WHEN it comes to predicting results in this season’s Premier League, Leicester City’s 3-1 win over Liverpool on Monday night was one of the easier matches to call.

Whatever you feel about the relative rights and wrongs of sacking the reigning FIFA World Coach of the Year less than a year after he was part of one of the greatest footballing fairy-tales ever told, something was clearly wrong with Claudio Ranieri’s Leicester. There was always going to be a response to his dismissal, and sure enough, it arrived in the form of a resounding home win that lifted the Foxes out of the bottom three.

Will the recovery be a sustained one? Time will tell. But with the end of the season now just 12 games away, it is not going to take much for Leicester’s controversial decision to sack Ranieri to be justified in terms of points on the board. Another couple of wins – potentially starting with tomorrow’s home game against Hull City - and Leicester could be as good as safe.

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Statistically, a team tends to improve in the immediate aftermath of a change of manager. A recent study concluded that while Premier League teams tend to average 0.9 points a game in the six matches leading up to a managerial dismissal, they gather an average of 1.3 points a game in the six games afterwards.

The ‘new manager bounce’ doesn’t last long, and within a month or so, teams are likely to have regressed to the standards they were setting before there was a change at the top. But if the timing is right, a short-term boost might be all that is required to turn a season around.

All of which leads us to Sunderland and Middlesbrough, and their current predicaments in the bottom four positions in the table. Leaving aside Bournemouth, who have tumbled into the relegation picture from pretty much nowhere in the last few weeks, of all the sides involved in the battle against the drop have changed their manager at some point this season. In all cases, the switch appears to have been beneficial.

Admittedly, with Leicester, we’re only talking about one game, but Paul Clement’s appointment undoubtedly improved Swansea’s performances, and while Sam Allardyce has taken a fair amount of time to get things going at Crystal Palace, last weekend’s win over Middlesbrough reinforced the impression that the relegation specialist will eventually lead the Eagles out of the mire. Hull remain in 19th position under Marco Silva, but surely have more chance of avoiding the drop under the Portuguese than they would have had under Mike Phelan, who was sacked at the start of January.

Would Sunderland and Boro benefit from jettisoning David Moyes and Aitor Karanka? Neither has come under too much pressure so far this season, and with games running out, it is getting to the stage where it will soon be too late for a change at the top to make any significant difference. But with a place in the Premier League worth a conservative estimate of at least £100m, Ellis Short and Steve Gibson would not be doing their jobs if they were not at least weighing up the relative merits of pulling the trigger.

In Sunderland’s case, Moyes’ position is strengthened by the lack of investment in each of the last two transfer windows. The Black Cats boss has spent all bar two weeks of August in the bottom three, but given the playing resources at his disposal, does anyone really think Sunderland should be doing significantly better? The squad lacks quality throughout, and depth in a number of key areas.

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It is possible to quibble with some of Moyes’ tactics, and his failure to adequately organise his side’s defence, which continues to look like an accident waiting to happen. A number of supporters are infuriated by what they perceive to be the Scotsman’s unnecessary pessimism, particularly when it comes to discussing Sunderland’s position in the Premier League’s natural order, and given the lack of funds at his disposal, it is possible to argue he squandered money last summer on some unsuccessful buys.

On the whole though, it is hard to dispute the notion that Moyes is hamstrung by the conditions he is operating under, and having chopped and changed managers constantly for the last four or five seasons, Sunderland chief executive Martin Bain is right to preach about the merits of stability.

Financially, Sunderland cannot afford another major bout of change, and if they are to find themselves in the Championship next season, Moyes looks the ideal person to lead the rebuilding project. As a result, Short is probably right to stick with him.

Things are slightly less clear cut at Middlesbrough, as there is a nagging sense that the Teessiders could be a fair bit better than their recent results if only tactics and personnel were changed.

Is Karanka getting the best from what is at his disposal? Perhaps, but while Boro remain hard to break down, they will be relegated unless they find a way of addressing their attacking shortcomings. More of the same will not suffice, but on all available evidence it is likely to be what Karanka continues to serve up.

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Might a change to a more flexible and attack-minded head coach change that? Gibson’s avowed loyalty to his managers means we will almost certainly not find out, and in this case, there are unique circumstances that mean it would be all-but-impossible to remove Karanka so late in a campaign.

Rightly or wrongly, Gibson has allowed the whole of his club to be built around Karanka. The Spaniard presides over a coaching team comprised largely of his own compatriots and confidantes, and if he was to go, they would all have to go with him.

The scouting and recruitment operation has been remodelled to accommodate Karanka’s wishes, with the appointment of technical director Victor Orta having occurred largely on the recommendation of the head coach. Take one cog out of the machine, and the whole thing has to be rebuilt. That might be an option in the summer, particularly if Boro go down, but it makes little sense now when survival could create an opportunity for stable rebuilding, which would understandably be Gibson’s preferred option.

With just over two months of the season to go, a managerial change on either Wearside or Teesside is therefore unlikely. That will please those who feel clubs are too quick to fire their bosses, but would deprive both Sunderland and Middlesbrough of the kind of short-term boost that their rivals have experienced. In the final reckoning, might that be crucial?