See on how SQLDataAdapter is used with command as parameter:
MSDN: SqlDataAdapter Constructor (SqlCommand)[
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Internally, it's the Select command that is initialized for it.
Try to use it like this as it will be simple to read and understand:
con = new SqlConnection(connection);
SqlCommand command = new SqlCommand("[dbo].[StoredProc1]", con);
command = new SqlCommand(qry, con);
SqlParameter("@player_id",DropDownList1.SelectedValue));
command.Parameters.Add("@player_id", SqlDbType.NVarChar).Value = DropDownList1.SelectedValue;
command.CommandType = CommandType.StoredProcedure;
SqlDataAdapter da = new SqlDataAdapter();
da.SelectCommand = command;
da.Fill(ds);
Further, you need to bind the list with a datatable and not dataset.
ListBox1.DataSource = ds.Tables[0];
ListBox1.DataTextField = "player_id";