R. Asher Meir, in his Jewish Ethicist column (link), writes:
Q. Many popular sports are quite violent and aggressive. What does Judaism say about this?
A. While traditional Jewish sources have certain reservations regarding public sporting events, fundamentally we view healthy bodily activity and friendly competition as constructive. Many noted religious figures are and have been gifted athletes or avid sports fans.
At the same time, Jewish tradition has the utmost disdain for violence and the violent urges. This is in contrast to the attitudes towards other basic urges. Human beings have a natural urge for material comforts, for physical intimacy, for status and honor and so on. In all these cases the attitude of Judaism is not to deny but rather to sanctify. The commandments applying to food, such as the kosher laws and the requirement for saying blessings, enables to channel our appetites to the service of holiness; the marital laws do the same for our sexual urges, and so on. As we have written, even anger can in a circumscribed way be used in the service of holiness.
We do not find any similar channeling mechanism regarding violence. While the Jews who left Egypt were commanded to conquer the land of Israel, there is no ideal of ongoing conflict so that we can exercise and channel our violent urges; on the contrary, the Jewish prophets constantly remind us that the natural and desirable state of the world is one of universal peace, where (Isaiah 2:4, New International Version) “They will beat their swords into plowshares and their spears into pruning hooks. Nation will not take up sword against nation, nor will they train for war anymore.”
Continued here: link
See also this post on Jews and jousting, which only suggests that Jews jousted in the twelfth century and not that it was approved by the rabbis: link.