6 (11th to 17th)
  • Richard III – just when it seemed like everything was starting to come right for Richard, our new scoring system means he drops by 7 places (21st to 28th)

But what about the actual top 10 (i.e. the 10 highest scores)? Well, here’s how it looked under the Pattiometre:

Three in our old top 10 were not Rex Factor winners (George III, Oliver Cromwell and, most controversially, Edgar the Peaceable) but how does it look now with the new system?


Well, the actual names in the top 10 remain the same (though Edward the Elder and Alfred the Great are only just behind Mr Cromwell!) Crucially, Henry II remains our top-scoring monarch, now with an even more impressive score of 74.18. However, Ali will be quick to point out that the new scoring system has not only seen Edward I get up to 2nd place but that Victoria (the previous second placed monarch) has now slipped down to 4th, also falling behind Edward IV (who also leapfrogged George III, down into 5th). Henry I and  Edward III have swapped places, while Edgar the Peaceable and Henry VIII share 8th place.

The Play-Offs

If you haven’t listened to the English play-offs and don’t want to know the results, then stop reading now!

Otherwise, you will recall that the play-off draw was partly seeded according to the total scores. So, what would the draw have been if we were to allocate each monarch according to their new seeding and put them back into the old draw?

So, in the image below, at the top we have the original play-off draw (Old) and in each group, I have highlighted those who went through, with gold for 1st, silver for 2nd and bronze for 3rd. In the bottom tables (New) I have kept the seeding numbers but switched the monarchs for how they would be seeded with the new scoring system. And it would have had a big impact!

Rex Play Off Draw Comparison.001

As you can see, the play-offs would have been very different! We said at the time that Group A was the group of death, but even more so now! All three group winners (Henry VIII, Elizabeth I and Edward III) would now be in Group A, along with a 2nd placer (Alfred the Great) and a 3rd placer (Victoria), with Charles II’s position looking just as bad as before! However, in Groups B and C the picture is very different, with each just having one 2nd placer and one 3rd placer (Henry II and Athelstan in Group B, Henry V and Edward I in Group C).

Of course it’s very difficult to know how people would have voted in a different draw, but it’s interesting to speculate. The Old Group A had both the Saxon monarchs whereas now Athelstan gets to enjoy the relatively easier (though incredibly battley!) Group B. Instead, Group A pits Henry VIII against his daughter Elizabeth I, which would have been a fascinating battle! We also have the two queens, Elizabeth I and Victoria, in Group A. Similarly, Group C would have seen William the Conqueror against his son, Henry I, while Group B retains its own father-son battle (Henry II and Richard the Lionheart).

A New Name

But there is one more problem that needs solving – what to call our new scoring system? The “Cadwalladerometre” is a bit of a mouthful, so can you think of anything better? Let us know your ideas for a funky new name and what you think might have happened in the play-offs if the draw had been different!

14 thoughts on “Longevity – A New Scoring System

  1. Pingback: John Balliol (1292-96) | Rex Factor

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  3. Pingback: Malcolm IV (1153-65) | Rex Factor

  4. I like “The Cadwallader” it sounds like something you could do calculations with, but if not acceptable then Edometer

    • Yes, I don’t know why I decided to calculate it differently to how it was actually done! It’s correct now but I should have said 20 divided by 63.58, so 0.3145 multiplied by 28.5 years = 8.97!

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