Long Distance Competition/Ultracycling, Randonneuring and Endurance Cycling - What's your Eddington number? (Interesting measure of LD cycling achievement)

Here's an interesting measurement of long-distance cycling achievement, credited to British astrophysicist Arther Stanley Eddington. Eddington defined the "Eddington number", represented as E. The most concise way to state the definition is:

A cyclist has an Eddington number of E if (s)he has cycled at least E miles on E different days. and has never cycled more than E miles on any other day.* You count the highest value of E for which this is true--i.e., if you have done 65 rides of at least 65 miles, but not 66 rides of 66 miles, your E is 65.

Here's another definition from Wikipedia:
http://en.wikipedia.org/wiki/Arthur_Stanley_Eddington
"Eddington number (cycling)

Eddington is credited with devising a measure of a cyclist's long distance riding achievements. The Eddington Number in this context is defined as E, the number of days a cyclist has cycled more than E miles[5][6]. For example an Eddington Number of 70 would imply that a cyclist has cycled more than 70 miles in a day on 70 occasions. Achieving a high Eddington number is difficult since moving from, say, 70 to 75 will probably require more than five new long distance rides since any rides shorter than 75 miles will no longer be included in the reckoning."

For example, reaching E=100 would require riding 100 centuries sometime during your life--and any century ride where you stop at exactly 100 miles wouldn't be part of the 101 rides of 101 miles needed to reach E=101. :eek: Eddington reportedly reached E=87 by the time of his death in 1944, at the age of 61.

I haven't robustly kept track of my ride totals, but I'd suspect I might be somewhere around E=30 (I've done a couple of centuries, and once followed a 200k brevet route to see how it would go, but not too many of my rec rides go a whole lot beyond 50 km):o

So, what do you think?
Any guesses at your Eddington number? (I'd call anything up to 24 hours a single "day"; anything longer than that would count as a two or more consecutive days.)

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*Footnote for academic types:

I ripped this definition from Jorge Hirsch's description of the "h-parameter" (quoted on Wikipedia), which he proposed (in 2005) as a measurement of the productivity and scientific impact of scientists.

A scientist has index h if h of [his/her] Np papers have at least h citations each,
and the other (Np − h) papers have at most h citations each.
This is identical to Eddington's definition of E, and came more than 60 years after Eddington's death.

I can say honestly that I don't think I've ever ridden any two courses which are the exact same length. Even if it's the same 200k twice, I'll be around a kilometer difference depending on how many laps around a parking lot or wide turns I took.

NO doubt I've ridden many more 100 mile rides than 99 or 101. But I've ridden a whole chitt-load of rides around 190-210. And not so many around 170 or 180. I guess my E-number isn't very high. But its way more than 30 or 40.....

How is this calculated? I guessed, as follows:
list all rides in descending order of distance, truncated to the next lowest integer
number the rows
scroll down the list, find the truncated distance number where the number equals the row number. That's E.

Yes? Other way to do it?

Unfortunately, I only have the detailed data since 4/2007 when I got a garmin and started loading my data into sporttracks.

But... what the heck does it measure? What about the whole rest of the world, that uses KM?

... What about the whole rest of the world, that uses KM?

Guess I'm not part of the rest of the world, what is KM? I'm kind of in the same boat as Richard. I don't keep that close of a track of the rides I do. I'm not really a paperwork/number guy unless I have a reason, like specific training...

A cyclist has an Eddington number of E if (s)he has cycled at least E miles on E different days, and has never cycled more than E miles on any other day.*

For example, reaching E=100 would require riding 100 centuries sometime during your life--and any century ride where you stop at exactly 100 miles wouldn't be part of the 101 rides of 101 miles needed to reach E=101. :eek: Eddington reportedly reached E=87 by the time of his death in 1944, at the age of 61.
I think this is a bit more complicated than it seems at first.

I have records since 2004, which is when my "adult" cycling career began. I keep my log in an Excel workbook, so it is easy to manipulate the information. Based on data through the end of 2009:

I have 63 rides that are at least 63.8 miles, so you might at first think my Eddington number is 63. However, I think that is not correct because I actually have 73 rides that are at least 63.0 miles.

The 63 (miles) and the 73 (rides) do not match up.

If I try to stop before 63 RIDES, the miles are more than the the number of rides. Therefore the two indices would not match.
If I try to stop with fewer than 63 MILES, there are more rides than miles. Therefore the indices woul not match.

Therefore, based on my understanding of the definition as stated, my Eddington number is: 0 (zero), or perhaps is "undefined". There is no "point" at which the number of rides equals the number of miles ridden, and I have "never cycled more than that number of miles on any other day."
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However, if I ride three rides that are at least 64.0 miles in the next whatever, then my Eddington number will jump from {0 / undefined** to 64.

[edit]:
So far in 2010, I have one ride that exceeded 64.0 miles (and the other rides are each less than 63.0 miles), so I only need two more rides that are at least 64.0 miles to jump from an E of {0 / undefined** to an E of 64.

However, as soon as I do three more rides of at least 64.0 miles, my E will drop back to {0 / undefined**. Until I get nine (9) more rides that are at least 65.0 miles, then my E will once again "jump", but it will "jump" to 65.

[end edit]
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The OP guessed that his E would be about 30. That would mean that "jefferee" has ridden 30 or more miles only 30 times in his life.

How is this calculated? I guessed, as follows:
list all rides in descending order of distance, truncated to the next lowest integer
number the rows
scroll down the list, find the truncated distance number where the number equals the row number. That's E.

Yes? Other way to do it?

Exactly.

Guess I'm not part of the rest of the world, what is KM? I'm kind of in the same boat as Richard. I don't keep that close of a track of the rides I do. I'm not really a paperwork/number guy unless I have a reason, like specific training...

KM = Kilometers

OP, I think you mis-stated the definition, in googling around for it, I'm not finding that second clause applied to cycing - which makes it make more sense (not that it makes much sense, but at least it's not total nonsense.) :)

http://en.wikipedia.org/wiki/Arthur_Stanley_Eddington
"Eddington number (cycling)

Eddington is credited with devising a measure of a cyclist's long distance riding achievements. The Eddington Number in this context is defined as E, the number of days a cyclist has cycled more than E miles[5][6]. For example an Eddington Number of 70 would imply that a cyclist has cycled more than 70 miles in a day on 70 occasions. Achieving a high Eddington number is difficult since moving from, say, 70 to 75 will probably require more than five new long distance rides since any rides shorter than 75 miles will no longer be included in the reckoning."

OK, time to whip out our new e-wang ruler!

71

edit - since 04/2007. This leaves out the first 5 years of my road cycling career including <blah blah blah>, so i think my real # is higher - but we'll all have some similar situation.

A cyclist has an Eddington number of E if (s)he has cycled at least E miles on E different days, and has never cycled more than E miles on any other day.

Correct me if I'm interpreting this one wrong, but since I've ridden 250 miles in a day, the lowest E number I could possibly hope for is 250; meaning I have to do 249 more rides of 250 miles (not 249, not 251... but EXACTLY 250 miles) to get there. And while acheiving those 249 rides, if I manage to ride a 251 mile day, I've ruined my chances at an E=250.

If I'm reading it right, the quest for a higher Eddington number is extremely self-limiting because it caps the maximum number of miles you can ride without starting your series over again.

I have 63 rides that are at least 63.8 miles, so you might at first think my Eddington number is 63. However, I think that is not correct because I actually have 73 rides that are at least 63.0 miles.

If you have logged 63 rides of at least 63 miles, but have not logged 64 rides of at least 64 miles, then your Eddington number is 63. That was what I was trying to say with the "never cycled more than E miles on any other day" bit. Sorry to confuse.


The OP guessed that his E would be about 30. That would mean that "jefferee" has ridden 30 or more miles only 30 times in his life.
Correct. I do plan to significantly upgrade that figure this summer.

Stay in School!

A cyclist has an Eddington number of E if (s)he has cycled at least E miles on E different days, and has never cycled more than E miles on any other day.

Correct me if I'm interpreting this one wrong, but since I've ridden 250 miles in a day, the lowest E number I could possibly hope for is 250; meaning I have to do 249 more rides of 250 miles (not 249, not 251... but EXACTLY 250 miles) to get there. And while acheiving those 249 rides, if I manage to ride a 251 mile day, I've ruined my chances at an E=250.

If I'm reading it right, the quest for a higher Eddington number is extremely self-limiting because it caps the maximum number of miles you can ride without starting your series over again.

Check my edited definition, and valygrl's definition 2 posts above yours. The "not cycled more than E miles on any other day" bit reflects the fact that E is defined as the maximum value that fits the definition--i.e., if you have done 65 rides of 65 miles or more (but not 66 rides of 66 miles or more), your E is 65. Again, sorry to confuse.

KM = Kilometers

OP, I think you mis-stated the definition, in googling around for it, I'm not finding that second clause applied to cycing - which makes it make more sense (not that it makes much sense, but at least it's not total nonsense.) :)

http://en.wikipedia.org/wiki/Arthur_Stanley_Eddington
"Eddington number (cycling)

Eddington is credited with devising a measure of a cyclist's long distance riding achievements. The Eddington Number in this context is defined as E, the number of days a cyclist has cycled more than E miles[5][6]. For example an Eddington Number of 70 would imply that a cyclist has cycled more than 70 miles in a day on 70 occasions. Achieving a high Eddington number is difficult since moving from, say, 70 to 75 will probably require more than five new long distance rides since any rides shorter than 75 miles will no longer be included in the reckoning."

It's a more-or-less identical definition, except that the part I added is intended to state that E is actually the maximum possible value for which this definition is true. (Otherwise, if you have E=50, for example, you also, by the same definition, have E=1, E=2, E=3, E=4,.....) My definition is more mathematically rigorous, but also, apparently a whole lot more confusing.

Note that the very next sentence in the Wikipedia article you quoted states that this is the same as the definition of the "h-parameter" used to evaluate scientific output--my definition is based on a description of the definition of h-parameter.

Stay in School!

I'm actually in the middle of a PhD in physics. I understand well; I just communicate badly.:innocent:

KM = Kilometers

That's easy enough, I was over thinking it. That's probably why I started my college life as a physics major and ended it in technical management. ;)

I thought the initial description was fine, and that it was an interesting concept, contrasting with median ride distance.
I was telling the others, and was surprised at the level of comprehension displayed.
I've never kept records, but figure my E# is roughly 60-65.

. . .
A cyclist has an Eddington number of E if (s)he has cycled at least E miles on E different days. and has never cycled more than E miles on any other day.* You count the highest value of E for which this is true--i.e., if you have done 65 rides of at least 65 miles, but not 66 rides of 66 miles, your E is 65.

Here's another definition from Wikipedia:
http://en.wikipedia.org/wiki/Arthur_Stanley_Eddington
"Eddington number (cycling)

Eddington is credited with devising a measure of a cyclist's long distance riding achievements. The Eddington Number in this context is defined as E, the number of days a cyclist has cycled more than E miles[5][6]. For example an Eddington Number of 70 would imply that a cyclist has cycled more than 70 miles in a day on 70 occasions. Achieving a high Eddington number is difficult since moving from, say, 70 to 75 will probably require more than five new long distance rides since any rides shorter than 75 miles will no longer be included in the reckoning." . . . .
I added the bold typeface above to highlight the point addressed below:

The edited definition(s) of E are not the same.

One refers to at least E miles, the other refers to more than E miles.

In the second definition ("more than"), a ride of exactly E.0 miles would not count towards the E.

In evaluating my personal data, the above discrepancy actually makes no difference because I record the length of my rides by truncating to the lower tenth-of-a-mile (therefore, what I have recorded as, e.g., 63.0 miles, was actually slightly more than 63.0 miles.
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I am still digesting what impact the revised definition has in a situation where one has, e.g., 61 rides of 64.0 miles or more, and 73 rides of 63.0 miles or more.

I added the bold typeface above to highlight the point addressed below:

The edited definition(s) of E are not the same.

One refers to at least E miles, the other refers to more than E miles.

Good catch--they are differently stated. In my defence, since E is an integer, calculating E with either definition will give you the same result.

It becomes difficult to determine your E number when the only record of your cycling accomplishments are a stack of bib numbers and brevet cards.
I've looked at analytic cycling sites before, and while I understand the benefit of number-crunching your rides if you're in serious training for something, I just don't see the fun in turning cycling into what I do for my job 8 - 10 hours a day.

That's easy enough, I was over thinking it. That's probably why I started my college life as a physics major and ended it in technical management. ;)

Ha! I just thought you were being a weisneheimer!:roflmao2:

I am still digesting what impact the revised definition has in a situation where one has, e.g., 61 rides of 64.0 miles or more, and 73 rides of 63.0 miles or more.

You can't say exactly what E is in those situations, but you can set a lower limit.

61 rides of 64.0 miles or more:
All you can say for sure with that information is that E is at least 61 (since you certainly have 61 rides of at least 61.0 miles).
If you have a few rides of between 61.0 and 64.0 miles, it's possible that E could be 62 (if you have 62 rides of at least 62.0 miles) or 63 (63 rides of at least 63 miles).

73 rides of 63.0 miles or more:
E is at least 63 (since you certainly have 63 rides of at least 63.0 miles).
But again, E could be larger--unless a large number (at least 10) of those 73 rides are between 63.0 and 64.0 miles, then you will have 64 rides of 64.0 miles or more, for E of 64, and then you have to check whether you qualify for E=65, and so on...

Hope that helps.

It becomes difficult to determine your E number when the only record of your cycling accomplishments are a stack of bib numbers and brevet cards.
I've looked at analytic cycling sites before, and while I understand the benefit of number-crunching your rides if you're in serious training for something, I just don't see the fun in turning cycling into what I do for my job 8 - 10 hours a day.

I never said it was useful, just interesting. ;)

Good catch--they are differently stated. In my defence, since E is an integer, calculating E with either definition will give you the same result.

You might want to rethink that.

The Wiki definition (why on Earth are we giving credence to anything on Wiki?) implies that the rides of length truncated E do NOT count for deteriming one's E, as the Wiki says that only rides MORE THAN E count in determining E. Therefore, taken literally, no rides that truncate to E count for determining the E. I suspect that the Wiki definition should refer to "at least".

However, this definiton does originate with thoughts from "Sir Arthur Adding-One". Makes me wonder how sloppy the definition was in the first place.
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However, knowing that Sir Arthur Adding-One was sloppy or fungeable in his view of N(Edd) in the world of physics, I think we can all surmise that the process that <I forget the poster's handle> put on the thread, of sorting one's rides in order, and scanning down until the number of rides and length of rides (truncated miles) are the same, is the way to go.

It is, however, sometimes fun to pretend to be "serious" about these kind of fun / silly things and try to "nail down" the definition more precisely.
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I think there are still a lot undefined in the E. For example, suppose someone has ridden 30.5 or more miles 29 times, and has ridden 29.5 miles once. Clearly the E is not 30. Is it 29? I think so, but I'm not 100% sure.

Would reference to quantum mechanics be of any usefulness here?

Btw, since I (as of Feb-11-2009) have only 62 rides that are 64 or more miles, and 74 rides that are 63 or more miles, I will currently claim an E of 63.

I love when multiple people are posting simultaneously, and the response one was making no longer applies to the immediately above post by the time you click "post" or "save".

Interesting. I have no records of rides from before the last year, and didn't record all of the last year, so all I can do is make a guess. I'd say I'm between 40 and 50. I'm sure I've done at least 40 rides over 40 miles in my lifetime. But I'm not sure I've done more than 50 that are over 50 miles. If I only go by rides I have records of, then I'm probably just at 16, since that's my commute and I doubt I have kept track of 17 longer rides.

It is an interesting metric, though.

Keith

OK, let me dig out the log here ....

According to my log I've done 82 rides of 100 miles (or slightly more) ... I don't think I've ever stopped right on exactly 100.
In addition to that, I've done 22 - 200K rides (125-ish miles).
In addition to that, I've done 13 - 300K rides (about 200 miles, some were 200 miles, some a bit less).
And in addition to that, I've done 12 - 400K rides.
(I've also done several longer rides but they would have technically taken more than one day and wouldn't apply here)


So, if I'm reading the calculation information correctly, I have done at least 100 centuries (82 + 22 is 104), which would give me a score of E=100. If I went through and looked up those 82 rides of 100 miles (or slightly more), I may well find that my score is E=101 or 102, because I rarely stopped right on 100 miles, I usually went over by a mile or two for good measure.

That is if we're doing the calculation in miles.

If we were doing the calculation in kilometers, my score would be more like E=162 or E=165 or something.

I can claim an E number of 100, and like Machka may get E=101 or 102, depending on exactly how long a lot of the century rides I've done are. Presently I'm at 50 RUSA/ACP/RM events of 200K or longer (the 50th was this past Saturday -- 50 starts; 50 completions!) and a whole host of club centuries and ultra-distance events -- probably another 75-100 rides of longer than 100 miles.

Like Machka and most other repeat offender randonneurs, my E-number will sometime in the next few years jump from 100 or 101 to 124 or 125 (depending on how short the shortest 200K I did was). Once that shift happens, no matter how much I ride for the rest of my life, my E number is very unlikely to increase. Probably not a lot of long-distance cyclists riding events between 200K and 300K. And I'd wager that completing 186 rides of 300K or longer has probably never been done, not even by those nut-cases down in texas. ;)

If we were doing the calculation in kilometers, my score would be more like E=162 or E=165 or something.

It only looks like you've got 129 rides of 162km or more, so your metric E number would be something smaller than 162. Assuming no other long rides, I guess it'd be 129. But every time you do another century+ ride, it'll go up by one until you reach ~162-165. Then you'll start needing longer rides as well.

Keith

It only looks like you've got 129 rides of 162km or more, so your metric E number would be something smaller than 162. Assuming no other long rides, I guess it'd be 129. But every time you do another century+ ride, it'll go up by one until you reach ~162-165. Then you'll start needing longer rides as well.

Keith

Good point, but ...

I've also got 6 - 600K rides, 1 - 900K ride, 1 - 1000K ride, and 4 - 1200K rides, which are each over multiple days, plus a couple of the 400Ks were spread over two days.

So, according to my log, I've got 163 days of riding where I did over 162 km on those days.

Hmmm, that brings up the question of whether a multi-day ride like a long brevet counts as one long ride or multiple shorter ones. Given the nature of a brevet (timed continuously from start to finish), I'd be inclined to call it one ride. Otherwise, if you do a 300k that starts at 6pm and goes through the night and finishes the next morning, would you call it 2 rides, broken at midnight? So depending on when you start it might be a 100k and a 200k, or 125k & 175k, or 2x150k? That doesn't make sense.

Most people (everyone?) would have a higher E number by breaking the long brevets up since only someone with a E(metric) of >200 would benefit from having 1 400k instead of 2x200k. But at what point do you do the breaking? And how does one distinguish between a 600K brevet with an 8 hour sleep in a motel room and two 300K rides on consecutive days? What's the difference between 4 days of covering 300k each, and a 1200k brevet? If you ride a 1200k straight through without sleeping, should it count as multiple rides?

I'm not trying to keep you from claiming an E(metric) of 163, Machka, really. :)

I guess it just boils down to each person deciding for themselves. If your brevet seemed line 2 rides because you stopped for a sleep break, then you should count it as two rides. But if you felt like it was really one ride, then count it as one. It's not like there's some international organization certifying E numbers.

Keith

When I created the log and "broke" my long rides into days, midnight was the dividing point, just for the sake of consistency.

But there is the question of whether a 1200K is one ride, or essentially multiple rides. In my personal logs, it shows up as both. I have a column for days where I've ridden more than 100 miles (162 km), of which there are 163. And I have a column of 100+ mile (162+ km) events/rides, of which there are 141.

Hmm, interesting perspective. My little ol' E-53 pales in comparison.
I've got to get out and ride not only more but longer as well....:innocent:

Wow, after reading all this I think we need a C number- the number of days you've sat at the computer for at least C minutes
And to keep it interesting, let's make it days that you didn't ride on (indoors or out).

:-)

Good point, but ...

I've also got 6 - 600K rides, 1 - 900K ride, 1 - 1000K ride, and 4 - 1200K rides, which are each over multiple days, plus a couple of the 400Ks were spread over two days.

So, according to my log, I've got 163 days of riding where I did over 162 km on those days.OP limited the miles ridden to those within a 24 hour period. Your 1200's are likely spread over 3 or more separate 24-hour periods. Your 600's are likely spread over 2 separate 24-hour periods unless you are pretty fast / strong -- which you may be, I don't know.

[edit]

I see that you addressed the multiple day thing subsequent to the quoted post.

Hmmm, that brings up the question of whether a multi-day ride like a long brevet counts as one long ride or multiple shorter ones. Given the nature of a brevet (timed continuously from start to finish), I'd be inclined to call it one ride. . . .The OP defined a 24 hour period. So the question has already been addressed / defined.

However, it is still worthwhile to address. Mostly because this whole exercise is just a fun / silly thing not-to-be-taken too seriously.

To give an example, treating a single 1200 km ride as one 750 mile ride versus three 250 mile rides may give a surprising result. Namely, treating as a single ride may reduce one's E. Obviously, it all depends the distribution and quantity of one's particular rides.

Thinking it over, I think I like the idea of treating the super-long, multi-day, single-event rides as only one ride instead of multiple daily rides.

Why?

It makes it harder to get a bigger E.

For randonneuring, I think it is meaningless to define E in terms of "days", since as khearn points out, how many days or miles/day depends on what time the ride starts. You could break it into sequences of 24-hours, but, really, what's the point of trying to go back to figure out how many miles of PBP I rode in the first 24 hours? It's easier to just track E in terms of "events". And as others have pointed out, once you've been randonneuring for a few years, E is approximately equal to 125, and it becomes very difficult to push above the next "natural" number 186 (in mi). Fifteen+ years of doing a 300K a month! Thirty years of doing one every other month!

So call "EE" the "Event Eddington" score.

I'm at EE=102 (mi) or 128 (km). I'm thirty-one 200K or longer events away from EE=125 (mi), so at my current riding pace I should get there in about November next year, at which time metric EE should be about 152. Plus, I've already got fifty events of distances between 125 and 138 miles, mostly slightly-longer-than-200K permanents, so I should be able to gradually push EE higher for a while. But only thirty-three events of 150 miles or longer, so it may turn out not be possible to push EE above 138.

As I PM'd to "jefferee" yesterday, the efficiently worded way to define one's cycling E is as follows:

"One's cycling E is defined as the maximum integer for which the following is a True Statement:

'I have at least E rides that were at least E miles long.' "

Why physicist Eddington and others use all those extra words is curious, at the least. Not to mention potentially confusing.

To my friend "thebulls": no need for an EE; let's just hijack and restore E to its proper usage. ;)

When I created the log and "broke" my long rides into days, midnight was the dividing point, just for the sake of consistency....


I break my rides up by sleep breaks. If there is no sleep break I count it as one ride in my ride log. One sleep break gives me 2 rides, etc.

BTW, as far as my log goes back it looks like my E number is 68 (in miles)