CEOs of large American companies saw their compensation fall in 2015, according to a data analysis by Theo Francis and Joann Lublin of the Wall Street Journal.

Not every S&P 500 company has yet released information on its 2015 pay, but about 300 members of that index of big publicly traded companies have. (The rest will do so over the next couple of months.) Of the companies in their sample, they found that median pay fell from $11.2 million to "only" $10.8 million — a decline of nearly 4 percent — largely because growth in cash bonuses slowed and pension contributions got less generous.

Nobody is going to cry for these CEOs, of course, but it is one measure in which inequality fell last year. Compensation growth for normal workers was not particularly robust by historical standards, but it did go up rather than down.

CEO pay is very strange

Alongside the aggregate data, the Journal put together a fun interactive comparing CEO pay to companies' stock performance. It shows that there's not a ton of rhyme or reason to who gets paid what at these lofty heights of the corporate world.

Google Inc. CEO Sundar Pichai had the highest pay of anyone by far, earning $100.5 million by taking over one of America's largest and most dynamic companies and delivering 45 percent shareholder return. But at No. 2 we have Philippe Dauman of Viacom, who earned $54.2 million while watching his company's stock slide 42 percent.

Steve Ells and Montgomery Moran of Chipotle earned $13.8 million and $13.6 million, respectively, while their company was plagued with food safety problems and lost 30 percent of its stock market value.

You don't need to be paid to get rich

The bottom of the pay rankings is dominated by founder-owners, like Whole Foods' John Mackey and Google's Larry Page, who both earned just $1 in 2015.

Of course for founders, share price accumulation is its own reward. That 45 percent increase in the value of Google stock made Page a lot richer than he was at the start of the year, even though it technically wasn't salary. Mark Zuckerberg paid himself $610,455, and Warren Buffett earned $470,244 — again, with both men making their real money through share price accumulation.

That's a reminder that as lavishly paid as CEOs are, for the truly rich, getting paid isn't the name of the game. The top 20 richest people in America all founded a company (most of them), inherited a fortune (Jim, Rob, and Alice Walton; Jacqueline, John, and Forrest Mars), or did a little of both (Charles and David Koch). No pay package, no matter how splendid, can compete with the possible rewards of owning things — either things you created yourself or things you inherited from your parents.