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A few weeks ago, the topic for the BP Lineup Card was "Unanswered questions for the second half." I noted that at the time, the Cardinals were several games behind both the Pirates and the Reds in the NL Central standings, despite the fact that they had a better Pythagorean record than either. In theory, the Cardinals should have been atop the NL Central.

As my father is fond of pointing out, everything works in theory.

The question that I posed was whether Pythagorean records were really a "true" gauge of a team's quality. It's a topic that has never been fully resolved. Are differences between actual record and Pythaogrean records a matter of luck, or do they reflect some underlying property of a team?

Both logic and previous research tell us that there's a really easy way to outperform your Pythagorean record: win a lot of one-run games. In one-run wins, the Pythagorean calculations see only that a team scored one more run than its opponent. The standings see that it won the game. So, are one-run wins a skill? The Orioles have a negative run-differential overall this season, but are an astounding 23-6 in one-run games so far this year, and as a result, are in the playoff hunt. Are they extremely lucky, or are they just gritty like that and "know how to win" the close ones?

There are a lot of theories on the issue: teams with good bullpens (or good closers) can protect close leads. Teams with good starters can overcome a bad offensive day. Teams with crafty managers can win because the manager can expertly push all the buttons. Then again, no one ever takes the contrary position. A team with a bunch of one-run wins might belie a bullpen or a manager who can bungle a five-run lead into a one-run lead, barely hanging on to fly the W flag over the stadium.

After studying the issue, I can boil down the recipe for winning one-run games to three words: wear white pants. Want to know how I got there?

First off, let's consider that there is a provision in the rules of baseball that encourages games to end with a difference of one run in the score. In the bottom of the ninth (or an extra inning), as soon as the home team takes the lead, the game ends. While the final margin of victory can be as many as four (game tied, home team hits a grand slam), the most common case is that the home team takes a one-run lead and then throws pies at each other.

In fact, while home teams win roughly 53-54 percent of all games, they won 61 percent of all one-run games from 1993-2011. Games won by the visiting team are decided by one run about 23 percent of the time, but home teams collect 31 percent of their wins by a single tally. Overall, 28.2 percent of all games are decided by one run.

The thing about a walk-off is that, by definition, the ninth inning (and game) ends before three outs are made. Suppose for a moment that we made the home team keep going until three were out. Indeed, a home team that protects a one-run lead in the top of the ninth leaves a whole bottom of the ninth on the table. If the home team took its turn as it was supposed to, it might score a few more runs… and suddenly, it's no longer a one-run game.

There are a few other interesting things about one-run games that might be instructive. First off, they are generally lower scoring than other types of games, with one-run games featuring an average of eight runs between the two teams vs. 10 for games decided by other margins. Then again, a good way to make sure a game is not a one-run game is for one team to score 12 all by itself. I restricted the non-one-run-game sample to games decided by either two or three runs. These games featured, on average, 8.6 runs, and the difference was still significant.

Not only that, but games decided by one run tended to be closer-played games, even after the first inning. In a game that is eventually decided by one run, the average deficit between the two teams after the first inning is .72 runs. In all other games, it's one run even. Restricting the non-one-run sample to games that end with a two- or three-run win (.82 runs, for the curious), the difference is still significant. One-run games tend to be low scoring and more closely played, even from the outset. A good starting pitcher might be helpful there.

But hold on: about 30 percent of one-run games are shootouts featuring at least 11 runs, and 10 percent feature 15 runs or more. An offense that can keep up with the Adam Jones-es would be helpful in these games, because the pitching staff isn't having such a good day.

What about the theory that a good closer is the key? Let's take a look at what games that are eventually decided by one run look like headed into the ninth.

• Fifty percent enter the ninth inning with the team that eventually wins by one run up by one run. Most commonly, this represents a scoreless ninth. This is the work of a good closer. Occasionally, it's the mark of a closer who gives up some runs, but his offense bails him out (or if he is the visiting pitcher, his team scores a few runs in the top of the ninth, and he does his best to give them back.)
• In roughly a quarter, the teams are tied after eight innings. Here, both the pitching and the offense need to come through.
• In 14 percent, the team that wins by one was actually ahead by more than one, meaning that the closer gave up runs.
• In 11 percent, the team that won went into the ninth trailing. Here, the heroics will have to come from the offense.

The thing about all these numbers is that you can make a case that strengths in certain areas of the roster would lead to success in one-run games. It's hard to argue that roster talent would be inconsequential to winning one-run games, but it's harder still to say that a general manager would get the most bang for his buck by focusing on X.

For a moment, I want to focus on the 25 percent of one-run games that go into the ninth tied. In some sense, from this point onward, the fundamental characteristic of the game has changed. From this point onward, the game is a series of one-inning sudden-death games. Prior to this, if the opponents scored in the fifth inning, you could make it up in the seventh. But no more. From a sampling perspective, we've gone from a nine-inning sample of team quality on that day to a one-inning sample. Smaller sample sizes mean more variance: anything can happen in extra innings. More than that, we're talking about a handful of plate appearances. Even a good reliever can have a bad day.

I once found that Pythagorean residuals—that is, how much a team over- or under-performs its Pythagorean record—are correlated with the team's overall winning percentage, although only moderately. Teams that win 100 games have somewhat of a tendency to out-perform their Pythagorean records, while 60-win teams tend to under-perform, but there are plenty of counter-examples. At the time, I wasn't sure what that was about. I'd hazard a guess now that what we're seeing is that teams that have good players are more likely to win games in general. These are players that you would want on the field in a close game where the game hangs in the balance. So, there probably is an advantage to having them that shows in the residuals. The problem is that as the game reaches its autumn, the element of randomness creeps in all the more. In extra innings, all you need is one good (lucky?) swing of the bat. Good players are more likely to take that swing, but even bad teams score runs now and again.

But let's do one more test. Let's look at how reliable performance in one-run games is. I'll use the KR-21 formula that I introduced a few weeks ago. For my sample, I'll look at all games between 1993-2011 that were decided by one run or more. For each franchise, I took a five-year block of games (1993-1997, 1998-2002, 2003-2007, 2008-2011… yes, I know that last one is only a four-year window) and treated them all as big long seasons. This was to increase the number of one-run games that I could look at: since real teams play only about 40 one-run games in a single season, I needed more data to work with. There are plenty of problems with this analysis strategy, but the idea is that even over the course of a few years, a team maintains a lot of the same players (usually). It's not perfect, but it's about the best we have available.

I looked at the reliability of a team's record in a single one-run game, then in two one-run games, then three, all the way up to 100. The KR-21 reliability settled in around .30 when I got all the way to 100 one-run games. At 40 games, which is roughly the number that most teams play over the course of a season, reliability was a paltry .17.

This suggests that the one-run records of most teams are not stable. If we gave the Orioles another 29 one-run games, they are not likely to go 23-6 again. Sorry, Orioles fans, those orange uniforms are probably going to turn back into pumpkins.

The Conclusion
To say that there is no skill in a team winning one-run games would be wrong. Teams that are good at scoring runs and preventing the other team from doing so will have a better chance at winning them. The problem is that one-run games actually happen in several different ways, and winning them would rely on the abilities of different parts of the roster. The way in which they unfold, often involving extra innings, adds an extra layer of variability over and above that of a normal game. Baseball is a game with a lot of randomness in it already, and that randomness overwhelms the effect of skill. Based on this, I wouldn't recommend reading much into a team's one-run record.

If your goal today is to win a game by one run, may I suggest the most predictable way of all to ensure that it happens: wear white pants.

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Agent007
8/27
I think you backed off in your analysis. There's no doubt that one-run games can hinge on a bloop single or swinging bunt, and that weak teams are as likely to get that kind of hit as are stronger teams. But weak teams have an inferior lineup to stronger teams, and almost always have a weaker bullpen. A team with a strong bullpen should prevail more often. Isn't that what the Orioles have been doing? Not only have Jim Johnson, Pedro Strop and Troy Patton been extraordinarily effective, but the rest of the members of the bullpen have also been effective most of the time. All of them, not just three of them. They've won their last 12 extra inning games, games which stretch the resources of any bullpen (and probably reward the deepest 'pen). The Orioles haven't won very often with nine-inning last at-bat heroics (like Oakland, for example), but have won in the 12th, 13th, 15th, 17th after not scoring (most of the time) in the earlier extra innings. It's the bullpen that stymied the other team... How often has the Oriole bullpen shut down their opponents in the 7th, 8th and (not "or") 9th? Doesn't that throw the model off?
pizzacutter
8/27
I recommend Sam Miller's article on the subject (from today). Bullpen performance is beset by all sorts of small sample size problems and luck.

It's true that the Orioles have played a lot of extra inning games, which are best won by good bullpen performance. To put it less charitably, the Orioles have been fortunate to be in a bunch of the type of one-run games that have called for a good bullpen and fortunate that their relievers all seem to have four-leaf clovers in their back pockets this year.

The model only sees games that end in one-run. Suppose that the O's go into the 7th inning leading by one, and pitch 3 shutout innings. The game ends with a one-run O's win. Conclusion: Good bullpen performance, but why didn't the offense make it a 3 run game?
Agent007
8/28
I agree. The Orioles do not have the best offense. The bullpen has been (most of) the story this year.
prs130
8/27
I would actually expect a team with a heterogenous bullpen, rather than a uniformly good bullpen, to outperform its pythag. Most managers use their two or three best relievers to protect slim leads, or to keep the other team's lead small. They use the rest of the bullpen to eat innings when the the score isn't so close.

So a relief core that's top-heavy -- two or three great relievers and three or four terrible ones -- would seem to play tough in close games; get landslided if the other team had an big early lead (negative effect on overall run diff); and cough up big leads, turning them into smaller ones (negative effect on overall run diff). Landslide victories would be rare, landslide losses would be occasional, and great relief arms would contribute to a higher W% in close games.
pizzacutter
8/27
A team with 2 or 3 good relievers wouldn't be able to hang around in a 19 inning game, unless the other team's pen is just as bad. Perhaps they are lucky enough to be involved in games that don't call for that. Perhaps not.
Agent007
8/27
Sorry. It should read "ninth-inning heroics", not nine-inning heroics.
CrashD
8/27

"Baseball is a game with a lot of randomness in it already, and that randomness overwhelms the effect of skill."

I would agree with the first part of the sentence, but not the latter. I could base my disagreement on Gory Mathematical Details about the many possible distributions of residuals, but in the interest of time I would suggest an alternative definition of skill, namely the capacity of an individual to overwhelm the effect of randomness.

I believe it was Confucius who responded, when he was asked what he would do if he were Emperor, "I would establish the precise meanings of words."

I also believe it was Confucius who was the first to say, "GO ORIOLES!!!!!"
pizzacutter
8/27
I believe that you mis-understand what I'm saying there. We agree that baseball is a game with a lot of randomness in it. At least the way that I'm measuring things, there doesn't seem to be a lot of repeatable skill on the team level as to what happens in a one-run game. In the same way that the playoffs are a crapshoot (because of the shortened timeframe, which breeds more noise), an extra inning game is really a 1-inning game... on the team level, that breeds more noise.

Also, 1000 bonus points for using antepentultimate correctly.
8/27
Look at the run differential of the AL Wild Card contenders and tell me what team doesn't belong...I predict an Oriole September swoon.
rbtgt3
8/27
Most of what I know about the topic is what Bill James said in devoting a chapter to the topic in an edition of Baseball Abstract.

And that was that a team's record in one run games was largely meaningless and that a team's records in blowout wins or losses was far more significant. I have stopped paying attention to one run blather ever since.

Great example. My Kansas City Royals. 56-70 overall. 20-16 in one run games. Pythagorean split is 58-68. More importantly, 12-19 in blowouts (defined as 5 runs or more). The shoe fits, here. In fairness, I checked no other team before posting, though.
Oleoay
8/27
Skill is the ability to create a situation where you are able to take advantage of luck.
CrashD
8/27
Or, "luck is the residue of design", as Branch Rickey is said to have said.

Oleoay
8/27
I was aware of the Branch Rickey quote, though after I came up independently with my own version. "Skill is the ability to turn luck into your advantage or to the disadvantage of your opponent." Except, that saying was applied to Battletech and dicerolling, not baseball ;)

And I'm glad you like them. Every so often I get a wave of minusbats so it's nice to be reassured.
mnsportsguy1
8/28
I ripped you a few months back Richard, and now i'm coming back to apologize. Your comments have been outstanding, keep it up, hopefully I can keep up with you someday.
Oleoay
8/28
Thanks for the apology but, not only wasn't it necessary, but I truly learned from that comment. I really hadn't noticed how much I commented when compared to others until you mentioned it and it made me reevaluate quite a few things.

I thought about quitting, not because I was pissed off or upset, but I felt I was too "locked in" to BP and wondered if my time should be spent elsewhere. So, I branched out a bit and explored other sites as well as worked on some side projects. I even went through an extended "quiet" period. Heck I even figured I could be quiet for at least a year until KG caught up to me.

So sincerely, thank you for that. It gave me a good opportunity to reassess and try to figure out if I still enjoyed here as much as I used to and whether it was worth my time or not, especially since most of my favorite authors had left. In any event, I'm still here for at least another year and the reality check definitely helped.
mnsportsguy1
8/30
You are very welcome, Good to know my occasional crankyness can also be helpful
therealn0d
8/27
Really, skill is he ability to keep luck from mattering. Skill should eliminate luck. Luck is a coin toss. Skill would create situations that avoid coin tosses, not create them...because they can't be taken advantage of reliably.
Oleoay
8/27
Luck always matters.

There's no level of skill that will make a baseball hit a rock and cause a bad bounce but there is a skill in being able to adapt to a bad bounce to successfully field a ball. Luck also has to do with mental coin flips, where people, when faced with a 50/50 or value judgement decision and arbitrarily decide one way or another. A runner deciding whether to go to an extra base has a skill (speed) but is also "betting" that the outfielder doesn't make the so-called perfect throw, that they don't twist an ankle on the basepaths, etc.

However, if you tend to do certain things well, you can, as you said, neutralize luck or use a lucky situation to your advantage. You are more likely to succeed in catching that bad hop or taking that extra base. If you're a batter and the incoming pitch is flat, a skilled hitter is more likely to use such a lucky occurence to hit the ball with power than an unskilled hitter.

Another way to put it is that you could be the best driver in the world and still be unlucky enough to be around a below average driver and get in a car accident. However, the best drivers are less likely to be in car accidents in general.
fantasyking
8/27
It seems that you effectively broke down some of the ways that baseball games end in a one-run differential. But did you actually test the hypotheses listed?

For example, did you compare the W-L percentages in one-run games of teams with superior and inferior bullpens? Did you look at managers over time to see which, if any, consistently outperformed the others in one-run games?
TGisriel
8/27
Unfortunately, I did not find this article particularly enlightening. There were some good, but common sense insights (Home teams win a higher percentage of 1 run games than games generally, and extra inning games are a series of one inning games)

The design of your study, I believe, is flawed. Grouping three years of a team as the element of your study undermines the study. Teams change year to year in personell, so it is hardly surprising that their one run record changes.

While I have not done a study, my observation is that being over or under Pythagorean record is not a "repeatable skill". The only team that I have observed be consistently over its Pythagorean record was the Earl Weaver Orioles. I'll chalk that up to one of the best managers in history.

Jay Jaffe did a study a few years ago that concluded that a strong bullpen correlated to being able to out perform a team's Pythagorean record. We agree that a better than Pythagorean record is correlated with an above average record in 1 run games.

I'll stick with that until a better study comes along.
rawagman
8/27
I think the issue here may be that teams tend to change most often (warning: this was not researched) in the makeup of their bullpens. It is much easier, and seemingly more prevalent, for teams to blow up their bullpens from year to year, than to significantly change their starting lineups or starting pitchers.
hitmannls
8/27
I think there is definitely something about roster construction and manager tactics that influences this. Since the bullpen has already be discussed I'll add another variable, how about the bench and positional flexibility of the position players. My hypothesis is that teams with a lot of unbalanced rosters may rack up margin of victory when staked to early leads, but teams that have balance 1-25 will have an advantage if the score is tight in the late innings.
hitmannls
8/27
I don't know how to articulate this, but I also think you can build a team that more "efficiently" allocates its run differential over 162 games.

Due to randomness wouldnt we expect a team that scores 600 runs and allows 500 to win more games than a team that scores 1200 and allows 1000?
eighteen
8/29
You gotta be kiddin' me. Everyone knows teams win one-run games because the players know how to win, and play the game the right way, and do the little things, and have great chemistry that motivates everyone to step up big in the clutch.

How hard is it to get that?
Oleoay
8/29
You got it wrong. What matters is who prays to God more.
KaiserD2
8/30
I'm a couple of days late here but this is one of my favorite topics. The Cleveland Indians of 1948, subject of my book Epic Season, had a dreadful record in one-run games. A number of them could easily be blamed on the very debatable bullpen decisions of manager Lou Boudreau. Nonetheless, I am convinced that one-run games are a matter of luck. No team or manager has ever demonstrated a consistent ability to win them. In general, better teams will win more of them. Teams in terrible hitters' parks will play more of them, and thus win and lose more of them. I think a lot of contemporary sabermetrics is really an attempt to deny the enormous role of luck in baseball--which incidentally is probably what makes it so entertaining.
AWBenkert
1/21
I think team analysis involving run differential would be more accurate if runaway scores were collapsed. Often, a team trailing by a large margin in the late innings will put in their worst reliever or even a position player to pitch. While there may be a significant difference between 3-2 and 7-2, there is not much difference between 7-2 and 12-2.