Gus Poyet, celebrating a Jan. 22 League Cup win at Manchester United, has led Sunderland to 12 wins in 23 games. Reuters

Analytics types will tell you that on a macro level total wage bill and total net spending are the main predictors of a team success and that firing managers, particularly during the season, has a scant overall effect. That may be accurate in absolute terms, but there are obviously outliers. And that is why managers keep getting the bullet.

When Sunderland's Gus Poyet took charge of his first game after taking over from interim boss Kevin Ball, who had himself replaced Paolo Di Canio, his club was dead last in the Premier League, with one point from seven games. Sunderland is still technically in the relegation zone—18th in the table—but it is level on points with West Bromwich Albion in 17th and has played one fewer game.

More telling is the "Poyet effect." If the season had begun on October 19, with Poyet's debut at the Sunderland helm, the club would be 10th in the table, despite having played one fewer game than most of its opponents. Include cup competitions and Poyet's Sunderland has won more than half its games (12 of 23), which goes some way toward explaining why they are in the final of the League Cup and—following Saturday's 1-0 victory over Southampton—in the quarterfinals of the FA Cup. Along the way, Poyet's resurgent Sunderland has won some huge games, including victories over both Manchester City and Manchester United, Chelsea in the League Cup and home and away triumphs over local rival Newcastle.

By almost any empirical measure, Poyet's Sunderland shouldn't be doing this well. Last season it avoided relegation with one game left. In the summer, there was plenty of player turnover at the Stadium of Light with 14 new players joining. But four of them were prospects aged 20 or younger, four were loan signings and another three were free agents, so the net amount spent was flat, leaving the club as the second-lowest net spenders in the Premier League. Meanwhile, the wage bill was substantially cut. Squad upheaval, lower wages, less spending…you'd expect the club to struggle.

And that's what happened in the first seven games, a situation that wasn't helped by Di Canio's decision to leave out certain veterans like Phil Bardsley, ostensibly for disciplinary reasons. (At the tail end of last season, a photograph of Bardsley lying face down on a casino floor covered in bank notes was disseminated on social media, infuriating Di Canio.) The media blamed Sunderland's poor start on Di Canio's drill-sergeant ways, but, in fact, it was the same rah-rah approach that helped the team avoid relegation when he was appointed late last season, so it is perhaps a bit too facile to suggest that Poyet is simply more of a player's coach than his predecessor.

The club added five players in the January transfer window, but only leftback Marcos Alonso has thus far seen any significant playing time; the other four have combined for 244 Premier League minutes. So apart from Bardsley and veteran defender Wes Brown, who was injured and returned in November after a layoff of nearly two years, this is largely the same cast of characters who underperformed in the first two months of the season.

The main variable in the resurgence seems to be Poyet. The affable, chatty Uruguayan—he was popular as a TV pundit—arrived with a reputation as a promising manager, albeit one who was untested in the top flight. In his only previous stint as a coach, he took Brighton from the third tier into the second and then into the playoffs for promotion to the Premier League, losing in the semifinals. He won plaudits for his attractive style of play, albeit with a club that spent heavily by lower-division standards.

Sunderland was a different proposition. Owner Ellis Short, after several seasons of spending big, appeared to be cutting back, as evidenced by last summer's shoestring operations. What's more, a relegation scrap often requires a different skill set and mindset than a promotion hunt and Poyet was an unknown quantity in that department.

Yet the outcome is there for all to see. Compared with Di Canio, he has been somewhat more possession-oriented and less direct, but these are minor differences. Beyond the results and the return of Brown and Bardsley, not much has changed on the pitch.

Most surprising of all have been the cup runs. Increasingly, teams in the relegation battle—which, this season, include as many as 11 of the Premier League's 20 teams—have tended to rest players and go at half-throttle in the cup competitions. The idea is that avoiding relegation is far more important and, indeed, the experience of Wigan Athletic—which won the FA Cup last season but was bounced out of the Premier League—seems to illustrate the perils of energy-sapping cup runs. Poyet has actually done the same, often fielding understrength teams in the cups, yet results continue to go his way.

With a whopping 11 teams either in the relegation zone or within a mere four points of it, anything can happen in the bottom half of the Premier League this season. Six of those 11 have already changed managers this season—most recently Fulham, who appointed former Bayern Munich coach Felix Magath on Friday, making him its third boss of this campaign—suggesting that despite what the analytics say, they know that there are enough outliers to make it worthwhile.

Poyet, undoubtedly, is one of those who strongly buck the trend. So is Tony Pulis, who took over Crystal Palace when it was at the bottom of the Premier League and, in the space of 13 games, took it up to 15th place, with the team having also played one fewer match than the teams around it. Pulis's clip of 19 points from 13 matches is the kind of pace that ordinarily sees a club finish comfortably in mid-table and is nearly three times as good as that of his predecessor, Ian Holloway.

As long as there are managers like Pulis and Poyet who can engineer such stunning turnarounds, clubs will continue to show bosses the door in midseason. Besides, in some ways it is a win-win proposition in the old decision matrix. If you're at the bottom, things can't get much worse, whether you make a change or not. If you don't make a change and enjoy a resurgence (and, while it seems unlikely, it is possible that Palace and Sunderland might have stormed back up the table if they had kept their respective incumbents) the plaudits will go to the manager who "turned it around." But if you do bring in a new boss and things work out, then the credit goes squarely to the club for picking the right guy and changing course at the right time.

Corrections & Amplifications
Sunderland avoided relegation from the English Premier League last season after Wigan's loss to Arsenal on May 14. A previous version of this story incorrectly said that Sunderland avoided relegation on the last day of the season.