In the last five completed seasons, they have been 9th, 8th, 8th, 10th and 7th. They have already won more matches during the current campaign and accumulated more points than in any previous season - and they still have six matches to play.
Head coach Pat Lam has turned them into the 'Leicester City' of the GUINNESS PRO12. A fourth straight win, 30-22 over the Ospreys in Galway last Saturday, put them five points clear of the field until Leinster reined them in by taking ten points out of ten in a fortnight at the expense of Zebre.
Three more wins ought to see Connacht safely into the play-offs, in fourth place at the very least. Given that his players have been setting the pace from the opening round at the start of last September, Lam has every reason to aim for a top-two finish and the priceless advantage of a play-off on home soil in Galway.
Since the introduction of the play-offs in 2010, only one team has got there losing more than seven matches. Ospreys, then defending champions after beating Leinster in the inaugural Grand Final, lost nine of their 22 fixtures five seasons ago and somehow still finished fourth - a luxury that has not been afforded anyone else although Munster did contrive to lose nine games twelve months earlier, before the Italian clubs signed up.
Munster (2012), Scarlets (2013) and Ulster (2014) are the only instances of teams losing seven matches and making the play-offs. Two of those currently in the top half of the table, Ulster and Edinburgh, have already lost seven.
While they appear to have precious little margin for further error, the same can be said of Munster - six defeats out of 15. The Warriors are in much the same boat, six defeats out of 14 which gives them two games in hand on most of their rivals. The first is on March 18 at home to Leinster, the second three weeks later against Zebre in Italy.
Leinster are in the strongest position. Apart from having lost fewer games than the rest, they alone among the play-off contenders have a majority of home games still to come. Four of their remaining seven are at the RDS Arena.
Just by way of a change, Round 17 at the weekend features only one collision between teams in the top six - at BT Murrayfield on Friday night when Edinburgh will provide another acid test of Connacht's durability.
As befitting their lofty status, the leaders go to Edinburgh armed with a record of having scored more tries than anyone else in the competition. Their total of 45 - an average only fractionally short of three per game - is eight more than the next highest, Leinster and Ulster.
No individual player has been trading in bigger numbers over the last three weeks than Connacht's Matt Healy. A hot streak of five in three matches has taken his GUINNESS PRO12 tally for the season to nine, within striking distance of Rhys Webb's twelve last year.
While the Wales scrum half claimed his first of a fractured season during the Ospreys' defeat in Galway, his region's next-door neighbours are still on course to fly the Welsh flag in the play-offs.
The Scarlets stay in touch despite the damage inflicted by Sunday's nerve-wracking finish at BT Murrayfield. Even after Ben Toolis' late try had given Edinburgh the narrowest of leads, Aled Thomas suffered the anguish of missing the eleventh-hour penalty that would surely have eliminated the Scots as credible challengers to make the GUINNESS PRO12 Final on home ground in their capital.
Alan Solomons' team had already been kicked to a last-minute defeat in Llanelli a fortnight earlier. The aggregate score over the two contests worked out at 45-45 - another indication of just how competitive the GUINNESS PRO12 has become.
When Connacht finished bottom not that long ago, guess who only just managed to clamber over them despite losing one match more? The Scarlets. And they will aim to take another step upwards at home to Benetton Treviso on Friday.
They will be wary of Jayden Hayward. Treviso's full-back has scored in all but one of his team's 16 matches hitherto this season, a level of consistency matched by the Blues' Rhys Patchell with points in 14 of his club's 15 matches.
His late try in Cardiff last Sunday, followed by an even later one from Aled Summerhill, sent Ulster home with nothing to show from a game that was theirs for the taking going into the final ten minutes.
It followed their failure to cope with the Scarlets in Belfast the previous week, a double Welsh jolt that makes it imperative Ulster resume normal service at home to Zebre on Friday.
Leinster and Munster are home on Saturday to Welsh opponents in the Ospreys and Dragons respectively, leaving the Warriors to complete another intriguing weekend against the Blues at Scotstoun on Sunday afternoon.
Guinness PRO12 top four finishes:
Last season: P W D L Pts
1 Warriors 22 16 1 5 75
2 Munster 22 15 2 5 75
3 Ospreys 22 16 1 5 74
4 Ulster 22 14 2 6 69
Season 2013-14:
1 Leinster 22 17 1 4 82
2 Warriors 22 18 0 4 79
3 Munster 22 16 0 6 74
4 Ulster 22 15 0 7 70
Season 2012-13:
1 Ulster 22 17 1 4 81
2 Leinster 22 17 0 5 78
3 Warriors 22 16 0 6 76
4 Scarlets 22 15 0 7 66
Season 2011-12:
1 Leinster 22 18 1 3 81
2 Ospreys 22 16 1 5 71
3 Munster 22 14 1 7 67
4 Warriors 22 13 4 5 65
Season 2010-11:
1 Munster 22 19 0 3 83
2 Leinster 22 15 1 6 70
3 Ulster 22 15 1 6 67
4 Ospreys 22 12 1 9 63
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