But it is not always so. Sometimes good players are crushed by the change, perhaps their mental or physical strength is not up to the new environment, maybe their style is unsuited. Dennis Bergkamp's unhappy spell at Internazionale, where neither tactics nor personnel were in harmony with him, is one of the best examples.
The reverse of the same coin is a good player flourishing among weaker ones precisely because he is the big fish. The responsibility prompts a concentration and consistency which previously proved elusive. The consequence is an upward spiral of growing confidence and success.
Such an example is Henrik Larsson who tomorrow celebrates his 27th birthday by carrying Celtic's hopes into Glasgow's West End for the first Old Firm derby of the season. With Rangers already edging clear in the Scottish Premiership the defending champions will be relying on a good performance from their Swedish striker.
To date Larsson has not reproduced his best in the frenetic derby atmosphere but, with his game continuing to blossom despite the club's internal troubles and lack of investment in new players, there is a measure of optimism among the Bhoys. Already this year he has shown his big-game temperament in Zagreb, where he was one of the few Celtic players to emerge with credit from their Champions' League qualifier; in Portugal in midweek where he scored Celtic's opener in the Uefa Cup tie against Vitoria Guimaraes, his fourth goal of the season; and in Stockholm where he gave England - and Ince in particular - the run-around in Sweden's European Championship win.
This match was especially significant for Larsson as he cemented his return to the national team having been out of favour under the previous manager, Tommy Svensson.
Lars Lagerback, assistant to the new coach, Tommy Soderberg, said of Larsson: "He has improved a lot. Since playing for Celtic his confidence has increased and that is an important thing."
Within Sweden the belief is that this is because the Scottish League lacks strength in depth, allowing Larsson to dominate more often than he did when emerging with Helsingborg in Sweden, or after moving to Feyenoord in the Netherlands. Quite possibly, but since neither the Swedish nor Dutch leagues are noted for their strength the way Larsson has taken to life in Scotland must also be factor.
"I like it in Scotland, it is a lovely country," he said. "There is a lot of attention from fans but it is expressed differently to when I was in Holland and I like it better.
"The home games are stunning: there is a big buzz every time we play there. It is something special and there are not many teams have a 60,000 crowd every game, even teams like Milan only get 30,000 for the smaller Serie A teams."
The Netherlands, said Larsson, were "polluted" in comparison to Scotland. A private man, he lives quietly in Bothwell, one of the footballers' "ghettos" south east of Glasgow, with his Swedish wife Magdalena and one-year-old son Jordan (named after the basketball player Michael).
Apart from an incident with Tosh McKinlay last November, which ended with the defender giving him a "Glasgow kiss", he has been free of controversy, a blissful release to Celtic after their problems with Pierre van Hooijdonk, Jorge Cadete and Paolo Di Canio.
Larsson would not even discuss the contract dispute, save to nod in response to the suggestion he must be pleased it was over.
Larsson was first attracted to Celtic by the presence of Wim Jansen, his former coach at Feyenoord. The relatively small fee, pounds 650,000, was dictated by a clause in his contract and though he had to go to a tribunal to gain his release from the Dutch club, he still arrived without fanfare.
Terry Butcher, the former England and Rangers defender, now a media observer of the Scottish game, said: "There was little expectation. People had heard of him but were not too sure how good he was and reserved judgement until they saw him in the flesh."
As the mass of shirts at Celtic Park bearing Larsson's name suggests, judgement was favourable.
"Though Celtic did not start well he did," Butcher added. "Celtic then went on a good run and his form was a major part of helping Celtic win the championship. When he plays Celtic play. If you can pinpoint a way to stop Celtic from playing it is to stop Larsson getting on the ball."
While Scottish domestic football does not have the best of reputations Lagerback thought it had improved significantly over the past 10 years and added that Celtic's passing game made it easier for Larsson to fit in.
"It is true that not every team in Scotland play like Celtic," Larsson said. "Maybe that is why we get the results we get, because we pass the ball more. But it is not true to say the league is easy. Whenever we play the so-called smaller teams there is a packed defence and they don't want to attack that much. It is always hard to break through."
Celtic having lost Van Hooijdonk, Cadete and Di Canio in quick succession, Larsson had to be both scorer and provider when he arrived. He began with a rush of goals, eight in his first nine League games, and had a dozen before Christmas.
The goals then came more slowly as he reverted to a more creative role but the 19th, and possibly most vital, eased the final-day nerves against St Johnstone as Celtic denied Rangers to clinch their first title in a decade.
"Without him I don't think they would have won the title," Butcher said. "The way he plays his football is so positive. He is a very good user of the ball, he can provide a pass, has good control, floats behind the main striker in that Peter Beardsley role.
"If you have somebody that can hold the ball up, turn and go at people and score good goals you always have a chance."Reuse content