BY group processing means that you have one or more variables used to define the group. When you say "points in a game" then the likely BY variable would be a TEAM identification. So here is a possible example:
data example;
input team $ score;
datalines;
A 15
B 26
A 3
B 18
C 3
C 6
C 27
;
proc sort data=example;
by team;
run;
proc means data=example mean;
by team;
var score;
run;
Please note the data step as way of documenting the data and providing something that you can run to create a data set that be used.
BY groups also usually require sorting by the group variables before any analysis.