User:Tim Ocean

Hi. I've been a wikipedist for many years. I'm a moderator of two Wikipedias. One of them is a little Wikipedia and this makes me naturally interested in such cross-wiki comparison.

Currently Wikis are mainly assessed by the depth defined as

depth:={\frac {edis}{articles}}\cdot {\frac {non{\underline {}}articles}{articles}}\cdot {\frac {non{\underline {}}articles}{pages}}.

This metrics poses a lot of problems:

It doesn't make much sense and lacks interpretation.
It produces weird results like English Wiki being tens or even hundreds times "better" than other big wikis, including those in large languages like French and German.
It experiences inflation for little wikis.
It's easy to manipulate by either number of edits or number of special pages of both and it's apparent that some wikis do exactly this.
This metrics makes large and little wikis actually incomparabe.

Second and third term in this equation do exactly the same thing - measure contribution of special pages (discuss pages, user pages, categories etc.). Their multiplication introduces a large dependence on the number of special pages and causes giant inflation for little wikis.

I experimented with various metrics and found that the easiest and best is

depth^{*}:={\frac {words}{articles}}\cdot {\frac {non{\underline {}}articles}{pages}}.

So third term is the same, second is removed, and first one is altered.

${\frac {non{\underline {}}articles}{pages}}={\frac {non{\underline {}}articles}{non{\underline {}}articles+articles}}$ is a function of the ${\frac {x}{x+1}}$ type. It grows slower and slower and has an asymptote at 1.

I tested this metrics on various Wikis (biggest Wikis, Wikis in conlangs + some interesting ones) and here are the results:

Wikipedia	Articles	Words	Pages	Words/Articles	Depth	Depth*
English	7085151	5029491210	64391921	709.86	1336	1336
Cebuano	6115898	1326291436	11230117	216.86	2	209
German	3065898	1691653886	8411434	551.76	93	742
French	2718357	1835692395	13711543	675.29	274	1145
Swedish	2619342	489510386	6339381	186.88	18	232
Dutch	2201228	545554446	4737644	247.84	19	281
Spanish	2071945	1314624852	8522690	634.49	193	1016
Russian	2069963	1158572748	8412457	559.71	166	892
Italian	1942793	1061416495	8440484	546.34	195	889
Polish	1673719	540889052	3948992	323.17	36	394
Ukrainian	1396184	551840693	5004148	395.25	61	603
Vietnamese	1296630	360188264	14609301	277.79	536	535
Portuguese	1159159	623934501	5998524	538.26	206	918
Catalan	783388	407411496	1965859	520.06	42	662
Finnish	606606	180505998	1559044	297.57	37	384
Czech	579646	282045339	1616471	486.58	50	660
Hungarian	562443	243447405	1599186	432.84	60	593
Serbo-Croatian	461167	121817798	4626946	264.15	749	503
Esperanto	377333	92540340	846921	245.25	16	288
Lithuanian	223935	50390882	558880	225.02	30	285
Latin	140669	21762451	290730	154.71	15	169
Ido	59986	7872035	84997	131.23	2	82
VolapĂĽk	45855	3295145	163486	71.86	133	109
Scots	34282	7730427	138167	225.50	59	359
Interlingua	30146	3329674	45762	110.45	4	80
Kotava	29896	2748601	36342	91.94	0	34
Interlingue	13358	4024721	17638	301.30	0	155
Sardinian	7728	2366856	17522	306.27	17	362
Kashubian	5495	443007	8892	80.62	8	65
Lingua Franca Nova	4490	1603991	7185	357.24	2	283
Pennsylvania German	2039	154774	6042	75.91	68	106
Novial	1877	155531	4812	82.86	91	107
Tetum	1380	269417	3952	195.23	61	269
Lojban	1348	464157	5816	344.33	214	559
Gothic	976	99310	3946	101.75	113	162
Dinka	338	90704	1126	268.36	43	397
Cree	14	2272	2342	162.29	483867	341

My findings/remarks are as follows:

I scaled the results so that English is the same to make it easier to compare.
This metrics doesn't produce such weird results like the previous ones.
It's inflation free (look at Cree).
It cannot be manipulated by number of edits because doesn't use them.
It's very hard to manipulate by the number of special pages (look at Serbo-Croatian and Vietnamese).
Cheating with the number of special pages has a natural limit which is words/articles.
This metrics makes it possible to compare all wikis - large and little.
Maybe it can be manipulated by altered script to count words - admins need to say.
This metrics is easy in form and has clear interpretation: length and/or quality of articles times contribution of community and/or quality or articles.

I proposed this metrics in the talk of the depth: https://meta.wikimedia.org/wiki/Talk:Wikipedia_article_depth#Depth%20metrics%20makes%20little%20sense%20-%20part%202.

UPDATE:

I made this graph for my statistics where I plotted the depth* statistics against number of articles and it seems that the metrics not only doesn't experience inflation for little wikipedias, but also it has this statistics generally lower for them as we would expect from little wikipedias where is few editors to develop the wiki.

Seems there is some logarithmic dependence. Perhaps it also allows to discern wikis that manipulated their number of articles. But I'd like to make additional analysis with all wikis.