Dravid's line-up is currently third in the list, two rating points behind second-placed England and trailing runaway leaders Australia by 20 points.
And with England poised to gain at least one point if it avoids defeat in the third and final Test of its series against Sri Lanka, also starting later today, it means the pressure is on India to stay within touching distance of its nearest rivals.
A 4-0 series win for Brian Lara's men will lift it to 82 rating points, cutting the gap between the West Indies and seventh-placed Sri Lanka to just 13 points, while even victory by the odd Test will improve its rating by six points.
That would be a disaster for India as it would drop it to fourth in the table, below Pakistan, just a couple of months after it appeared poised to assume second place, something it would have done had it avoided defeat against England in Mumbai.
India goes into the four-match Test series knowing it needs a conclusive win to maintain the pressure on the sides above it in the LG ICC Test Championship table.
That can only be done with a crushing success for the visitors as, with India 39 points ahead of the hosts in the LG ICC Test Championship table, it will need to win all its matches against the West Indies to boost its rating.
However, that will be easier said than done. The home side is on a high after its 4-1 ODI series win and history is also against India as the Asian side has only ever won a single Test series in the Caribbean, way back in 1971.
A 4-0 success for India will lift it to 112 rating points and drop the West Indies to 70, but if the West Indies can turn the LG ICC Test Championship table and the Test formbook upside down then it has the chance to really boost its stock.
The India-West Indies Test series starts with Dravid and Lara going head-to-head as captains and their sides' top batsmen in LG ICC Player Rankings.
So, the stakes are high and, on paper at least, India appears to have the edge before the first ball is bowled.
It has two players -- Dravid (2nd) and Virender Sehwag (12th) -- among the top 20 batsmen in the LG ICC Player Rankings while the West Indies has just one -- Lara (6th). He will have a special reason to start the series in style as the action begins at the venue of his two world-record innings of 375 and 400 not out, against England in 1994 and 2004 respectively.