Why the Way There Is Never the Way Back: Wikipedia's One-Way Links

On Spanish Wikipedia, WikiRacing players have raced from Antigua Roma (Ancient Rome) to Vegetta777, one of Spain's best-known YouTubers, ten times on seven different days. The median race took 23.5 clicks and almost nine minutes. The best of the ten needed 8.

Now turn it around. I took six big Spanish YouTubers (Vegetta777, El Rubius, Willyrex, AuronPlay, TheGrefg, Ibai Llanos) and pulled every finished race that touched them. When one of them was the start, across 119 races, the median was 5 clicks and about two minutes. When one of them was the target, across 126 races, it was 14 clicks and more than seven minutes.

Same six articles, same encyclopedia, nearly three times the clicks depending only on which end they sit at. My first reaction was a grouping error, so I pulled up the individual paths. No error. It's how links work, and once you see it, a whole family of "why is this race so hard?" moments explains itself.

A link is a one-way street

When one article links to another, it doesn't build a road between them. It builds a one-way street. The Vegetta777 article on Spanish Wikipedia links to España and to YouTube. Neither of those links back to Vegetta777, and nothing forces them to: the Spain article covers history, geography and politics, and has no reason to single out one YouTuber among millions of Spaniards.

Mathematicians call a network like this a directed graph. Every edge carries an arrow. In a race you can only walk with the arrows, so the distance from A to B and the distance from B to A are two separate numbers. Nothing says they have to be close.

Counting the doors

Here is what those articles look like from the inside, counted with Wikipedia's own API on the Spanish edition, articles only:

• Vegetta777: 68 links out, 8 links in.
• Antigua Roma: 437 links out. Links in: roughly 8,700 pages, all page types included.
• España: 1,791 links out. Links in: Wikipedia's own link counter reports more than 280,000 pages pointing at it, all page types included.

Leaving Vegetta777 is easy. Two of its 68 exits are España and YouTube, and from either one most of the encyclopedia is a couple of clicks away. Arriving at Vegetta777 is the problem. Eight articles in the whole Spanish encyclopedia point at it: a date (12 de abril), a decade (Años 2010), two pages with similar names (Vegeta, Vegueta), the Karmaland series, a page about the Spanish-language YouTube Rewind, and two fellow YouTubers, El Rubius and Willyrex.

Those are the only doors. If you are not standing in front of one of them, you can't get in.

You can check this without me. Every Wikipedia article has a "What links here" page in its tools menu. For Vegetta777 it is this very short list. Try the same thing on a country and you'll be scrolling for a long time.

What the ten races actually did

All ten Antigua Roma to Vegetta777 races came in through one of just three doors: El Rubius (five times), Willyrex (four) and Rewind hispano (once). Nobody found a fourth. The hard part was reaching that neighborhood at all. Here is the fastest of the ten, 8 clicks, with the article titles exactly as the player saw them:

Antigua Roma → Mar Mediterráneo → España → OTAN → Estados Unidos → YouTube → Twitch → El Rubius → Vegetta777

Five clicks to climb from Rome to YouTube, by way of the Mediterranean, Spain, NATO and the United States. Then Twitch, El Rubius, done. The slower races lost their time in the middle, not at the end. One of the 17-click runs spent about ten clicks circling communication theory (Comunicación, then Canal de comunicación three times in a row, Relación social, Trabajo) before it landed on Teléfono and finally YouTube.

That is the real shape of a race toward a small article. Climb until you reach the big page that sits above its whole world, then walk down through narrower and narrower pages until you hit one of the few doors. The climb is fast. Finding the right way down is where the minutes go.

When the gap disappears

This isn't a law that the reverse is always harder. The gap shrinks, or flips, depending on who has more doors.

France to Paris and Paris to France on French Wikipedia: one click each way, across 109 races. Two giant hubs that link to each other directly. There's nothing to be lopsided about.

German Wikipedia gives a nice middle case. Schokolade (chocolate) to Napoleon Bonaparte took a median of 3.5 clicks in the four races on record. Napoleon to Schokolade took 5.5 across thirty. Neither article links to the other. But roughly 14,700 pages point at Napoleon against about 1,000 for Schokolade, so arriving at Napoleon is the easy half. Three of the four chocolate races went through Frankreich and walked straight in. The other direction means finding the door into chocolate: cocoa, a confectioner, a colonial trade route.

So the useful rule isn't "backwards is harder." It's this: the target decides the difficulty far more than the start does. A start article only needs one decent exit. A target needs you to find one of its entrances, and small articles have very few.

What to do with it in a race

Size up the target before your first click. Ask how many pages would plausibly mention it. A country, a war, a famous scientist: thousands. A YouTuber, a village, a single album: a handful, and they'll be very specific ones (a collaborator, the surrounding district, the band). Those specific pages are your real destination. The target is just the last step.

Climb toward the right world, not the biggest one. The slow races above burned their clicks in communication theory and technology pages while the target lived in internet culture. The fastest one went straight for a country, then the United States, then YouTube. The advice in our strategy guide still stands, go through a hub, but pick the hub that sits above your target rather than the largest one in sight.

Come down through peers. From YouTube, the fastest descent went YouTuber to YouTuber. People on Wikipedia get linked from their peers: musicians from bandmates, villages from their municipality, researchers from their students and advisors. Find the peer group and you have found the doors.

This also explains two things we've written about before. The busiest articles in our count of 205,000 real clicks are countries because they have enormous numbers of exits, so everyone passes through them on the way up. And it is the missing footnote to the small-world explanation: the network is small on average, but only when you walk with the arrows.

A few honest questions

Isn't comparing starts and targets a bit loose? The other end isn't the same article. Fair, and it isn't a lab experiment: the 119 races that started on a YouTuber were heading to all sorts of targets, and the 126 that ended on one came from all sorts of starts. But both samples are big, each spread over more than 40 different days, and single pairs point the same way: El Rubius to Michael Jackson took a median of 4 clicks over five races, Antigua Roma to Vegetta777 took 23.5 over ten. Nobody has raced Vegetta777 to Antigua Roma yet. I'd expect it to be short.

Why doesn't Wikipedia link both ways? Because a link is an editorial decision. The España article is about Spain; linking every notable Spaniard from it, YouTubers included, would make it unreadable. Wikipedia's linking guidelines explicitly ask editors not to overlink, and only to add links that help the reader of that particular article. Lopsided links are the system working as intended.

Does it make some pairs unfair? I don't think so. It makes them a different kind of puzzle, the kind where knowing how Wikipedia is built beats clicking fast. If you want to feel it for yourself, set up a manual race toward a small article you know well, then swap the two ends and play it again.