Robbie Butler, an Economics lecturer at University College Cork, wrote in December 2011 an article on his blog, also featured on The Score section of TheJournal.ie.
Although the title of the article is "FIFA Rankings explained", there are many things wrong. While Robbie gets points for actually looking at the mechanism behind the rankings, he failed to get the formula right.
First of all, Bosnia-Herzegovina didn't overtake the Republic of Ireland in December because they managed a draw against Portugal. The play-off results were already included in the November ranking. Their friendly draw against Poland (10 December 2010) dropped out of the most recent time frame and thus the Bosnians gained 31 points. The Irish don't have any games between 23 November and 21 December in the last four years so their points didn't change.
When trying to explain the calculation of match points, he makes another mistake. The individual match points are divided by the number of matches in the relevant time frame.
Thus, looking only at Georgia: 3 (win) * 2.5 (qualifier) * 1 (UEFA vs. UEFA) * (200 - 77) (Georgia's rank) * 0.2 (oldest time frame) / 8 (games in that time frame) = 23.0625, not 8.55.
Robbie used the August 2008 ranking, but he should have used the September 2008 ranking (published on 3 Sep) - available at the time of the match (6 Sep).
Nigeria: 1 (draw) * 1 (friendly) * 0.925 ( UEFA vs. CAF) * (200 - 30) (Nigeria's rank) * 0.3 / 12 = 3.93125, not 0.4743.
The confederations weightings are updated after each World Cup. More here.
Armenia: 3 * 2.5 * 1 * (200 - 96) * 0.5 / 9 = 43.333, not 3.9.
Russia: 1 * 2.5 * 1 * (200 - 13) * 1 / 14 = 33.3928 not 4.675.
Robbie is right on one account though. Had the Irish won the return leg against Estonia, they would have had 914 points and would have been ahead of Bosnia-Herzegovina.
The detailed totals section of my blog could prove helpful for those trying to understand the rankings.