Reblog: Stumbleupon mathematics for stumblers

As an enthusiastic new stumbler, I am continuously impressed with the content I discover on StumbleUpon, and I was wondering what is the algorithm behind.

I quickly understood that it is an undisclosed secret sauce – but I found on Mashable a reference to an old blog post published in 2007, entitled “StumbleUpon mathematics for stumblers“.

The post is not available since almost 9 years but we was able to find it on Internet Archive, so here it is – including the original discussion from 2007 in the bottom of the page.

Stumbleupon mathematics for stumblers

Source: Internet Archive Wayback Machine
Original version September 19th, 2007 Tim Nash

What follows is my understanding of the stumbleupon algorithm it is based on some pretty extensive testing using several volunteers however it has been incredibly simplified to make it easier to understand. We may be totally wrong so just a heads up but I hope this will at least give you some idea of what your thumb up is doing. I have also written up a few questions and answers to help people understand what Im trying to do.

Audience score

Every stumbler has an audience score in the old days stumbleupon told you what your score was but have since taken this facility away. The audience score was based on number of fans, number of pages thumbed up, number of pages thumbed down and number of reviews written. The score is what determines how much stumble juice a person carries.
The audience score has one other factor stumble history. If a stumbler initially stumbles a site and the site receives a large quantity of thumbs up their audience score increases conversely if they initially stumble a site and it’s thumbed down their audience score goes down. Stumblers who stumble a site after the initial stumble also have changes to their audience score but not to the same extent.
It is hard to weight which factor is most important when increasing audience score but the factors as I see them are:

  • Number of fans
  • Number of thumbs up and down you have given
  • Stumble thumb bonus – increase to score based on number of thumbs received on a page.

This model means that the obvious technique to get a “power account” is to find more fans, thumb up loads of pages and start stumbles on pages you expect to be popular – sound familiar its pretty much the same on every social media site.

Once we have our idea of an audience score its time to look at a few basic models that stumbleupon might use, you can skip to the big one if you want but these smaller models I think are important to demonstrate individual parts of the algorithm.

A Basic model

Initial stumbler + (number of thumbs up / number of thumbs down) = visitors

This basic model is based on the idea that the initial stumblers audience score will dictate how many visitors will initially see the page and then the number of thumbs up will dictate how many additional people see the page it also presumes that thumbs down have equal weighting to thumbs up.

Audience driven model

Initial stumbler audience + (% of audience of stumbler per thumb up / number of thumbs down) = visitor

This model is a little more complex it presumes that the full audience score is used for the initial stumbler while each additional thumbs up passes a percentage of each stumblers audience score. This model would account for the stumble wave effect, where stumbleupon sends continual waves of varying sizes.

Audience + Domain model

(Initial stumbler audience/#stumbled domain)+ ((% of audience of stumbler per thumb up/#stumbled domain) / number of thumbs down) = visitor

This model presumes the number of times the domain is stumbled by a user is a factor therefore the initial stumblers audience score is affected by the number of times they have previously stumbled the domain. If this is done for both the initial stumbler and all stumblers thumbing the page up or down it would explain why mailing lists and friends stumbling the same domain has less and less effect.

The models above show a continual development but there are few more factors rather then showing endless models I will just discuss these factors

Friends

Being friends is not a bad thing while stumbleupon does not provide a bonus it is my belief it does penalise accounts that continue to stumble the same things without being friends or at least one party being a fan. I do not believe the penalty to be huge just a balancing factor to flag that the accounts routinely stumble the same information.

Organic bonus

This I think is a huge factor when a user arrives on a site via the toolbar it is “organic” in the way your arrived, stumbleupon presumes you are judging the page on merits having not seen it before it therefore gives more weight to thumbs up that come via organic stumbling. This is another reason mailing lists fail to work over time on stumbleupon.

Send to

I initially categorised the use of send to as “organic” stumbling but my current belief is that it is not considered organic and therefore does not provide a bonus from organic stumbling, more experiments need to be carried out but I believe it may indeed be the reverse and actually cause a penalty.

The Big one(Initial stumbler audience /# domain) + ((% stumbler audience /# domain)+ organic bonus – nonfriend) – (((% stumbler audience + organic bonus) + N

So initial stumbler juice is his audience plus his previous stumble bonus which is divided by the number of times the domain has been stumbled by the user. Plus for each thumb up the juice is a percentage of their audience score plus their previous stumble bonus divided by the number of times the domain has been stumbled by that user plus a bonus if the stumble was organic and any to close penalties that may apply. The audience score is reduced by a percentage for each thumb down stumbler plus a bonus if organically stumbled. Finally N which is a random number generator or a Tim get out of jail free card.

The big model is simplified to the extreme but I think is fairly accurate but it does not explain stumble wave suitably so within our model we need to look at time. Sadly we haven’t been able to run an experiment beyond a month but based on previous statistical evidence time stumbleupon waves occur on an almost logarithmically with large quantity of waves occurring after the first stumble and then petering out, until the next thumb which sends another series of waves.

Lets follow some examples we will use totally fake numbers to make life easy.

A stumble upon user

Our user lets call him Fred has an audience score of 10 he goes along and starts a new stumble at a site he has never visited it gets a couple of hundred visits and 3 thumbs up
Fred gains a point to his audience score for thumbing something up +a further bonus because others liked his stumble so fred now has an audience score of 13
Fred is really impressed that so many visitors came to his site so he thumbed up another page, even with his increased score it didn’t do so well and only 2 people thumbed it up and 2 thumbed it down!

His score is now 14 (increased for thumbing up – no bonus )
Fred tries a different domain it does well and 10 people thumb it up his score goes up to 25, Fred has realised stumbleupon can make him money so thumbs up his proxy site it gets a few visitors but 7 people thumb down the site and 2 marked it as spam. Fred audience score plummets (18 but has been marked by spam so temporarily has his score halved) so his score is now 9 poor Fred will have to work hard to regain his score.

A Domain

Some nice person stumbles the site they had an audience score of 10 which brought a 100 people 3 other people thumbed the site (all came via organic) with scores of 30/100/40 they bring a further 150.

Next day the domain is stumbled again but the number of stumbles is much lower, the owner tries to encourage people to visit the site by using the send to button and while there are lots of thumbs few extra visitors other then those he sent the send to to.

Mailing lists

A secret group of stumblers have a mailing list, they send an email when they want something stumbled. The first time it worked great and large amount of stumbles followed, the second time it didn’t work quite so well soon the mailing list stumbles are counting for little or nothing. (this happens an awful lot repeatedly stumbling the same domain reduces the chance of a stumble wave next time particularly if people outside of the group are not also thumbing up the groups stumbles.

What do you think have we got it right? Wrong? Am I completely off my trolley?

 

Original Comments (2007)

 

57 Responses to Stumbleupon mathematics for stumblers

  1. Breaking Down The StumbleUpon Algorithm : The Blog Herald Says:
    [] Check his thoughts out over here, but Steve basically tries to break things down into understanding an Audience Score, where he attempts to break down some variables that lead to a power stumbler; several models that might explain how any given site might get popular through StumbleUpon (taking into account, for example, the first stumbler); and finally some bonus factors that might influence things in ways that deserve a lot more working out. []
  2. Stumbleupon list of articles Says:
    [] Stumbleupon mathematics for stumblers Stumbleupon vs Digg – Page layouts Stumbleupon vs Digg – Voyeurs vs Sheep []
  3. Stumble Gods :: Our Thumbs Move Masses » Blog Archive » Cracking the StumbleUpon Algorithm, one blogger tries to work out the math Says:
    [] what Steve over at the Venture Skills blog has worked out for the StumbleUpon algorithm, or the mathematical equation that happens when you click that happy little thumbs up button on []
  4. eyeflare.com Says:
    I think youre absolutely right in your assessment. Subsequent mailings are less effective, consecutive stumbles are less effectiveThen you get an initial stumble from a top stumbler and traffic rockets!More confirmation that just being a good active stumbler actually works!
  5. Stumbleupon Algorithm Unearthed? | Andy Beard – Niche Marketing Says:
    [] geeky, but for those that like delving into how things might work, Tims modelling of the Stumbleupon algorithm is just pure []
  6. Glen Allsopp Says:
    Very interesting write-up Tim, Ive bookmarked this one to come back to it later.Stumbled aswell.
  7. Admin Says:
    cheers guys :)
    The initial stumbler has a lot to do with how a stumble behaves but even a top stumbler coming in 3 weeks later can have a dramatic effect on the number of stumbles.
  8. How To Find Your Social Media Mix | How To Split An Atom Says:
    [] talking about today? How about Social Media to start. It looks like Stumble Upon power users have a new grail at their disposal, a fantastic guide to finding out your SU Juice. Still, the problem []
  9. Has the StumbleUpon Algorithm Been De-Coded? Says:
    [] blogger has done extensive research into the StumbleUpon algorithm to see how exactly the service works. According to the researchers, []
  10. Marketing Viral : Le fonctionnement de Stumble Upon décrypté « So chouette! Says:
    [] vous invite à consulter son post si vous avez un peu de temps; cest du travail []
  11. James – Visualized.Feel.Abundance Says:
    This is a very interesting write up and I have to agree that the initial stumbler factors heavily in the algo. I had a post where the initial stumbler had no friends at all. Despite the fact that subsequently, I got 8 reviews + a small load of thumbs up. It was never shown once on SU.Cheers
    JamesPS: Stumbled this article. Keep the great work going.
  12. Josh Says:
    Very nice post! I just gave you a thumbs up. Keep up the good work.
  13. Anchor Text?: social media consultant Says:
    you tried to solve few things . but think you must have put some light on theword stumbler
    i am not able to get that .
  14. Ash Says:
    Very interesting Tim. Im not 100% sure i agree with you on a secret mailing list not carrying any weight.I think the stumbling habits of the members is a much more important factor. If they solely stumble their own pages and only suggested pages rather than actually naturally stumbling other 3rd party pages, they will see little benefit.There is a huge benefit in being an active stumbler though.
  15. Admin Says:
    @James – The initial stumblers audience is a huge factor as you say quite a few of our experiments when run resulted in null results even when I would stumble immediately afterwards and one particular stumble which had nearly 20 thumbs up had the total of 8 visits from stumbleupon. Interestingly this post which has received a large quantity of thumbs up has very little traffic via stumbleupon. The reason the first few stumblers were people who read the blog and regularly stumble it, now that non regulars are thumbing it its starting build traction.@Ash The secret mailing list really is a non starter its great for helping a new domain out but within a few stumbles it looses all its authority. The best results is to wait for the page to come up organic and then stumble it. I think many mailing lists are fooled into thinking they are working because they see stumbleupon visitors but do not realise it was not there votes but the votes of others that did it.Of course there are exceptions if you were planning on running such a group I would a have a very large user base, have the system select 10-30 at random to send the request to, only send the request after a non member had stumbled it etc by the time you got such a system running think how many posts you could have made :)
  16. rob Says:
    Nice read Tim, love these deconstructive type posts.Stumbling this, hope you can draw a bit more evidence from any resultant traffic boost!
  17. Anonymous Says:
    Stumbleupon mathematics for stumblersGreat article from Tim Nash about how SU calculates the stumbles authority. A high value of authority is important for the stumbler who wants to promote his website or blog together with other stumblers:
    A lot of stumbles from uses with high athority =
  18. More questions then answers « The Venture Skills Blog Says:
    [] Posts Stumbleupon mathematics for stumblersStumbleupon vs Digg – Voyeurs vs SheepWant to create a site like Digg with no programming?Top 5 CSS []
  19. Reztar Says:
    Very nice and detailed but easy to read article :D stumbled yours. I hope you monitor this page stumble statistics for your future stumble articles to share to us.
  20. Tim Nash Says:
    Hi Rob & Reztar cheers guys, yes we are watching this page but as it stands its not doing very well on stumbleupon at all :( I think when I last looked stumbleupon had sent a 100 visitors.
  21. Aldian Prakoso Says:
    Thanks for this great information. Now I can utilize SU better.
    Stumbled this page, too!
  22. An Ode to StumbleUpon Says:
    [] you, StumbleUpon. You have stayed true to us. We want to know you very well, but dont change a thing. We like you just the way you []
  23. ecommerce-well.com » Blog Archive » Stumbleupon juice: How influential are your stumbles? Says:
    [] more details check out the blog post here. Our blog entries withTags: seo, []
  24. StumbleUpon How it might work | TechWag Says:
    [] Like all reverse engineering, this may or may not really work. Every stumbler has an audience score in the old days stumbleupon told you what your score was but have since taken this facility away. The audience score was based on number of fans, number of pages thumbed up, number of pages thumbed down and number of reviews written. The score is what determines how much stumble juice a person carries. The audience score has one other factor stumble history. If a stumbler initially stumbles a site and the site receives a large quantity of thumbs up their audience score increases conversely if they initially stumble a site and it’s thumbed down their audience score goes down. Stumblers who stumble a site after the initial stumble also have changes to their audience score but not to the same extent. Source: Venture Skills Blog []
  25. Five Tips for Getting Traffic From Stumble : Big Bucks Blogger Says:
    [] Give them your Stumble profile link (heres mine Lucia Liljegren. ) Hopefully, they will make you their StumbleUpon friend and will Stumble your best posts (especially when you link them.) Then, you will both increase your reputations with Stumble and get more traffic. (To read more about how Stumble rates stumblers, visit Stumble Upon Mathematics. []
  26. Stumble into the Weekend 09/21 Says:
    [] analyzes the algorithm behind StumbleUpon. Okay, its just a theory, but a really interesting read. Maybe itll help you with you []
  27. Lars Says:
    interesting read.. def. a thumbs up from me!
    thank you
  28. Stumbleupon Algorithm – A Reasoned Theory Says:
    [] Andy Beard, we find Stumbleupon mathematics for stumblers. We may be totally wrong so just a heads up but I hope this will at least give you some idea of []
  29. SEO WORLD NEWS » Blog Archive » Stumbleupon Algorithm – A Reasoned Theory Says:
    [] Andy Beard, we find Stumbleupon mathematics for stumblers. We may be totally wrong so just a heads up but I hope this will at least give you some idea of []
  30. Internet Alchemy » links for 2007-09-22 Says:
    [] Stumbleupon mathematics for stumblers An analysis of the algorithm that stumbleupon (may) use (tags: algorithm blogging stumbleupon recommendations) []
  31. Social Poster » Stumbleupon mathematics for stumblers Says:
    [] Stumbleupon mathematics for stumblers It is hard to weight which factor is most important when increasing audience score but the factors as I see them are: * Number of fans * Number of thumbs up and down you have given * Stumble thumb bonus – increase to score based on number of thumbs received on a page. []
  32. SearchCap: The Day In Search, September 21, 2007 Says:
    [] Stumbleupon maths for stumblers, The Venture Skills Blog []
  33. rob Says:
    Hey Tim perhaps it was that mathematics term in the headline .Im not one for overtly clickbaity headlines, but I know a man who is
  34. Tim Nash Says:
    The lack of stumbleupon activity is because there was no initial stumbler. But the headline was a bit of a mistake given that a search for stumbleupon algorithm puts this blog 3rd :)we live and learn
  35. Andy Beard Says:
    I have seen that no initial Stumbler a few times on my site and have no idea how that actually happens.
    When I use the toolbar, if I am discovering something I have to give it a review or it doesnt accept my Stumble
  36. Tim Nash Says:
    In this case it was down to the misuse of the send-to button, I sent out a send to to a friend to proof read as I had lost her email address, but didnt initially stumble it myself. So a record was made in the system, but with no initial stumbler. I tried to thumb up and leave a review hoping it would recognise me after I noticed the mistake but to no avail.So if using send-to button make sure the domain is already stumbled
  37. Best of Feeds – 22 links – programming, blogging, tips, javascript, rails « Internet Duct Tape Says:
    [] [SMO] Stumbleupon mathematics for stumblers []
  38. Technology » Blog Archive » The StumbleUpon Algorithm Unearthed? Says:
    [] geeky, but for those that like delving into how things might work, Tims modeling of the Stumbleupon algorithm is just pure []
  39. SEO 2.0 | 12 Great SEO Blogs You Might Have Missed Says:
    [] Skills Blog – Tim Nash again! Analytical blog for the heroic reader. Here he will go deep inside StumbleUpon []
  40. Do You Want To Make Money Online? Says:
    [] Stumbleupon mathematics for stumblers []
  41. Speedlinking – 24 Sep 2007 » Derek Semmler dot com Says:
    [] Continuing the theme of social media, Tim Nash put together a detailed look at the StumbleUpon mathematics for stumblers. This is a great look at Tims understanding of how the SU algorithm works and how that may []
  42. 7 Ways to Use StumbleUpon as a Discovery Tool | Dipping into the BlogpondSays:
    [] Nash has written a very thorough explanation of how the StumbleUpon algorithm might work, which is a great read for anyone interested in how StumbleUpon weights stumbles. In the []
  43. Funny thing happened on the way to 3,000 Stumbles | danawallert.comSays:
    [] Ive found out firsthand is that StumbleUpons algorithm really does work. Im no algorithm expert (see Tim Nash). I trudged along in high school to make it through AP Calculus and Physics classes specifically to []
  44. Links Roundup – September 25th 2007 | Blogging Tips Says:
    [] Stumbleupon mathematics for stumblers – Tim Nash looks at some algorithms which stumbleupon might use. []
  45. turbofool Says:
    Wow, Tom, this is amazing. I was beginning to wonder whether there really WAS an algorithm in place. The depth of this is pretty darn cool, and Im more impressed with StumbleUpon than ever. Also makes me think differently about how Im going to use the service in the future for the greatest effect.
  46. jana Says:
    I found your article facinating. But it doesnt seem to me as if my thumbs up has any more pull or juice than someone who just started stumbling. (Im a top 25 stumbler). Perhaps it does and I just am not seeing it. But thanks for the article, I am always interested in these kinds of things.
  47. SearchCap: The Day In Search, September 21, 2007 · Seo Alchemist Says:
    [] Stumbleupon mathematics for stumblers, The Venture Skills Blog []
  48. chessnoid Says:
    This was an excellent post. You could teach a semester of this at the university.
  49. sn0wflake Says:
    Is there any point giving a page a thumbs down rating?
  50. Tim Nash Says:
    @jana you are ;) particularly if you are the initial stumbler@Chessnoid this will make up about an hour of a class, however two dissertation papers from students will use some of their work from this project.@snowflake each time you thumb down you pass a percentage of your weight against the thumbs up, its not as greater percentage as a thumbs up but is cumulative so it doesnt take to many thumbs down to stop a stumble.
  51. This Week In SEO – 9/28/07 – TheVanBlog Says:
    [] Stumbleupon mathematics for stumblers []
  52. Boost Your StumbleUpon Traffic with Outbound Links | Caroline Middlebrook :: Livin’ Online Says:
    [] but that wont be as effective. Much has been written about the possible ways on which the StumbleUpon traffic algorithm []
  53. Jake Says:
    Great post on Stumble and how it works. I have had great results but never looked into the make-up of it.
  54. Martin Says:
    Great article! Stumbleupon was purchased by Ebay and I feel Ebay could make good use of it as a suggestion tool for those that might want to opt in to it. In my opinion too much of the web revolves around search. Show me what I might want to see based on who I am , what I like. QVC and Home Shopping suggest items that you might like based on themes (jewelry, coins etc) and you never search for a thing. I Truly think a smart model along these lines will be part of the next generation of the web.Marty
  55. Tim Nash Says:
    Martin you might be right some one sent me some details of what they thought were uses of the stumbling algorithm appearing on Ebay, it would be interesting to see if they can harness the suggestion system on an auction well interesting as long as they dont use the SU community as the test group in this idea
  56. 34 StumbleUpon Posts That Aren’t Crap – DanaWallert.com Says:
    [] StumbleUpon Mathematics for Stumblers []
  57. Happy Birthday to us! « The Venture Skills Blog Says:
    [] Posts Stumbleupon mathematics for stumblersTop 5 CSS layout tipsWant to create a site like Digg with no programming?CCK & Views the []

 

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