How Much Luck Is Involved in One-Run Games?

The Orioles shocked the baseball world by making the American League playoffs last season, based largely on a 29-9 record in one-run games. This .763 winning percentage in one-run games was the best in baseball and had every analyst who knew how to calculate a Pythagorean record screaming, “Lucky!”  Was the Orioles record in one-run games lucky? Or, the better question is, how much of it was luck?

“Luck” is a dangerous word in baseball analysis. If a hitter has a .450 BABIP or a pitcher has a 3.5% HR/FB, us saber-minded analysts usually chalk it up to luck and move on. To equate the difference of the rate from the league average is a disservice to the players. Oftentimes, some of that middle-ground can be explained. For example, a few years ago I looked at Matt Cain’s HR/FB rate and found that much of his “luck” can be attributed to inducing a lot of infield fly balls and out-of-the-zone contact.

By modeling a team’s record in one-run games, it becomes possible to find if there are certain types of teams that are just better equipped for tight games. The goal is to better determine how much of one-run record is skill, and how much is still unexplained.

I used a logit model, with the team’s win-loss record in one-run games as the dependent variable. I used 2007-2011, holding last year out of the sample to make projections. The independent variables were measures of the team’s skills for hitters, starters, and relievers and the team’s park effect. Included were measures of strike out rate, walk rate, power, fielding, and baserunning.

The resulting model showed that there are certain team attributes which lend themselves to better records in close games. However, the model had limited explanatory power. There were only three significant coefficients: isolated power for hitters, and strikeouts per nine and walks per nine of relievers. This means that those three variables are the most important for explaining a team’s one-run winning percentage. The reliever skill is not surprising, but it is unexpected that hitter power is more important in one-run games than contact rate or walk rate. It is also surprising that baserunning and fielding skill have almost no effect on one-run games.

I also ran the same model for greater-than-one-run games for comparison. The below graph shows the three significant variables’ effect on one-run games compared to their effect in greater-than-one-run games. Understandably  a team’s relievers have more effect on one-run games than in all other games.


This model helps make sense of the 2012 Orioles and shows just how much we can’t explain. On one hand, the skills that this model identified were strengths for Baltimore. The model projects that the 2012 Orioles would have had a .647 winning percentage in one-run games, not bad considering they only had a .512 winning percentage in non-one-run games. On the other hand, the projection is still 116 points lower than Baltimore’s actual performance.

one-run2 fixed

Is that gap luck? Certainly there are variables that my model does not include because they are difficult to measure; managerial skill, bench composition, clutch. Even with those and others included, a model would be unlikely to project any team for a .763 winning percentage in one-run games.

It would be hard to argue, at least from a stats perspective, that the 2012 Orioles weren’t lucky on some level. However, their magical season cannot just be dismissed. Baltimore had a perfect storm of team skills which led them to an excellent record in one-run games. Using a model, we can better explain how much of their performance was due to those skills and how much was, well, TWTW.


Print This Post

Jesse has been writing for FanGraphs since 2010. He is the director of Consumer Insights at GroupM Next, the innovation unit of GroupM, the world’s largest global media investment management operation. Follow him on Twitter @jesseberger.

39 Responses to “How Much Luck Is Involved in One-Run Games?”

You can follow any responses to this entry through the RSS 2.0 feed.
  1. Steve says:

    Is that last graph legend flip/flopped? Orange is saying their win % in 1-run games is around .500

    Vote -1 Vote +1

  2. Bill says:

    O’s did not win the AL East last year, unless, like me, you irrationally believe the Yankees are all juicers and so their accomplishments should be ignored. In which case, no edit required.

    Vote -1 Vote +1

  3. Nelson Harper says:

    It’s always interesting when professed scientific analysts of baseball fall back on “luck” when they cannot explain something. I commend the author here for making a reasoned analysis of close game win %. Using “luck” as an explanation of what has escaped rational explanation to date is akin to using religion to explain the unexplainable in the natural world.

    -10 Vote -1 Vote +1

    • NeilS says:

      No, not at all. Random chance exists, and we know that it exists. It’s not that there’s a luck dragon out there, controlling who is lucky and unlucky – luck isn’t actually a ‘thing’. It’s just a word to describe an unlikely outcome. Getting five tails in a row is lucky, and we know that based on math, if not simple observation. Pretty simple.

      Religion, on the other hand, does premise that a ‘thing’ exists that controls outcomes. And you can’t use math to divine it, nor can you observe it – in fact, the whole idea of faith suggests that you’re supposed to NOT do either of those things. You just accept it. That TWTW joke at the end of the article? Now THAT’S religion.

      +28 Vote -1 Vote +1

    • Ryan says:

      Awful analogy.

      +12 Vote -1 Vote +1

    • Synovia says:

      “No, not at all. Random chance exists, and we know that it exists”

      Of course it does, but that doesn’t make the baseball world’s fallback on luck for everything they haven’t been able to explain yet any less lazy.

      I still see people on this site saying Pitcher BABIP is luck, and then half a second later talk about weak contact because of hitters swinging at pitches outside the zone, indicating that its most likely not luck.

      Why can’t people just say “we don’t understand this yet,” when they don’t understand, instead of foisting it off on luck.

      +5 Vote -1 Vote +1

      • Nelson Harper says:


        Vote -1 Vote +1

      • Baltar says:

        Because every time a thing can’t be explained or has no predictive ability it would be extremely awkward to put in all kinds of hedge words and phrases. Understand that when most of say “luck,” it’s kind of a shorthand for something like “a thing that can’t be proved yet, if ever, so is assumed to be random chance until proven otherwise.

        Vote -1 Vote +1

        • rbenchley says:

          Very similar to a quote from the Douglas Coupland book Microserfs: “Randomness is a useful shorthand for describing a pattern that’s bigger than anything we can hold in our minds”

          Vote -1 Vote +1

  4. AJP says:

    And so begins TWTW’s era of sabermetrics.

    Vote -1 Vote +1

  5. MyrEn says:

    The conclusion is that it wasn’t all luck.

    Can you make any other conclusions? Would a follow on conclusion be that those three factors help you to an overall better record? In other words, does a better record in one run games lead directly to a better overall record? Or do those additional wins come as a subset of how much they should have won anyway, just that they won in closer games?

    Vote -1 Vote +1

  6. kdm628496 says:

    using .647 as the “true” win percentage and normal approximation, i got a z-score of ~1.5 for 29-9 in 38 games, which is within the 90% confidence interval.

    cool stuff, jesse. keep up the good work.

    Vote -1 Vote +1

    • Baltar says:

      Yes, Jesse’s work here is extremely cool. I would love to see how well using these 3 factors predicted other teams one-run game success, specifically Tampa, who was at or near the other end of the scale to Baltimore last year and is starting out the same this year.

      Vote -1 Vote +1

  7. Frank Campagnola says:

    “it is unexpected that hitter power is more important in one-run games than contact rate or walk rate.” I don’t find this too unexpected at all. SLG has the highest correlation to scoring runs of the BA/OBP/SLG triple slash. It would then seem to follow that ISO would be a factor in late and close games.

    Vote -1 Vote +1

    • Ryan says:

      Indeed, it seems from examining the graph that while ISO is much LESS valuable in 1-run games than >1-run games, ISO is simply a very powerful component in general.

      Vote -1 Vote +1

  8. Incitatus says:

    Speaking of luck…

    I was thinking yesterday about the degree to which clustering your hits or walks together influences scoring. It seems to me that, unless you believe in a clutch factor, individual hitters can’t choose to get on base just because another hitter did so in the same inning (although if the pitcher is melting down, it might look that way). Hitters are going to get on base some percentage of the time, but they can’t all agree to do it in the same inning. And yet getting all your OBP for the game in a single inning is going to make for a lot more runs scored than scattering your hits and walks across the full nine. So clustering of OBP events should constitute a major “luck” factor in runs scored (and therefore winning percentage). Has anyone ever looked at analyzing that? Crudely, and off the top of my head, I wonder how often a typical team bats around in a season, and if that number could be somehow normalized for the team’s overall OBP to find out which teams were “lucky” in terms of OBP clustering.

    I’m no statistician, though, so I will not be posting an article about this to community research anytime soon. Does anyone know if someone else has looked into the subject?

    Vote -1 Vote +1

    • Jon L. says:

      Offhand, I’d say there are too many factors in play to ever say when a team batting around is “luck.” Any pitcher can, at will, induce opposing batters to reach base safely, and it’s not really fair to credit an offense for a pitcher losing command.

      Then again, I suppose you could look at big-inning BABIP. I remember a couple of weeks ago the Angels knocked Rick Porcello out in the first inning while barely hitting the ball hard (well, at least until Mike Trout stepped up with the bases loaded and a 5-0 lead). Peter Bourjos hit bouncers to the shortstop both times up (fielded cleanly, no less) and finished the inning 2 for 2 with 2 runs scored.

      Vote -1 Vote +1

  9. OldDogScout says:

    Nice departure, with a LOGIT routine, from the usual approach exhibited here of attempting to determine everything thru a strict interpretation of linear modeling.

    However, you’re stats are limited due to the data.

    Hypothesis to test: consider the % of RISP as well as the quality of those RISP setups inherited vs allowed as your independent variables along with SLG as you’re now capturing the effect, but not the cause.

    Food for thought for an interesting start.

    Vote -1 Vote +1

  10. Synovia says:

    “but it is unexpected that hitter power is more important in one-run games than contact rate or walk rate”

    This isn’t surprising to me at all. Close games are usually low scoring games, and low scoring games usually aren’t won in the sort of situations where there are a couple of walks and a single, etc. They’re won by a double or triple early in an inning, or a homerun.

    IE, in games where LOB is going to be high, walks and singles have less value than usual. Homers and XBH have more.

    Vote -1 Vote +1

    • Baltar says:

      Are one-run games usually low-scoring? I’ve often seen that assumption said but never supported.

      Vote -1 Vote +1

      • Mike Tremblay says:

        I believe that “one-run games are usually low-scoring” is a wrong assumption to make, especially in this situation. As you note, it is a common assumption with little support demonstrated.

        In this case it is more valid to point out that the run differential is small and therefore home runs and extra base hits have more value. Larger run differentials make getting on base more valuable – you can’t score two or three runs with one hit if you have nobody on base.

        Vote -1 Vote +1

  11. Rufus says:

    Interesting analysis for sure. But I feel pretty confident in saying that there’s a very good chance the model is overfit, and that the effects (if they persists) will decline in magnitude going forward. A lot easier to explain something than predict it…

    Vote -1 Vote +1

  12. D. Russo says:

    Is there any chance you could reveal what software you used for this analysis?

    Vote -1 Vote +1

  13. Jesse, great analysis! Hope to see more articles from you on this.

    About your findings about isolated power for hitters and K/9 and BB/9 for relievers, those do make some sense to me.

    Power relates to SLG which is the key lever in the formula for runs scored, in terms of driving in runs. The more power involved, the more likely the team is to drive in a run (you mentioned OBP and contact rate, and it is true that you can’t win without the runner, but once you do have that runner, you need to be able to drive them in, and that, ultimately, is the key to winning, not getting on base).

    Of course, K/9 is obviously a key thing because that very rarely results in any runners moving up 90 feet. BB/9 is perhaps key, not because of the getting on base aspect, which as we saw with hitters, not that important, but because it is an indicator of how wild the reliever is in general, and that lack of control would lead to poorly thrown balls that results in a run scoring.

    Vote -1 Vote +1

    • Hopefully you can start with this idea as your next article. :^)

      I was looking at Bruce Bochy’s record in one-run games in recent seasons, a couple of years ago, and the saber rubric is that there should be a regression to .500, and he had a very high plus differential in W/L. He had some very high numbers so that got me curious. So I dug deeper into his managerial career and worked my way to his start, as I found that, during his time in the NL managing, he has the highest plus differential.

      Using simple null hypothesis, I could show that, assuming .500 is a manager’s talent as the null hypothesis, it was more likely that his talent level was above .500 in terms of one-run games at the 90 or 95% level (can’t remember which). Given that it was just barely met and that he was the highest, it appeared to me that he’s the only NL manager during his career that can have that said about him.

      I have no idea what statistical tools you are using, but I’m hoping you can investigate Bochy’s career numbers the same way you dissected the Orioles for 2012, and see what can be said about his abilities in one-run games.

      The interesting thing about Bochy is that when you rank each season by +/-, he was among the top managers in NL in plus differential in over 40% of his managerial seasons (he represented about 6-7% of the total managerial seasons), and has averaged roughly 4 wins above .500 in one-run games over his career.

      Vote -1 Vote +1

      • channelclemente says:

        OCGF, do you see any indications of your hypothesis in Bochy’s performance as a manager with regard to his teams’ performances relative the Pythagorean expectation?

        Vote -1 Vote +1

        • Sorry, channelclemente, didn’t see your response until now.

          I’ve not looked into it, but that’s a good idea, I had done analysis regarding differences with Pythagorean before and found that some managers were consistently over (like Dusty and Felipe) and some managers consistently under (Lasorda) and some managers who were bad when their teams were bad but good when their teams were good (Joe Torre). It was not perfect, but generally the good managers were above, the bad were below, with anomalies galore (relative to reputation, like Lasorda; based on this, he really cost his team a lot during those years).

          I did a null hypothesis examination of 0 being the mean, and found no manager to be above the 95% threshold, but there were plenty of them in the 60-80% level, so very close.

          Vote -1 Vote +1

      • David Bowser says:

        I would point out one thing that is not a knock on Bochy, but simply a factor of his teams, and more specifically the closers for most of Bochy’s career wins: Trevor Hoffman career 9.4 SO/9 and 2.4 BB/9, Brian Wilson career 9.6 SO/9 and 4.0 BB/9. Those those SO/9 numbers are pretty good averages when totaled for 20 years.

        Vote -1 Vote +1

  14. beckett19 says:

    Could you post the actual formula for the logit regression? I’d be interested in playing around with it/ using it on this year’s teams

    Vote -1 Vote +1

  15. Sports Enthusiast says:

    Maybe teams should put out a team of all-bat no-glove players behind a ground-ball inducing soft-tosser late in games and in extra innings rather than, as they usually do, put in glove-first no-bat replacements behind a flame thrower.

    Vote -1 Vote +1

  16. adrian_brody says:

    Is there any metric to determine player bowel movements yet? I would imagine that teams with bathrooms in their bullpens tend to have an advantage over teams that do not.

    I would never put a bathroom in the visiting team’s bullpen

    Vote -1 Vote +1

  17. Andre the Angels Fan says:

    Amazing. This also does a lot in explaining the Angels World Series victory in 2002 (high ISOs, shut down relievers), and at least partially validates that particular theory of post season success. Great work!

    Vote -1 Vote +1

  18. Fu Manchu says:

    It looks like the Rangers had a better ISO, reliever BB/9, and reliever K/9 than the Orioles last season. Their record in one run games was 24-22.

    Vote -1 Vote +1

  19. VeveJones007 says:

    “However, the model had limited explanatory power.”

    Can you provide this information? It’s useless to consider the rest of the article unless we see a Pseudo-R^2 (or similar) >.300. After that, it would be useful to run it against all teams over a period of time to see how well the model fits.

    Vote -1 Vote +1

  20. DJ Tofu says:

    What’s your sample size of one-run games? And how many variables you have in total? I imagine if you will use more years, you’d get less spurious results.

    Vote -1 Vote +1

Leave a Reply

Your email address will not be published. Required fields are marked *

You may use these HTML tags and attributes: <a href="" title=""> <abbr title=""> <acronym title=""> <b> <blockquote cite=""> <cite> <code> <del datetime=""> <em> <i> <q cite=""> <strike> <strong>