Finding the trend whether the team is improving or not

#1
Suppose a basketball team scored 44,58,50,61,62 in the previous 5 games, and scored 50 in the next game. How to statistically determine if the team is improving or not, apart from comparing the immediately previous games (i.e 62 and 50).
 
#2
For the 6 games in your sample, you could calculate a Pearson correlation coefficient
between score and number of the game (from game 1 to game 6). This would tell you
whether there was a marked linear trend within your sample of 6. But maybe I did not
understand your question correctely.

With kind regards

Karabiner
 
#3
@Karabiner is correct. However such an approach does not control for differences between competitor teams, percentage of playing time per player, home/away court advantage, etc. So just keep that in mind. You would be able to note an association, but not ascribe that the approach controlled for endogeneity.