Ninety-eight percent of baseball happens in the first nine innings, marching toward a conclusion that can be counted down with arithmetic precision: Nine outs to go, six outs to go, three outs to go, down to the last strike. But the other 2 percent happens in a different realm, the open-ended default of extra innings, when a game might go on forever and ever and ever and ever and ever.

The New York Yankees and Boston Red Sox played 16 innings Saturday, a game that featured one team playing under protest, four umpire reviews, a batter tripping over his own bat, one of the weirdest baserunning decisions we've ever seen and a whole lot of high-leverage Doug Fister. There will probably be a time, not long from now, when such games are almost impossible, when crowd sizes in the triple digits and pitchers playing left field that we see in the seventh hour of play are quirks of old-time box scores.

Extra innings -- or, at least, extra-extra innings -- are endangered. The mood around the 16th inning has changed. Major League Baseball is experimenting, in rookie ball, with rules to shorten these games by seeding the basepaths with extra runners. "This isn't real baseball," some of us will protest. But what is real baseball once 28 or more outs are required? After the 10th inning starts, baseball begins a gradual deconstruction, each out pushing the teams further from Plan A and deeper into Plans B, C and D.

Using the play index at Baseball Reference, MLB.com's Statcast search, PITCHf/x data from Baseball Prospectus' database and game stories from a dozen of the longest games of the past half-decade, we studied the progressive breakdown of baseball in extra innings. Here's what happens to baseball when it stays up past its bedtime.

The 10th inning

The 10th inning is a pitcher's inning. Both teams have a handful of relievers available -- if the home team came from behind in the ninth, it'll have its closer left and use him here -- and before the desperate teamwide exhaustion has set in, the best remaining reliever will pitch with the confidence of a man asked to reach the end of this inning and no more. Some 24 percent of batters will strike out in the 10th inning, same as in the ninth inning and higher than any other inning of the game. The average fastball thrown is 94.0 mph, down slightly -- but only slightly -- from 94.4 mph in these same games' ninth innings. Home runs are less frequent in the 10th than in any inning before or after. When the Yankees and Cubs went long on May 7, 10 consecutive batters (both teams combined) struck out in the 10th and 11th innings.

Batters' swing speeds -- as estimated by Statcast -- drop in extra innings. Exit velocity drops by 1 mph in extra innings. Launch angle does, too, defying the conventional wisdom that batters are simply swinging for the fences once the game gets long. Some 44 percent of extra-inning games will end right here. Dinner might be a little bit hurried, but you'll still make it to your movie on time.

The 11th inning

The managers start getting a little nervous; 30 years ago a team could get to the 25th inning using only six pitchers, but major league rosters, major league players and major league reliever usage are not constructed to go much deeper than this. By the 11th, situational pitching changes are done. All relievers become "long" men, and the guy who pitches this inning will likely pitch the next one. The visiting team, if it tried to hold its closer for a save situation, will often decide to use him now (ideally for two innings) before it's too late, which might help explain why the visiting team temporarily erases the home team's advantage in this and the 12th inning.

Sacrifice bunts go up, from 1.7 percent of all plate appearances in the 10th to 2.0 percent in the 11th, and intentional walks go up by a similar margin. Batters are more patient than in any other inning, swinging at just 46 percent of pitches -- down from 47 percent in the 10th, 48 percent in the ninth inning of these same games, and the last decline before a slow and steady rise in swing rates for the rest of the game. Strikeouts drop to 21 percent of plate appearances, and plate appearances get shorter: from 3.83 pitches on average to 3.80, a downward slope that will get steeper as the game gets longer. The plate appearances get faster, too, with about a half-second less time between pitches compared to the ninth.

The 12th inning

Both teams have now gone through the bottom of their order at least once in extra innings and have emptied their benches of pinch hitters. Backup catchers will be used, so from here on out there will be no relief for the man behind the plate, adding extra import to every potentially injurious foul tip. This is the inning with the most bunts, with nearly twice as many pitches bunted at compared to the ninth inning of these same games.

The manager has one or two traditional relievers left, and if things go right, he'll get four more innings out of those two. This is the time of the game when the next day's starting pitcher, or an overworked reliever who had previously been told he'd have the day off, will be alerted that he needs to be prepared to go in if the game never ends.

This is the inning a bank of lights went out in New York two years ago, causing a 16-minute delay at Yankees manager Joe Girardi's request. Fans booed.

The 13th inning

Pitches have slowly been moving up in the zone, not much, but measurable: from 2.28 feet above the ground in the ninth to 2.32 feet here in the 13th, incremental rises adding up to about a half-inch, on average, by this point. The average fastball is down a full tick, to 92.9 mph. Yet scoring doesn't go up, perhaps because the middle of each team's lineup has been gutted -- a pinch runner who stayed in the game, or a pitcher's spot moved in a double-switch, might now be batting fourth, interrupting rallies and setting up easy intentional-walk calls. Intentional walks are now 60 percent more frequent than they were in the 10th inning. This is the inning when, in August 2013, pitcher Tyler Cloyd had to bat for himself with two outs and the bases loaded. The game went on.

This is the inning Russell Martin was abruptly ejected by a fed-up umpire in Toronto last July. This is the inning plate umpire Tony Randazzo had to leave a Reds-Giants game this year with concussion symptoms after taking his fourth foul tip off the mask. It's just after this point that Wrigley fans were chanting "Joe West sucks" this year. It's a long game for everybody.

The 14th inning

Velocity keeps dropping; this is the latest inning (since 2014) in which a pitch has been thrown at least 100 mph. Pitchers are now batting for themselves, or in many cases being pinch hit for by pitchers. (On May 7, the Cubs' Jake Arrieta, John Lackey and Kyle Hendricks all batted as pinch hitters.) Intentional walks spike absurdly in this inning, to a rate five times higher than in the 10th inning, though it's just a one-inning blip.

This is the inning somebody puts a gum bucket on his head, or some such weirdness. This is when we get our second seventh-inning stretch. The average 14-inning game is 10 minutes shy of five hours, which means midnight -- and #weirdbaseball -- approaches.

The 15th inning

Hanley Ramirez's home run ended Tuesday night's Red Sox/Blue Jays game in the 15th. In the 16th inning, though, the chances of a walk-off jump from about 15 percent of games to almost 19 percent. AP Photo/Charles Krupa

The game is speeding up; there are now only 21.4 seconds between pitches, down a second per pitch from the previous inning and two seconds from when we started.

Pitches have just kept rising; they're now 2.36 feet off the ground, on average, a full inch higher than they were in the ninth and 10th.

The next day's starting pitcher, if he's going to pitch, is likely in the game or warming up. This is the inning when, in April 2015, Ryan Hanigan caught a knuckleballer for the first time.

The 16th inning

Pitch selection hasn't changed much to this point, but fastball rates suddenly spike, from about 55 percent to 60 percent. Meanwhile, those fastballs are getting slower: 92.6 mph on average, almost 2 mph slower than they were in the ninth. The catcher, if he wasn't replaced in the 12th, has now spent half of (on average) 317 minutes in a squat, and wild pitches and passed balls spike -- even though the likelihood of a passed ball or a wild pitch, based on Baseball Prospectus' PITCHf/x-based calculations, should be much lower. Batters are more aggressive, swinging at 49 percent of pitches, up from 46 percent in the 11th. The chances that the game will end on a walk-off home run -- if it ever ends -- go up, from about 15 percent of games to almost 19 percent.

This is the inning Anthony Rizzo gets walked intentionally with nobody on base. This is the inning Eric Fryer gets thrown out at home on "the best relay in the history of the game in the 16th inning," as Clint Hurdle put it. This is the inning that Hansel Robles, given the day off after working in each of the three previous games, was called in to pitch -- and then asked to throw a second inning.

This is the inning that home-field advantage finally evaporates. Excepting the 11th and 12th innings, the home team has maintained its advantage inning by inning, and if a game makes it to the 13th inning the home team wins about 54 percent of the time -- roughly the same as the overall home-field advantage in baseball. But starting in the 16th, home teams have been no more likely to win than road teams. The samples are small, but it also makes sense. Home-field advantage is a marginal edge that nudges one closely matched team just past its closely matched opponent. But there is a good chance that by the 17th or 18th inning there is a huge gulf between the team that has a fresh major league pitcher on the mound and the one that's using a position player or a reliever in his fourth frame.

The style of play has changed fairly dramatically over two extra hours. Compare the 10th inning to innings 15-18:

Strikeouts are down 25 percent from the 10th

Home runs are up 20 percent, while doubles are down 20 percent (and triples 40 percent)

Walks and hit-by-pitches are both down 20 percent, even as intentional walks have gone up by 60 percent

Pitches per plate appearance have dropped from 3.86 to 3.57 -- effectively sending baseball back in time to 1988

Is baseball in the 16th still interesting? When the New York Mets and Miami Marlins went 16 innings, there were only "a couple of hundred people at Marlins Park" by the final inning, according to the New York Post, but viewership at home doesn't drop as much as you'd think. "The peak viewing audience on SNY ... fell off by nearly 26 percent by the time the game ended at 12:50 a.m., yet to be fair, still was above 390,000," according to the NY Post. Had that game gone one more inning, Mets manager Terry Collins planned to let catcher Rene Rivera pitch, and pitcher Zack Wheeler would have played first base. You might not stay at the park an extra hour to see that, but you might keep the TV on.

The 17th inning

Exhaustion and depletion have set in. The average pitch thrown is two inches higher than in the 10th, and an inch higher even than in the 16th.

Players aren't just tired, they're hungry. The average 17-inning game goes 5 hours, 40 minutes. "Chad Kuhl was starving. He sat in the clubhouse with Arquimedes Caminero and Juan Nicasio, waiting for a game that exemplified the phrase 'no end in sight' to conclude so he could eat. ... He allowed himself a banana but nothing more."

This is the inning that the sprinklers at Petco came on last year.

At least one player on each team will be sent down after the game so his team can call up a fresh reliever for the next day's game. The guy on the mound, the final reliever trying to keep the game from ending, is quite likely the one getting demoted. The longer he preserves the game, the more pitches he throws, the more likely he'll be riding a Triple-A bus two days later.

When Martin Maldonado homers in the 17th in May 2015 -- after catching 253 pitches from nine pitchers -- he slides into home plate.

The 18th inning

The pitching is barely major league quality anymore. The average fastball is 90 mph. In recent years, Casper Wells, John McDonald and Darwin Barney -- position players -- have pitched in this inning. Yasiel Puig was going to pitch an 18th inning last year, but his team won in the 17th. Utility man Alexi Amarista was a batter away from taking the mound in the same game. The next day's starter, if he has pitched, might be nearing exhaustion himself. Esmil Rogers, pitching for the Yankees in 2015, threw 81 pitches after throwing 35 the night before. If the game had gone one inning longer, Garrett Jones was going to pitch -- though Rogers said afterward he would have fought to stay in the game.

The scorecard is so messy that, even with few tactical moves left to anticipate, managers get disoriented. This is the inning in which, last year, Dusty Baker failed to intentionally walk Starling Marte with the pitcher on deck. Marte homered to end the game. "I just said to [pitching coach Mike Maddux], 'We got [Jon] Niese on deck.' Before I could put the four fingers up, Marte hit the first pitch out. I take full responsibility. I've got a scorecard next to me. There were so many names scratched out and double switches."

"All plots tend to move deathward," a novelist once wrote. "This is the nature of plots." This is also the nature of 98 percent of baseball, where the most likely outcome of every at-bat is an out, and where every out moves the game closer to a decisive conclusion.

But this is not the nature of extra innings, where every out moves the game deeper into stagnation. The plot advances, and the play changes, but those changes don't really do anything to move the game closer to conclusion. The chances of a game ending in any individual inning stay below 50 percent through the 18th, with the exception of the 14th, which we can probably write off as a small-sample blip. Every new inning starts exactly like the one before it: tied, with no end in sight.

The plot of extra innings, then, moves not toward a conclusion but toward Yasiel Puig maybe pitching in the 18th. If the primary reason you watch baseball is to see something you've never seen before, this is a worthwhile plot. This is me. It might be you. It's not unreasonable for MLB to conclude, though, that most fans just want to see somebody win.