But, unlike his dad, there have been few Hall of Fame moments in the young Gossage's baseball career.
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Sandwiched between a brief stint in the Chicago White Sox minor-league system have been stops with independent teams in Chico, Calif., Newark; and now Rockland County as he tries to catch the eye of major-league scouts while playing in the independent Canadian-American League.
He has never stepped on a major-league field, unless of course you count the days he shagged fly balls in the outfield when he was 11 and his father was playing out his career with the Seattle Mariners.
"It was every kid's dream," Todd Gossage said Tuesday as his newest team, the Rockland Boulders, got ready to play their home opener against the Newark Bears at Provident Bank Park in Pomona. "You really don't appreciate it until you get older."
Todd Gossage says he wasn't sure he wanted to continue playing baseball.
At his age, most minor-leaguers are thinking about what to do with the rest of their lives. Last year ended in disappointment for him after he was released by the Bears despite tagging three homers in the last week of the season. He hit just .191 in 29 games.
Then a vision came to him at night back home in Colorado.
"I started playing baseball in my dreams," Todd Gossage recalled. His father told him, "As long as you're still having fun, don't quit."
"I've got the talent," he said. "I just need to be more consistent, day in and day out."
Todd Gossage started two games in the opening series but wasn't in Tuesday night's starting lineup.
"He doesn't have the Goose Gossage fire," LaPoint said of his lefthand-hitting first baseman. "He's a lot more low-key than his dad. ... His father had a strong will to win. It didn't matter if he was in the game or not."
Todd Gossage says neither he nor his two older brothers inherited their father's outsized personality. "He's pretty extroverted," Todd Gossage said. "He's just got a very big personality."
Todd Gossage won't be the only former major-leaguer's son playing for the Boulders this season. Glen Johnson, the son of former Mets third baseman and hitting coach Howard Johnson, is projected as a starter and is slated to be the Boulders' designated hitter for Tuesday night's game against the Bears.
The senior Johnson, at Tuesday's opener, coached his son's baseball teams when his son was growing up.
"As long as he still loves the game, I'm behind him," Howard Johnson said.
Like his teammate Gossage, Glen Johnson said he doesn't mind the comparisons to his famous father.
"I'm here because of him," Glen Johnson said. "He deserves as much of the credit."
Both players are hoping some home cooking also will help them get going. After four games on the road to open the season, neither batter has a hit: Glen Johnson is 0-for-6 and Todd Gossage is 0-for-12.
Rich Gossage said he encouraged his son to give it another try despite last season's struggles.
"The game has a way of telling you goodbye," Gossage said. "When it's time to say goodbye, you give it a salute and say thank you very much."
He said he always got annoyed at coaches who tried to compare Todd or his other sons to him.
"Everybody expects him to be like me," Gossage said. "My three boys are all different. He's a lot more laid-back than me. I used to hear coaches say, 'You don't throw like your father.' These people are idiots. There aren't many people with the arm that I had. There aren't many people on the planet who had an arm like I had. It's not fair. We're different."
The Hall of Famer added: "I always told my kids, go out, have fun and play hard. Everybody puts too much pressure on their kids."
He hopes that some day Todd will find his way into management on a baseball team.
"I'd like to see him in the front office, building a ballclub," Rich Gossage said. "If some of these guys who've never worn a jock can run a ballclub, he can do it."