“We welcome the actions and the investigations by the U.S. and Swiss authorities, and believe that it will help to reinforce measures that FIFA has already taken to root out any wrongdoing in football.” So read FIFA President Sepp Blatter’s statement released Wednesday, hours after law enforcement arrested seven of the most senior officials in his organization in what appears to be the beginning of a major sweep of the international governing authority of soccer.

If this is your first exposure to Blatter, as it surely is for most Americans, you’re probably dizzy from his industrial-grade spin. But to anyone who follows world soccer — which is to say most humans — FIFA’s corruption, and Blatter’s brazenness about it, have been features of the game for more than a decade. This latest episode seemed different from all the revelations of corruption that have come before because it looks like there will be legal consequences for the bad guys. Yet, Blatter as FIFA president on Friday, was making clear that reforming the organization won’t come easily.

While arresting and punishing soccer executives is one way that changes might be forced upon FIFA, Blatter’s reelection demonstrates that it won’t be enough. There are two other possibilities: either Blatter finally follows through on reforming the way his organization conducts business — something he has repeatedly promised and never delivered — or FIFA’s commercial sponsors can decide to stop giving it money.

Why do so many global corporations — Visa, Adidas, Coca-Cola, Hyundai, Gazprom, McDonald’s, and Budweiser, to name a few — give FIFA money? Because the World Cup is one of the most marketable products ever created. A reliable estimate of how many people watched the 2014 tournament is tough to find, but it’s not unreasonable to say that the last time a greater percentage of the earth’s population was participating in a common experience, it was perishing from the Black Death back in the 14th century. This ability to bring together so many people every four years gives FIFA real power, and Blatter and company claim to use it to “achieve positive change,” as he said in his remarks opening the 65th FIFA Congress on Thursday. In reality, FIFA’s leaders use that power to enrich themselves while worsening the lives of a great many people.

FIFA is not as bad as the Bubonic plague, but it has been complicit in the deaths of human beings. Nearly 1,000 migrant workers have died in Qatar while building infrastructure to host the 2022 World Cup — and they still have seven years to go. Of the 24 FIFA executive committee members that had a say in where the 2022 cup would be played, two were suspended ahead of the vote for accepting bribes; three later resigned for the same reason; and two have now been arrested. Draw a straight line between the bribes and the deaths, then remember that it’s all for a month-long soccer tournament paid for by Coke and McDonald’s.

Aside from the preventable deaths of poor migrant workers, why would a global brand want to distance itself from FIFA? For one thing, there’s Blatter’s flagrant behavior. He loves to talk about fair play and inclusiveness, but has proven himself to be prone to bigotry. Among his transgressions: his suggestion that gay people shouldn’t have sex while attending the Qatar World Cup so as not to break local laws; the many offensive things he has said about women soccer players, including a suggestion that they wear hotpants to attract more fans; and the fact that a photo exists of him laughing and shaking hands with Robert Mugabe, the tyrannical dictator of Zimbabwe. On top of all that, the willingness to alter local laws that FIFA anticipates wanting to violate has become a precondition of a successful World Cup bid. For the 2014 World Cup, Brazil had to allow the consumption of alcohol in its stadiums, which is normally banned. In Russia, authorities are drafting legislation to allow the use of prison labor to build the 2018 World Cup facilities at a lower cost. Russia’s willingness to implement such rules is an example of what prompted FIFA’s Secretary General Jérôme Valcke to proclaim that “Less democracy is sometimes better for organizing a World Cup.”

Valcke’s comment confirms what the workers of Qatar already know: that the people who run FIFA are not only greedy, but also dangerous. Advertisers, on the other hand, have been slow to realize that. Visa maintains trust that FIFA is capable of “rebuilding a culture with strong ethical practices.” Both Hyundai and Budweiser have said they will simply “monitor the situation.” And after Blatter’s reelection, Coca-Cola released an oddly optimistic statement encouraging FIFA to “seize the opportunity to begin winning back the trust it has lost.” But let’s assume all of these signs of corruption eventually make Visa, Adidas, Coca-Cola, Hyundai, Gazprom, McDonald’s and Budweiser nervous enough to stop sponsoring FIFA. And let’s assume that none of their competitors were craven enough to take their place. Blatter would suddenly find it very difficult to maintain the support that keeps getting him reelected.

Every FIFA member country gets to cast a single vote for the organization’s president, and Blatter has taken advantage of this structure. He maintains power by doling out largesse in the form of development projects, luxury travel, expense accounts, and, it seems, tacit permission to use the status of running a country’s soccer establishment for personal gain. These are the tools of Blatter’s soft power, and he uses them to shore up the loyalty of the people who oversee soccer federations the world over.

For instance, the two men who ran the Confederation of North, Central American and Caribbean Association Football for years have said they received money for delivering the region’s votes to Blatter or making other shady deals. One, Jack Warner of Trinidad, turned himself in to police on Wednesday after law enforcement there cooperated with the FBI’s warrant. (He resigned from FIFA’s executive committee in 2011 and is now a member of Trinidad’s parliament.)

The other, an American soccer dad turned impresario named Chuck Blazer, who became an FBI informant, made so much money from his dealings – at least $15 million according to reports – that he rented an $18,000-per-month apartment in New York’s Trump Towers as well as a second, $6,000-per-month unit as living quarters for his “unruly cats.”

Warner and Blazer were run out of FIFA several years ago and replaced by Jeffrey Webb, who promised reform, though it’s doubtful how well that worked out: Webb was also named as a defendant in the case.

“The FIFA family” is one of Blatter’s most frequent platitudes; he likes it because it casts him in the role of the father. But if advertisers take the moral high ground and pull out of this dysfunctional clan, Blatter’s slush funds will evaporate, making him less of a patriarch and more of a pariah. He will become the man who caused FIFA’s taps to run dry even when companies from all parts of the world want nothing more than to shovel money into its coffers. The loss of that corporate cash flow would pressure the blocs that have consistently elected Blatter (including most of Asia and Africa) to back a regime change. Certainly, there’s no guarantee that whoever replaced Blatter would be any more palatable from a moral point of view. But 17 years have proven that FIFA can’t be cleaned up with Blatter at the helm.

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