The Crowd Support:
In a cricket fanatic country like INDIA, you generally have tens of thousands of people watching a cricket match in the stadium. In such a case you have people behind you chanting your name and your country's name cheering on every success of yours.
Goosebumps right! . Generally this will get the best of an individual. Seeing many people believing in you to do well for your team will lift your confidence.
This might also dent the confidence of the visiting team.
Generally the pitches will be designed in such a way that the home team has an edge over the visiting team. This is something like testing the other person in the field you are good at. There will be an advantage for the home team in this case as the opposition has to play to the strengths of the home team.
If the home team is any of the sub continent team then you cannot expect a green wicket that helps the fast bowlers. They will generally be spin friendly. Similarly ,In Australia, SA the pitches will be seam friendly. If you are habituated to something you will generally be good at it.
This might not be a big factor like the above ones but it does play its part. Suppose a player from the north of England comes to play match in chennai the max temprature in north of england is less than the min temprature in chennai . This will take a toll on the fitness of the player. And with the new rules, a batsman is not allowed a runner so , if he is so drained that he can't run, he has no option other than retireing hurt and comming back at a later point of time. By then the situation of the match might change and he litreally has to start from scratch again.