In this newsletter, you will find a detailed discussion of the various viewpoints regarding what is prohibited during the Sefira. The discussion focuses on the activities that you mentioned, namely, shaving, haircuts, and listening to music. Every opinion that I have seen including Shulchan Aruch prohibits weddings (except for an "emergency such as if a shidduch were to be cancelled b/c of a long engagement.)
I've seen no opinion nor have I heard of anyone that prohibits sports games, either individually or as a team.
One common denominator to deciding what is prohibited was established by Rav Soloveichik who said:
that the aveilut customs observed during the period of the Omer, as
well as those observed during Bein Ha-Metzarim, must conform to some
prior halakhic pattern. He notes that in the laws of aveilut, we
generally speak of three periods of mourning: shiva (the seven day
period after the burial), sheloshim (the thirty days after burial),
and the yud-bet chodesh (the twelve month period after the death of a
parent). R. Soloveitchik maintained that the mourning practices of
Sefirat Ha-Omer conform to the halakhic category of “yud-bet chodesh,”
the twelve month period of mourning for one’s parent. Indeed, the laws
that characterize the yud-bet chodesh include the prohibition of
attending a “beit ha-mishteh” (Mo’ed Katan 22b; Shulchan Arukh, Yoreh
De’ah 391) and taking a haircut (Mo’ed Katan 22b, Shulchan Arukh,
Yoreh Deah 390:4; Rama), similar to the original two laws mentioned by
Emanating from this principle, the article states, further:
If so, then the Geonim fundamentally only prohibited social
gatherings, known as simchat meri’ut. Therefore, while a concert
might be prohibited, privately listening to music, or even attending a
movie, certainly is not. Furthermore, social gatherings, even without
music, such as a baseball game, may also be prohibited, against the
view of the Magen Avraham.
Note that the last part about ball games and concerts is disputed, as well.
The point is, that attending public ball games, MAY cause a type of prohibited joy. I'm assuming this may be because the nature of being at such an event with a large public crowd cheering a team may cause this "joy problem".