That's what the Cubs great told Chuck Wasserstrom, a 25-year veteran of the franchise in media relations and baseball operations, in an interview for Wasserstrom's blog: "But look, I have my pride, and I know I had a tremendous career in Chicago. When nobody knew who Chicago was, I put Chicago on the map."
This led to some inevitable eye-rolling, and Sosa is—surprise—exaggerating. But he's also got something of a point.
Sosa joined the Cubs in 1992 as a 23-year-old after two mediocre seasons with the White Sox, in which he flashed some power (26 doubles, 10 triples, and 15 home runs as a 21-year-old, his first major-league season) but couldn't crack an .800 OPS or an OPS+ of 100 (in which 100 is the major-league average). He played a marginally better half-season in 1992 for the Cubs, then started his breakout in 1993, in which he hit 33 home runs and stole 36 bases.
His first great year was 1994, when he hit 25 home runs and had a well-above-average OPS+ of 112 in that strike-shortened season. The next year he made the all-star team and was eighth in the MVP vote, and you probably know the rest.
Here's what happened to the Cubs' attendance over that time (keep in mind that the 1994 strike cost the team almost 60 games, so it's artificially low).
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Greg Maddux's last year with the Cubs was 1992. Ryne Sandberg's last good year was 1993 (though he put up average-to-bad seasons in 1994, 1996, and 1997). Shawon Dunston's last year with the team was 1995.
After that it was Sosa, Mark Grace, and not much else. The 1999 Cubs, for example had a starting lineup with an average age of 33, featuring Benito Santiago, Micky Morandini, 40-year-old Gary Gaetti—who had an OPS+ of 52, meaning he was about half as good as an average player—and 35-year-old Lance Johnson. The team's best starter was Jon Lieber, with a 4.07 ERA; every other starter had an ERA at 4.83 or higher.
They fell from a second-place finish in 1998, the year Sosa put up 66 home runs and won the MVP award, to last place. They finished 30 games back with their worst winning percentage, .406, since 1974.
And that year the Cubs set an attendance record, 2,813,854, while attendance across the league was stagnant.
In 2000, Lieber was their best pitcher again, but his ERA was up to 4.41; Kerry Wood was next at 4.80 and it got much worse from there (Ruben Quevedo somehow started 15 games with an ERA of 7.47). The Cubs finished last again; Sosa hit 50 home runs, leading the league.
Sosa's best year was 2001, with career- and league-highs in runs (146), RBI (160), and total bases (425), with 64 home runs and a career-high 203 OPS+, meaning he was about twice as good as the average player. Attendance plateaued—the Cubs finished 30 games back in 1999, 2000, and 2002—but broke 3,000,000 in 2004, Sosa's last year with the team, and stayed above that for eight of the next 11 years.
And you can make a case—a bad one, but still–for Sosa as the best-ever Cub. Per Fangraphs, Sosa has the fifth-highest WAR in team history, behind Cap Anson, Ron Santo, Ernie Banks, and Ryne Sandberg, and just ahead of Billy Williams. But WAR is a cumulative stat, and Sosa was the only one of those players to play fewer than 2,000 games for the team.
WAR also includes defense, which was not Sosa's strength (he was barely above average by Fangraphs' measures) and has to be taken with a grain of salt. So just by Fangraphs' cumulative "offense" stat, a measure of offensive runs above average, Sosa is third all time, behind Anson and Williams, but with 400-plus fewer games.
Was Sosa the best Cub ever? No, probably not, as you'd have to toss out longevity and defense. But his peak puts him among the team's best players, and at a time when there wasn't much else to recommend the team. Likewise, he didn't "put Chicago on the map," but he kept the team interesting during some bleak years, and that interest is apparent in the attendance numbers.