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 Long Distance Competition/Ultracycling, Randonneuring and Endurance Cycling Do you enjoy centuries, double centuries, brevets, randonnees, and 24-hour time trials? Share ride reports, and exchange training, equipment, and nutrition information specific to long distance cycling. This isn't for tours, this is for endurance events cycling

02-10-10, 07:16 PM   #1
jefferee
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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. [STRIKE]and has never cycled more than E miles on any other day.[/STRIKE]* 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. 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)

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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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.
Quote:
 Originally Posted by Jorge Hirsch 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.

Last edited by jefferee; 02-11-10 at 10:44 AM. Reason: Edited for clarity of the definition--updates in red.

 02-10-10, 09:26 PM #2 CliftonGK1 Senior Member     Join Date: Jul 2006 Location: Columbus, OH Bikes: '08 Surly Cross-Check, 2011 Redline Conquest Pro, 2012 Spesh FSR Comp EVO, 2015 Trek Domane 6.2 disc Posts: 11,380 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) 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. __________________ "I feel like my world was classier before I found cyclocross." - Mandi M.
 02-11-10, 07:23 AM #3 Richard Cranium Senior Member     Join Date: Jun 2002 Location: Deep in the Shawnee Forest Bikes: LeMond - Gunnar Posts: 2,845 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 7 Post(s) 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.....
 02-11-10, 08:28 AM #4 valygrl Senior Member   Join Date: Jul 2003 Location: Boulder, CO Bikes: Posts: 8,530 Mentioned: 76 Post(s) Tagged: 0 Thread(s) Quoted: 154 Post(s) 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?
02-11-10, 09:06 AM   #5
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 Originally Posted by valygrl ... 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...

02-11-10, 09:40 AM   #6
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 Originally Posted by jefferee 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. 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.

:
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.

Last edited by skiffrun; 02-11-10 at 12:35 PM.

02-11-10, 10:13 AM   #7
jefferee
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 Originally Posted by valygrl 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.

02-11-10, 10:16 AM   #8
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 Originally Posted by Homeyba 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."

 02-11-10, 10:19 AM #9 valygrl Senior Member   Join Date: Jul 2003 Location: Boulder, CO Bikes: Posts: 8,530 Mentioned: 76 Post(s) Tagged: 0 Thread(s) Quoted: 154 Post(s) 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 , so i think my real # is higher - but we'll all have some similar situation.
 02-11-10, 10:20 AM #10 CliftonGK1 Senior Member     Join Date: Jul 2006 Location: Columbus, OH Bikes: '08 Surly Cross-Check, 2011 Redline Conquest Pro, 2012 Spesh FSR Comp EVO, 2015 Trek Domane 6.2 disc Posts: 11,380 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) 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 feel like my world was classier before I found cyclocross." - Mandi M.
02-11-10, 10:23 AM   #11
jefferee
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 Originally Posted by skiffrun 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.

Quote:
 Originally Posted by skiffrun 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.

 02-11-10, 10:29 AM #12 Metzinger Primate     Join Date: Jan 2006 Location: gone Bikes: Concorde Columbus SL, Rocky Mountain Edge, Sparta stadfiets Posts: 2,582 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) Stay in School!
02-11-10, 10:32 AM   #13
jefferee
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 Originally Posted by CliftonGK1 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.

02-11-10, 10:37 AM   #14
jefferee
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 Originally Posted by valygrl 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.

Last edited by jefferee; 02-11-10 at 10:42 AM.

02-11-10, 10:38 AM   #15
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 Originally Posted by Metzinger Stay in School!
I'm actually in the middle of a PhD in physics. I understand well; I just communicate badly.

02-11-10, 11:17 AM   #16
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 Originally Posted by valygrl 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.

 02-11-10, 11:25 AM #17 Metzinger Primate     Join Date: Jan 2006 Location: gone Bikes: Concorde Columbus SL, Rocky Mountain Edge, Sparta stadfiets Posts: 2,582 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 0 Post(s) 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.
02-11-10, 12:14 PM   #18
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 Originally Posted by jefferee . . . A cyclist has an Eddington number of E if (s)he has cycled at least E miles on E different days. [STRIKE]and has never cycled more than E miles on any other day.[/STRIKE]* 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.

Last edited by skiffrun; 02-11-10 at 12:31 PM.

02-11-10, 12:36 PM   #19
jefferee
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 Originally Posted by skiffrun 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.

 02-11-10, 12:44 PM #20 CliftonGK1 Senior Member     Join Date: Jul 2006 Location: Columbus, OH Bikes: '08 Surly Cross-Check, 2011 Redline Conquest Pro, 2012 Spesh FSR Comp EVO, 2015 Trek Domane 6.2 disc Posts: 11,380 Mentioned: 0 Post(s) Tagged: 0 Thread(s) Quoted: 1 Post(s) 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 feel like my world was classier before I found cyclocross." - Mandi M.
02-11-10, 12:45 PM   #21
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 Originally Posted by Homeyba 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!

02-11-10, 12:50 PM   #22
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 Originally Posted by skiffrun 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.

02-11-10, 12:57 PM   #23
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 Originally Posted by CliftonGK1 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.

02-11-10, 01:05 PM   #24
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 Originally Posted by jefferee 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?

 02-11-10, 01:11 PM #25 skiffrun Senior Member     Join Date: Apr 2007 Location: Raleigh, NC Bikes: Posts: 742 Mentioned: 2 Post(s) Tagged: 0 Thread(s) Quoted: 14 Post(s) 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.