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Let me begin by laying my cards on the table. I have a soft spot in my heart for post-apocalyptic survivalist fiction. What would happen if it were really the end of the world as we knew it and we didn’t feel fine? What would happen if all of the phones and lights and motorcars on which we have come to rely were taken away suddenly and we had to survive off the land, Gilligan’s Island style? Now, I’d never want to actually live that way, but it’s fun to torture the edges of anything, including our notions of civilization.

And the same impulse that draws me to watch Tiny House Hunters makes me love a good extra-inning game. By definition it’s a close game, but in baseball there’s the possibility that the game could go on until sunrise. I suppose I can say that because I’m not the one who has to drag himself back to the team hotel through a nuclear wasteland after losing 5-4 in 19 exhausting innings. But the truth is that baseball teams aren’t made to last 19 innings and it’s fun to watch them try. We usually end up with pitchers pinch-hitting and position players pitching and someone trying to play a position he’s played as many times as I have in a major-league game.

But last week, a little bit of news came out about a potential change to the game to try to curtail my survivalist fantasies. This season, in rookie-ball, when a game gets to the 10th inning, rather than starting with no runners on base each team will be given a free runner on second base with the price of admission. The goal is to make it easier for teams to score and thus get the game over with. It wouldn’t set a hard cap on innings after which the teams would settle the matter with a home run derby, but in theory it would encourage games to come to an end more quickly, and someone can still throw a shaving cream pie in someone else’s face.

Whether you think the art of it is appealing or not, this is one of those things that lends itself quite well to a little #GoryMath.

Warning! Gory Mathematical Details Ahead!

Let’s set the landscape for a moment. From 2012-2016, 91.2 percent of all games finished in the ninth inning (or earlier for a few rained out, partially-completed-but-still-official games). So, the average team during those years played 14 extra-inning games. Of those 1,064 games that went extra innings, here’s the breakdown of when they ended. On average, teams played an extra 2.3 innings.

Inning

Percentage

10

43.3%

11

24.1%

12

13.9%

13

8.6%

14

5.2%

15

1.8%

16

1.4%

17

0.4%

18

0.7%

19

0.6%

20

0.1%

Most extra-inning games don’t turn into marathons. In fact, 98.4 percent of all games were done by the end of the 12th inning, but even that suggests that the average team will have 2-3 games per year when they have to get someone warmed up in case they need to sing “Take Me Out to the Ballgame” again for the 14th-inning stretch.

The idea of putting a runner on second base is that it makes it easier to score a run, which is of course demonstrably true, but both teams get the benefit of the runner. Again, from 2012-2016, here’s a comparison of how many runs a team could expect to score in a standard inning (no runs, no outs) vs. when they began the inning with a double or a single/walk/HBP and a stolen base.

Number of Runs

No runners, No outs (all situations)

No runners, No outs (extra innings only)

Runner on second, No outs (all situations)

0

73.4%

73.9%

38.6%

1

14.8%

17.4%

34.7%

2

6.6%

5.3%

13.9%

3

3.0%

1.9%

7.0%

4

1.3%

0.9%

3.3%

5

0.5%

0.3%

1.4%

6+

0.4%

0.3%

1.0%

The average team scored 0.47 runs per inning in all innings from 2012-2016, but had a goose-egg to show for their efforts nearly three-quarters of the time. The team that started off with a runner on second base scored an average of 1.11 runs and the majority of the time scored at least one run. No one is surprised by this. We now simply know that there’s going to be more scoring in these extra innings.

That last column probably isn’t a perfect proxy for figuring out what might happen if MLB tried this “automatic runner on second” plan in real life. For one thing, the numbers in that column are based on all innings against all pitchers, regardless of their quality. In these new 10th innings, we’re almost certainly dealing with relievers (who tend to get better results than do starters) and probably the better relievers in the bullpen. We can see that comparing the general run distribution (column 1) to that of extra innings (column 2), extra-innings relievers are slightly more likely to keep a clean sheet. (The bump in one-run innings is due to the fact that in extra innings, often that’s the home team scoring the one run they need to break the tie and walk off, and we don’t get to find out how many more runs they might have scored if they had played until three were out.)

There have been some extra innings that started with a runner on second–329 in fact–and that’s not a great sample size, but we can look at that distribution as well (this is the second column in the chart below, with the first being the same numbers as above, just re-printed). Again, the one-run innings are going to be over-represented here because it’s the home team breaking a tie in the bottom of the inning. If we look only at the top half of extra innings–sample size is down to 174–we get results that are closer to the full sample, but we might be baking in some visiting field disadvantage.

Number of Runs

Runner on second, No outs (all)

Runner on second, No outs (extra innings only)

Runner on second, No outs (top of extra innings only)

0

38.6%

43.8%

39.7%

1

34.7%

36.5%

27.0%

2

13.9%

12.2%

19.5%

3

7.0%

2.7%

5.2%

4

3.3%

3.0%

5.2%

5

1.4%

1.5%

2.9%

6+

1.0%

0.3%

0.6%

Also, there’s the fact that our historical look at what happens after a double is going to be skewed toward teams that get a lot of runners to second, i.e., the teams that are good at hitting and scoring runs in general. It also means that they were hitting off a pitcher who gave up a double. Those teams are going to score more runs. In regular play, it’s impossible to unwind the fact that there is currently a runner on second base and that a double occurred. Baseball has never seen runners just appear for no reason before.

So, I made an executive decision. I’m going to use the distribution from all innings with the understanding that it’s probably not quite right, but it’s going to be close enough. Now, with that in mind, I decided to run a Monte Carlo simulation with one million games. The model was a simple random draw from that distribution for both the visiting and home teams. This was how many runs each team “scored” in the 10th inning, starting with a free runner on second. If the two teams matched, then they went on to the 11th and did another random draw.

Here are the results of how long the games went in the simulation, paired with the real-life data from 2012-2016 (which was shown above).

Inning

2012-2016 actual

Monte Carlo simulation

10

43.3%

70.5%

11

24.1%

20.8%

12

13.9%

6.1%

13

8.6%

1.8%

14

5.2%

0.5%

15

1.8%

0.2%

16

1.4%

<0.1%

17

0.4%

<0.1%

18

0.7%

<0.1%

19

0.6%

<0.1%

20

0.1%

<0.1%

In real life, the average extra-inning game included 2.3 extra frames. In the Monte Carlo simulation, we got it down to 1.4. It’s probably that there wouldn’t be quite that much scoring, so we might see slightly longer games, Then again, the simulation assumes one million games between two perfectly evenly matched teams. The reality is that one team is going to be somewhat better than the other, which means the chances that they draw unequal numbers (and end the game) just went up. But adjust all you want, the big message is that it really would put an end to a lot of those Homeric epics masquerading as baseball games and would probably save about 15 bullpen innings over the course of a year.

Once the idea was announced, there was speculation as to whether the runner on second base with no one out was an invitation for a leadoff(?) bunt. In the top of the inning, the game is guaranteed to be tied, and in the bottom of the inning, if the game is tied, the home team can play for one run because that’s all they need. It’s likely that we’d see more bunting than we would in a random Tuesday night at-bat, but when I looked at the historical record it didn’t suggest that it would be an automatic bunt sign. In fact, from 2012-2016, when the game was tied in the ninth inning or later and a team had a runner on second with no outs, teams bunted roughly 21 percent of the time, both home and away (21.0 percent of visitors, 21.2 percent of home teams). Four out of five times, they were swinging away.

What’s weird is that, despite the historical record of what teams have done in the exact same strategic situation, it would not shock me if the rates of bunting went up. That makes no logical sense, because mathematically the incentives for bunting or not bunting are exactly the same, but framing is a powerful tool. The runner on second is being given by the league office for the express purpose of making it easier to score a run and that will likely act as a social pressure to ensure that the runner scores. Teams still hit the center fielder first even though he’s an awful hitter.

One other minor side effect of the new plan might be a small increase in the number of runs scored overall in a game. (Side note: The “free” runner would be unearned, right? What about any other runs?) The “put a runner at second” plan sounds vaguely like college football’s overtime system in which teams get the ball at their opponent’s 25-yard line. This makes it easier to score (as does putting a runner at second) but the touchdowns still count for the same number of points. This leads to the occasional three-overtime game in which teams tack on an extra 20 points or so.

In the Monte Carlo model above, the “visiting teams” scored an average of 1.57 runs in the extra innings. I restricted the home team such that if they drew the bigger number, their “final score” was one more than the visiting team. Home teams that walk off are most commonly going to win by one. They can hit a multi-run home run and win by two (or three or four), but I kept them from going too crazy. They scored an average of 1.17 extra runs. As a point of comparison, in real extra-inning games from 2012-2016 visitors scored 1.09 extra runs per extra-inning game and home teams scored an average of 0.77. The average team would score (and give up) about six or seven “extra” runs per season. That’s roughly 200 runs over the course of a season, league wide. In 2016, there were 21,744 runs scored, so run scoring will “increase” by about one percent because of the new rule.

Finally, the other unintended consequence is that it will probably mess with the double-switch a little bit. This sort of extra-inning rule has been test driven in the World Baseball Classic and, presumably similar to the WBC, the person who is the physical runner will be the person who made the last out (or was at-bat last) in the previous inning. That is, if the sixth hitter is due up, the fifth hitter will go to second base and be the actual runner. In extra innings, some managers like the idea of having a pitcher go multiple innings, because it conserves the number of pitchers who have to pitch in the game. The manager has to think about tomorrow as well. When the double-switch happens, normally the new pitcher is slotted into the spot of the last hitter who came up. I’m guessing that most teams wouldn’t want their pitcher pulling double duties as a ghost runner. This can be easily worked around by simply inserting the new pitcher into the second-to-last spot due up, but I thought it was interesting that the ripple effects ended up there.

It Probably Does What It Says on the Label

Yeah, the strategy probably does tamp down on the ultra-long marathon games. It still leaves open the possibility that one would happen, but it’s not going to be as likely. It seems odd for a sport that is trying to re-invent itself as more interesting, because the innings that would be lost are the most interesting innings of the year. Or at least the people who would have stuck around past the 10th inning of a three- (going on four-) hour game understand that these are the most interesting innings of the year. Or at least they’re the kind of people who wouldn’t mind a game stretching on for another half-hour. Hey, even the people who are casual fans can appreciate a good “sudden death” sort of scenario.

If this is about the bullpen blowout games and utility infielders pitching, then yeah, it probably takes that joy away from all of us. Again, the people who are still around in the 10th inning are the people who would probably get a kick out of it, but hey I’m not going to be the one with a sore arm tomorrow or the one who has to make frantic calls to the team’s Triple-A affiliate asking who’s available for an emergency flight out to provide some cover in the bullpen.

I do wonder if the spectre of having to face this sort of alternate situation changes a manager’s strategy. On offense, a team would certainly try to score when they could, but would bullpen usage change? We know that teams are loathe to use their closers in tied extra-inning games even though they should, especially on the road. If his team didn’t score in the top of the 10th, would the urgency of knowing that there was going to be a runner on second change his mind and would he send the closer out in the bottom of the 10th inning? His closer would have to get through the 10th unharmed and in a best-case scenario would still have to escape the 11th when the other team will once again get a free runner at second. Again, despite the fact that managers tend not to send out their closers into a tied bottom of the 10th now, perhaps the salience of the fact that his team is only one hit, rather than one run, away from losing might tempt him to be a bit more cautious.

In the top of the inning, if the visitors bunted their free runner over to third, would the home team play the infield in to try to cut down the run, knowing that they would go into the bottom half of the inning with a runner at second, and thus a decent chance to tie? My guess is yes, but it’s one of those things that we need to ask.

If the game is still tied after the top of the 10th, would we begin to see a lot of leadoff intentional walks or … pointings down to first? If the guy due to leadoff is a threat, why bother pitching to him? In the old rules, you don’t put the winning run on base, but he’s no longer the winning run. In fact, his run is meaningless if he does score because there’s already a runner on second. Plus, let’s set up more force plays! In fact, in the top of the inning why not intentionally walk the first batter if he’s not someone you want to face? It is putting extra runners on, but the most important run that you have to worry about is the run that unties the game.

Ack, so many questions for such a little rule change.

By the way, for those of us who are keeping score in the stands, how do we notate how that runner got there on our scorecards?