The monks, nuns, as well as other members of the clerus, often compiled their work partially from older sources available to them. They borrowed from these older sources to include preceding histories relevant to their own work. Also, in the case of many annals and chronicles, as well as necrologies (obituaries), they were continued by a new author on the death of his predecessor.

The relation between sources of different authors and different periods is often complicated but is nonetheless important to deduce in order to establish a source's credibility. Although I am unfamiliar with the primary sources concerning the reign of Alfred the Great, I can showcase the intricacies of how sources can be connected through another example.

In 1018 a punitive expedition led by the Duke of Lower Lorraine met its end at the hands of a numerically smaller force commanded by the Count of West-Frisia. Due to the unlikely outcome as well as the death of a number of nobles and bishops, the events found their way into numerous sources: 65 to be exact (that we know of); 37 narratives, such as annals and chronicles; 8 necrologies; 15 diplomatic sources, mainly charters; 5 others, a couple letters as well as a 17th century forgery.

In the context of your question, the narrative sources are the most interesting, as academics have established the relation between these sources through comparative analysis; there were some striking similarities. The 37 narrative sources that allude to the Battle of Vlaardingen are listed below, ordered roughly on the year they were written. The number in the first column will be used later to illustrate how the sources are connected.

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#	TITLE	AUTHOR	YEAR
1	Thietmarus chronicon	Thietmar of Merseburg	1018
2	De diversitate temporum	Alpertus of Metz	1021-1024
3	Miraculae S. Waldburgae Tielensia	Alpertus of Metz	1022-1023
4	Gesta episcoporum Cameracensium	Unknown	1024-1025
5	Annales Queldinburgenses	Unknown	~1025
6	Codex Augiensis	Herman of Reichenau	1048-1054
7	Annales Sancti Maximini	Unknown	Mid 11th century
8	Gesta ep. Tungrensium, Trajectensium, et Leodensium	Anselmus	1052-1056
9	Annales Leodienses	Unknown	1058-1086
10	Brunwilarensis Monasterii Fundatorum Actus	Unknown	Shorty after 1063
11	Bertholdi Annales	Berthold of Reichenau	1066-1080
12	Annales Altahenses Maiores	Unknown	1073-1075
13	Bernoldi Chronicon	Bernold of Konstanz	1075-1100
14	Lamberti Hersfeldensis Annales	Lamberti of Herfeld	~1078
15	Iocundi Translatio S. Servatii	Jocundus	1088
16	Sigeberti Gemblacensis chronica	Sigebert of Gembloers	1088-1111
17	Chronicon sancti Huberti Andaginensis	Lambertus Parvus	1098-1106
18	Annales Laubienses	Unknown	After 1098-16th century
19	Ruperti Chronicon sancti Laurentii Leodiensis	Rupert of Deutz	~1100
20	Annales Egmundenses	Unknown	1112-1121
21	Liber Sancti Adalberti	Unknown	1125-1133
22	Annales Parchenses	Unknown	1140-1148
23	Gesta episcoporum Virdunensium	Laurentius of Liege	1144
24	Annales Remenses et Colonienses	Unknown	~1150
25	Vita Wolbodonis Episcopi Leodiensis	Reinerus	1161-1182
26	Annales Sancti Iacoba Leodiensis	Lambertus Parvus	1173-1194
27	Vita Balderici episcopi Leodiensis	Unknown	Late 12th century
28	Annales Elmarenses	Unknown	12th century
29	Annales Yburgenses	Unknown	12th century
30	Balduini Ninovensis Chronicon	Boudewijn of Ninove	Mid 13th century
31	Chronicon Egmundanum	Unknown	1269-1272
32	Rijmkroniek van Holland	Unknown	1280-1282
33	Chronographia Johannis de Beke	Johannis de Beke	~1346
34	Bella campestria inter episcopos Trajectenses et comites Hollandie	Unknown	~1348
35	Annales Tielenses	Unknown	14th-15th century
36	Chronicon Tielense	Unknown	~1450
37	Annala Uladh	Ruaidhri Ó Luinín	Late 15th century

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Medieval historians didn’t always write ‘centuries’ after events happened. There were chroniclers who kept records of current events; history as we think of it today was what was received either orally (and usually only spanned one or two generations) or what was given via written texts, but only a select few of the medieval population would have had either the access or ability to read those texts. It might help to refocus your question: why did medieval historians record what they did? By looking at what they noted and recorded, you can get a glimpse into what was important to them. A major part of a historian’s skill set is the ability to get their head into the heads of other people, rather than the other way around.