I've seen some complaints about the short length of the championship match. Like, if it were longer, Anand would still have the chance to catch up. Yes, there were instances of recovering from -3 disadvantage (Steinitz, Euwe and Smyslov pulled those off against Zukertort, Alekhine and Botvinnik respectively, though Smyslov didn't win). But still, let's study the outcome of World Championship matches' first ten games and compare them with the final results.
The first name in the pairing and the first number in the score (except 1886) is the champion.
3-7:
1894, Steinitz - Lasker. Lasker won 12-7.
3.5-6.5:
1937, Euwe - Alekhine. Alekhine won 15.5-9.5.
1958, Smyslov - Botvinnik. Botvinnik won 12.5-10.5.
1961, Tal - Botvinnik. Botvinnik won 13-8.
1972, Spassky - Fischer. Fischer won 12.5-8.5.
4-6:
1892, Steinitz - Chigorin. Steinitz drew 10-10 and then won the tie-breaks 2.5-0.5.
1921, Lasker - Capablanca. Lasker forfeited the match when Capablanca led 9-5.
4.5-5.5
1957, Botvinnik - Smyslov. Smyslov won 12.5-9.5.
1960, Botvinnik - Tal. Tal won 12.5-8.5.
1963, Botvinnik - Petrosian. Petrosian won 12.5-9.5.
1969, Petrosian - Spassky. Spassky won 12.5-10.5.
5-5
1886, Steinitz - Zukertort. Steinitz won 12.5-7.5.
1910, Lasker - Schlechter. That was the final result of a 10-game match.
1954, Botvinnik - Smyslov. The match was drawn 12-12.
1987, Kasparov - Karpov. The match was drawn 12-12.
1990, Kasparov - Karpov. Kasparov won 12.5-11.5.
1995, Kasparov - Anand. Kasparov won 10.5-7.5.
5.5-4.5
1927, Capablanca - Alekhine. Alekhine won 18.5-15.5.
1951, Botvinnik - Bronstein. The match was drawn 12-12.
1978, Karpov - Korchnoi. Karpov won 16.5-15.5.
1985, Karpov - Kasparov. Kasparov won 13-11.
1986, Kasparov - Karpov. Kasparov won 12.5-11.5.
6-4
1889, Steinitz - Chigorin. Steinitz won 10.5-6.5.
1891, Steinitz - Gunsberg. Steinitz won 10.5-8.5.
1934, Alekhine - Bogoljubov. Alekhine won 15.5-10.5.
1935, Alekhine - Euwe. Euwe won 15.5-14.5.
1966, Petrosian - Spassky. Petrosian won 12.5-11.5.
1993, Karpov - Timman. Karpov won 12.5-8.5.
6.5-3.5
1908, Lasker - Tarrasch. Lasker won 10.5-5.5.
1929, Alekhine - Bogoljubov. Alekhine won 15.5-9.5.
1996, Karpov - Kamsky. Karpov won 10.5-7.5.
7-3
1907, Lasker - Marshall. Lasker won 11.5-3.5.
1984, Karpov - Kasparov. The match was stopped with score 25-23.
7.5-2.5
1981, Karpov - Korchnoi. Karpov won 11-7.
1993, Kasparov - Short. Kasparov won 12.5-7.5.
8-2
1897, Lasker - Steinitz. Lasker won 12.5-4.5.
8.5-1.5
1910, Lasker - Janowski. Lasker won 9.5-1.5.
After 1996, the matches took on the present short format where 10 games constituted more than half of the match.
There were only seven instances when the result of the first 10 games wasn't indicative of the match's final result. Of those seven, three were draws, three more involved the challenger overcoming -1 (Alekhine 1927, Kasparov 1985) or -2 (Euwe 1935) odds, and in the last example, Steinitz overturned a -2 score to defeat Chigorin in 1892.
No match where one player lead 6.5-3.5 or more against the other ever ended with a draw or defeat of the first player. With this in mind, we can only reach one conclusion - should the match be longer, Carlsen would have still won. So, basically, the only thing that could have changed - in a longer match, we would have possibly seen more exciting and interesting games from those two players. This is indeed sad for the chess world, but it still wouldn't have changed the name of the new champion.
Congratulations to Magnus, and let's hope that he pulls "a Karpov" or "a Kasparov" (continues actively playing and winning tournaments) rather than "a Fischer" (everybody knows what that was).