So what can they be expecting? Surely not Tumminia, one member of a growing wave of women with prominent roles within the game. Tumminia, who manages the day-to-day responsibilities of five Minor League teams in her current role, dreams of shattering the glass ceiling in baseball.
One day, Tumminia would like to own a Major League team, putting her in extremely limited company. The chairman of her company, Marv Goldklang, is a minority owner of the Yankees, and Tumminia has been able to quickly rise through the organization and distinguish herself.
And by taking that journey, she said she's learned that she can do so much more.
"The people that I've worked with made me a believer that I can do it," Tumminia said. "I got really lucky to work for an individual that allowed me to have a voice and allowed me to be wrong from time to time. It probably would've taken me a lot longer if I worked for another organization. I've worked for IBM, and I've worked for a lot of companies that are just straight by the book.
"But I can sit at a Yankees game with my boss and just have a really heated conversation about an employee or the direction of the group, and then we can finish up and say, 'All right, let's have a hot dog.' And there's no hard feelings."
Just 10 years ago, Tumminia was on a different career path, one that brought her bountiful compensation, but not a chance to work in the game she loved. Tumminia, the daughter of longtime White Sox scout John Tumminia, yearned for a change, but didn't know how to make it.
Enter Kim Ng, one of Tumminia's mentors and a fellow pioneer for women in baseball. Ng, currently employed as Major League Baseball's senior vice president for baseball operations, advised Tumminia that if she wanted into the game, she needed to take a different avenue.
Forget coming into the game the traditional way, Ng told Tumminia, because your gender has already made that impossible. Focus on another route, on building your resume on the business side, Ng said. And Tumminia took that counsel to heart, causing her to make a major life change.
Tumminia, who had been working in the financial services industry, got that business experience, and then she left that field to take an internship with the Class A Hudson Valley Renegades. It was a leap of faith, she said, and everyone in her life -- even her family -- questioned why she did it.
"I was making a lot of money, but my love of the game was more than I could put a value on," she said. "It was isolating, but also motivating. It inspired me, and that's my character. I don't like to be told what to do, and when somebody starts telling me I can't do something, that's when I want to do it. And I do think that makeup -- not to use scout terminology -- is what I have in common with Kim Ng or [Yankees executive] Jean Afterman, or a lot of these other women who have had success in baseball."
And it's never been easy. Since Tumminia runs five Minor League teams, she has to speak daily with the general managers and groundskeepers of those teams. Her job contains elements of marketing, accounting and public relations, and that's just before noon.
There's also her active speaking career, which means that she rarely wakes up in the same city for an extended period of time. Tumminia, who will speak at the NCAA Women's Leadership Symposium next month, said that she loves addressing young audiences and that she's glad her job leaves room for her to do it.
"The speaking is becoming almost a full-time job," she said. "If you look at any snapshot of a week, you might ask, 'How do you do it?' I fly into Indiana University, but that's after I've spent some time in Florida with one of my teams. I may speak from 6-8, but I try to get that midnight flight out because I'm going to Kentucky or somewhere else.
"Or maybe I'm speaking out in San Diego State, and I have to switch gears and try to get a left-handed pitcher for my team in Pittsfield. And that's just my work life. I'm on the train and people think I'm crazy because I'm working on two phones at a time."
If they think she's crazy, it may be because she wanted this life at all. Tumminia knew exactly how arduous a career in the game can be because her dad is a baseball lifer, a man who was often away from home for 250 days a year, and who missed her high school graduation along the way.
But he also instilled an uncommon love of the game. The elder Tumminia wasn't always able to attend his daughter's softball games, but he would send an area scout to keep him apprised of her progress.
Tyler lovingly remembers her dad drilling her shins with a fungo bat to make sure she didn't flinch on ground balls, and she recalls a Super Bowl Sunday when she broke her wrist learning to slide.
"Tyler's commitment to the game and the industry as such is an admirable gift to behold," her father said in an email response. "This feeling I know goes beyond a parental view. She has worked extremely hard to manage the course she is on in a male-dominated profession. She has earned the respect of all parties mainly because she is fair, firm and consistent."
Tumminia has always loved the game, and she's shown a willingness to do things other executives may not be willing to do. For instance, Tumminia graduated scout school -- one of just two women in a class of 71 potential scouts -- just to better understand what the entire profession entails.
And while she doesn't plan on stepping down from her executive perch to scout high school games on a regular basis, she can't help but better herself by having the requisite knowledge. At the very least, Tumminia can now better respect and appreciate the work her scouts do for the team.
"I like to say I've known the game prior to working in the game," Tumminia said. "I grew up with my father being a scout, and he's been doing it for 30-something years. And that's when my father would've disowned me, if I didn't pass scout school.
"But I'm grateful for my Dad, because that's hard to separate father-daughter. We have a very unique relationship, because we talk like we're in the game. The twist of it is that there are some situations where all of a sudden he goes into Dad mode."
So what could cause that sudden conflict of interest to crop up? Tumminia, a theater major in college, has a knack for the unexpected, and a flair that can sometimes make her dad uncomfortable.
Take a recent game promotion in Pittsfield, for instance, in which Tumminia's team gave away 500 athletic supporters to the fans. She knows that her Minor League teams are competing against movie theaters for suburban bucks, and she's not afraid to swing and miss on an idea.
"I thought it was hilarious. And we gave them free soft drinks, but of course that doesn't work because the cup is ventilated," she said. "It was very successful. I always say it's successful when we only get five or six complaints. When I start getting a cease-and-desist letter, that's when I start thinking, 'This wasn't a great promotion.' But you can spin that the other way if it gets people talking."
Indeed, Tumminia isn't afraid to fail, and she thinks that's been one of the biggest factors in her meteoric rise with the Goldklang Group.
And it's also manifested itself in her personal life: Tumminia loves to ride horses in her free time, and she's returned to the saddle after a few intimidating falls.
Tumminia, who holds an MBA from Mount St. Mary, is also navigating the path of marriage with husband Ben Cherington, the general manager of the Red Sox. Tumminia and Cherington became parents for the first time this summer, a job made more difficult by their respective pursuits.
"It's very hard," she said. "But even if I didn't live in another city, I'm always somewhere else anyway. Communication is key, but the greatest thing is that at the end of the day, it's kind of neat. He's in Major League Baseball and I'm in Minor League Baseball. We do cross every now and then, but it's kind of nice that we can talk openly and discuss what's going on in our day. It's not a conflict, he just may be sick of hearing about [my job]. But it is unique that we're both working in the game."
One of Tumminia's great accomplishments within the game -- at this early juncture of her career -- is the recognition that she's brought to the scouting profession. Tumminia worked to establish a local Scouts Hall of Fame at each of her Minor League parks, a concept that quickly took developed.
Each park has a wall that pays tribute to various scouts that have brought important players to the organization, and the Goldklang Group later teamed with Topps to make a special order of baseball cards that celebrate scouts. For those twin initiatives, Tumminia -- along with fellow Minor League executive Mike Veeck -- was named the 2008 winner of the Roland Hemond Award.
Hemond, one of the sport's grand old figures, used to be the general manager of the White Sox early in the elder Tumminia's tenure and has known Tyler for more than a decade. More important, though, Hemond respects Tumminia's contribution to the game beyond their shared connection.
"Tyler is very personable, dynamic and kind," said Hemond. "She was raised in a baseball family, and she recognizes the sacrifices scouts make in being away from their families. I like to say they're the unsung heroes of the game, and they were the backbone of providing me with information. She had the right exposure to that life, but if you don't do anything with that, the exposure is negligible."
Clearly, baseball isn't all box scores and boxes of Cracker Jack, and Tumminia has shown both an ability and an affinity for the back-breaking work that goes on behind the scenes. For now, her gender is just a talking point, and one that she hopes will dissolve like yesterday's win or loss.
"Any time I walk into a boardroom, we might be trying to make a major deal. Am I usually the only female in that room?" asked Tumminia, leaving it unanswered. "It's actually quite comical when I walk in. And I almost chuckle. Here we go again. But I always think it's really how you present yourself.
"Issues may arise that are out of your control, but for the most part, I'm hoping that my colleagues are not seeing my gender. I hope they're hearing the ideas coming out of my mouth."