Finally, I get to participate!

The best source for information on this is Mike Sowell's book The Pitch that Killed, which covers both the context of Chapman's death and the pennant race of 1920. Statistical information is generally taken from Baseball-Reference.com.

Baseball was in a transitional period already when Chapman died. The game, which had been nominally professional since 1867 and truly professional a few years after that, had only recently consolidated around the National and American Leagues as the true, major leagues. The game had been dominated by pitchers for much of its 20th century history; huge bats, fast players, improving fielding technology, and a variety of other factors had combined to pull down what had been very high scores in the 19th century. The game had been growing rapidly in popularity for a couple of decades, and was seen as a fast-paced, rowdy alternative to other, more gentlemanly pursuits such as cricket.

But in 1920, baseball was undergoing a true, existential crisis unlike any that it has seen since. Though emblematized in the Black Sox scandal of 1919, which was unfolding through the 1920 season, gambling had become a plague on the game, as many players openly took bribes and few were punished for it -- Hal Chase, who was about as big a star as baseball had in the 1910s, was famous for it, and may have been a go-between for Arnold Rothstein and the Black Sox conspirators, and he wasn't alone in doing this sort of thing.

Though star players were well-paid (Ty Cobb made $20,000 in 1919, or about $275,000 in today's dollars), most players in this period were working class guys who went home and worked in the offseason. For many men, including most of the Black Sox, the hint of real riches that came from game-fixing and side-betting was more than just greed: it could materially change their financial situation, and all for a modicum of effort (though a fair amount of risk). With its credibility shot and its finances vastly more precarious than they are today, MLB faced ruin.

Meanwhile, the way the game was played was being revolutionized by Babe Ruth. I won't wax too poetic about Ruth, but it's important to understand some bullet points about him, because what happened after Chapman plays into how Ruth changed the game:

1. It's not just that Ruth had those seasons in which he was hitting as many home runs as the rest of the league combined; to some degree, it was almost inevitable that someone would start swinging for the fences and discover that it worked. It's that Ruth's descendants and contemporaries explored the area near, and under, his records, but almost never surpassed them.

2. The way Ruth played the game was not only incredibly successful, but it was hugely profitable. Why do the Yankees have the highest payroll in baseball, while the Giants play in San Francisco? The Giants had been a vastly more successful and profitable team to that point -- but Ruth revolutionized the game, and along the way, revolutionized the Yankees' finances.

3. For more than 40 years after Ruth's advent, baseball was played in a slow, station-to-station manner that emphasized home runs, a state of affairs that did not begin to change until massive integration and westward expansion changed the environment in the 1960s.

Okay, now that we've got that out of the way, Chapman, Mays, and the pitch that killed. Mays was Ruth's teammate, a submariner, the Yankees' ace, and not a popular man within the game. He was a hard man, a bit of a loner, and he threw pitches that took full advantage of batters' fears of being hit to get his outs. This was in the days before night baseball, remember, and one of the jobs of a pitcher was to dirty up a ball, using dirt, spit, tobacco, shoe black, and any number of other things that might obscure the ball; too, umpires were not nearly so quick to replace balls, and so, as the game wore on, the ball came to take on a gray-brown color, and was often misshapen and prone to flying in unpredictable ways when pitched or hit. Mays, as a right-handed submariner, used this (and was not alone in using this) as a way of disguising his pitches and keeping batters off guard: especially in early- and late-season games, later innings were often played in semi-crepuscular conditions, meaning that any batter digging in against Mays and his brown ball was literally gambling his life on his ability to pick a speck of brown out of the darkling skies.

Now, is this actually why Chapman was hit? It was the middle innings of an August game in New York, a game that only lasted a couple of hours and would have been started in mid-afternoon -- in other words, probably not, at least the weather conditions part of it. But Mays was famous for dirtying the balls, and it's probably true that a brown ball would be harder to see in almost any conditions than a shiny white one. And a lot of people assumed it was. The death of Chapman, coming at the same time as the Black Sox scandal, put a real fright into people. It contributed to the culture of reform that brought forth increasing professionalism, the hiring of a commissioner (the vastly overrated Kenesaw Mountain Landis), and similar things.

The main thing that happened to the culture of the game is that the practice of scuffing the ball became much less common, as rules that were already on the books started to be enforced. Also, though it's hard to find hard data on the matter, umpires were instructed to constantly cycle in new, white balls, so even those that were doctored never became brown and flat. These two changes, along with Ruth's teaching the world to play baseball, fed into the game changing massively -- the game changing, basically, into what it is now.

Mays was left bitter after the incident, if later interviews he gave were any indication. He'd always been a rough-and-tumble pitcher with a reputation for throwing at people, including a notorious incident with Ty Cobb several years earlier. He felt he became a pariah within the game, though he'd never been popular, and there is evidence to contradict him (a substantial raise over the offseason, for instance). Some were shocked that he, unlike some Yankees teammates, never went to Chapman's assistance; he also pitched several more innings that day. It's true that, despite a fairly illustrious career that continued for several more years, he received only passing support for the Hall of Fame -- though he, like Chance and the Black Sox, was dogged by gambling rumors that he denied but couldn't shake.

Were guys scared of Mays? Well, yeah. But they'd always been scared of him. It was how he got outs. Baseball was a tough man's game in those days, and though I'm sure it gave guys pause, there wasn't a wave of people refusing to play when Mays pitched. I can't imagine there were a lot of illusions about what was possible when playing baseball for those guys. Chapman wasn't the first guy to get beaned. He was just the first one (that we know of) who died.

Interestingly, the Indians -- who won on the day Chapman was hit -- would overtake the Yankees in September to win the pennant even without their star shortstop, and eventually beat Brooklyn in the World Series. (Chapman was a good hitter and known to be a good fielder, though there's no statistical data to give us any accurate reading on the latter statement.) This may have been because the man who took over for Chapman was a 21-year-old former football star named Joe Sewell, who would end up in the Hall of Fame himself eventually.

EDIT: Additional sources: The New Bill James Historical Baseball Abstract, retrosheet.org

FURTHER EDIT: I noticed two minor errors in rereading this. They are:

1. Though there were rules about ball conditions that were generally not enforced, I left a clause off that sentence -- after the Chapman incident, and almost directly as a result of it, the spitball per se was disallowed, with a small list of pitchers grandfathered in. Mays was not on that list, but still had his best season in 1921.

2. The 1920 pennant race was tight straight through, but I implied that the Indians were behind the Yankees in the standings on 16 August, the day Chapman was hit. They were, in fact, tied with the White Sox, half a game ahead of New York, on that date. Both the Indians and Yankees fell behind Chicago after the Chapman game, and Cleveland would be behind New York and Chicago both as late as 30 August.