How Big is Home Field Advantage? Intro (by JonathanF)

Alex has asked me to do something that scares me a little bit. So I’m going to try it. I am troubled by the size of the home field advantage in baseball — it seems way too small. So I’m going to do a study, but Alex wants me to do it in public at Braves Journal, so I’ll give it a try. Let this post be an introduction, and we’ll see how it goes.

Baseball is unique as a sport in a number of ways. First, more than any other game, the rules as written favor the home team. (I am limiting this thought experiment to the four big US sports, plus soccer.) Hockey is a distant second, and football, basketball and soccer are essentially home/road neutral. Hockey comes in second because it allows the last change to the home team in a faceoff situation. But the baseball rule which allows the home team the last at-bat should be a sizeable advantage for any number of strategic reasons, and no other sport has anything like it.

Baseball is played on the least uniform set of fields, by far, allowing teams to differentially accomodate themselves to their home parks where they play half their games. This should both increase their fitness at home and decrease it doubly on the road. (Hockey gives a penalty box placement advantage to the home team, and of course some rinks are smaller than others, though most are the same size. Football has surface, weather and wind differences. Basketball has, I suppose, different sightlines and the famed Boston Garden dead spots, but that’s about all I could come up with. Qualitatively, the Pesky Pole, Citizens Bank Park’s fences and Coors Field should easily surpass all of these.)

Baseball also has by far the longest season and a unique pattern of series of games, rather than one-off games randomly sequenced through the season. Thus, when a baseball team arrives in a town, they play two, three or four games; almost never one. No other sport does this. I think this effect should lower the home-field advantage somewhat, although the mechanism is to me somewhat unclear.

There have been a number of studies of home-field advantage in a number of sports, and a fairly recently published metastudy, by Jeremy Jamieson of Northeastern University, across sports. The result is that baseball has by far the smallest homefield advantage. This is attributed (at least in this article and somewhat tentatively) to the long season, though I have no idea why a longer season should lower the home field advantage.

Jamieson makes the argument that in long seasons, individual games are less important, so whatever effects there are of fan rooting or umpire’s psychological desires to please rabid home fans will be reduced by a less boisterous crowd. In addition, he notes that playing three games in a row somewhere might lower the home field advantage somewhat by some sort of acclimatization or reduced travel per game effect.

I don’t buy it, but of course I’d like to see what the data say. And they certainly don’t account for the fact that sport that by its rules ought to have the highest home field advantage has the weakest. Somehow, the long-season effect must be much bigger than the rules and parks effects which go the other way. Does that make sense to you?

So what I’ve done thus far is download the linescore of every baseball game in history. I’ve made a few quick tabulations that I’ll present in the next installment (if there is one!), but I’d like people to look at the Jamieson study and/or give me their thoughts in the absence of data. As I said above, this is, to my mind, a different way to do research, and a somewhat scary one, but we’ll see how it goes. I want to understand the home field advantage in baseball (I really don’t care about it in the other sports very much.) So… what do you guys think?

109 thoughts on “How Big is Home Field Advantage? Intro (by JonathanF)”

  1. Determining just how big the home team’s advantage is should be interesting. Fredi’s management might have something to do with it, but if a game is late and close on the road, I definitely find myself preparing to lose more readily than I would if the game were at home. I’d like to see how much the numbers back that up.

    I guess that’s something else to consider…does the homefield advantage look bigger than it should because of managers’ suboptimal bullpen choices in late-and-close road games?

  2. This is indeed a fascinating topic and you’ve done a great job of identifying the issues and apparent counter-intuitives. I look forward to this thread.

    Let me be the first to quote the “Momentum is today’s starting pitcher” canard – but it’s probably a canard because it seems to often be true.

    Without steroids, baseball approaches chess in spikes. My guess is Spassky won pretty much wherever he played.

    But this brings up a point I’ve been wondering about for awhile – assuming a healthy McCann, should the Braves move the RF fence in about 15 feet? Brian seems to hit a lot of fly balls that fall just short.

  3. Thought-provoking!

    So what I’ve done thus far is download the linescore of every baseball game in history.


    Skimming the study, the authors make brief mention of the innate differences between the games themselves, but restrict themselves to variables which can be contrasted directly (crowd size and density, season length, uniformity of playing fields, etc). One such innate difference is the democratizing effect of random error, which I take to be much higher in baseball than in other sports. That might be an avenue you could explore. Looking forward to reading more!

  4. Well, he mentions travel a couple of times early in the article, and that seems to be a really important factor. As he mentions, air travel wasn’t common until after 1950, and home field advantage was much greater before 1950. He also mentions research that provides evidence that the length of travel increases home field advantage.

    I would go one step further and look at rest. I would look specifically at the following questions:

    * What’s the difference between home field in the first game of a series and subsequent games of a series?
    * What’s the difference between home field after a rest (travel) day for an away team and home field after a game day?

    Rest doesn’t explain soccer at all, where teams travel short distances, and the games are spread out, but it could go a long way to explaining the other sports.

  5. Way to go, JonathanF! Can’t wait to see what you come up with.

    One other odd bit of homefield advantages is turf control. I bet that the groundskeepers left the grass long by third base for the last several years to slow down grounders for Chipper.

  6. It has always been my thought that because baseball is a team sport composed of individual efforts, home field advantage would be the smallest. The other sports require concerted group efforts that are far more subject to morale/esprit that would be helped by the home environment.

  7. This sounds so totally fascinating and cool. I’d really love to follow it as you proceed and understand what you are doing and how you are constructing your analysis. In reading this post, I’m wondering if you are not missing a big point about baseball – that any advantage or trend plays itself out across a long, long period, but is usually invisible at the more micro level. Micro level analysis of baseball is almost an exercise in chaos theory, while the macro trends of baseball are quite amenable to statistical analysis. So while the home field advantage might not be detectable when looking at game three of a three game weekend series featuring the Nationals hosting the Braves, over the course of the season this advantage should become more apparent.

    I’m looking forward to following this, and especially in seeing how you handle confounding factors in your analysis. That’s always been quite the trick in baseball.

  8. From the previous thread, I know Matt Harrison has been pretty decent, but I marvel at the possibility that he may be worth 5/55.

  9. The Braves Journal home-field advantage is astronomical. You’re not gonna get this sort of discussion at Metsblog!

  10. Harrison has been way better than decent, though, not to mention way better than anyone thought he’d be when he was in our minor league system. Over 2011-2012, he has thrown 399 innings with a 3.34 ERA, 134 ERA+.

    There’s no doubt that he’s outpitched his components. His K/BB over the period is just 2.2, and K/9 is just 5.8, so his FIP over the period is 3.79 and his xFIP is 4.00.

    But still, he’s pitched like a legitimate ace, and $11 million per year for a legitimate ace is a crazy bargain. Even if he regresses, he’ll be worth the money.

  11. Winning 60% of 162 games (97 wins) is enough for most divisional championships in baseball. Sometimes, but not often in other sports. Different starters creates 5 different line ups or teams. Hitters go 0 for 4 more often than QBs, RBs or receivers do nothing. More variancene than basketball and hockey too. Should performance of #1 and 2 pitchers be compared to 4s & 5s home and away? Baseball is a better game.

  12. I will sound old and out of touch with the scholarly study of the subject, but I would think the Cubs and Wrigley Field will be the outlier of any statistical analysis.

  13. Couple of thoughts. First, I’ve always wondered whether the last at bat is as much of an advantage as is commonly supposed. Has anyone studied the percentage of games won in the 9th or extra innings by the home team? I have a feeling it’s not as high a percentage as one would expect.

    Second, it seems to me that the affect of the crowd is less in baseball than in other sports. In football, the home crowd can literally affect the game by making it more difficult for the opposing team to hear snap counts.

    Third, I think the value of emotion is less in baseball than in football or basketball. Pumping up a team is probably useful in football or basketball but, if anything, being overly emotional in baseball can be a negative. I wonder if sometimes being tired can actually help a team by making it more relaxed. Plus, for a variety of reasons, most baseball crowds I think are far less raucous than football or basketball crowds.

    Fourth, I wonder if the random nature of baseball makes the home field less important. Almost every game sees line drives that are caught and seeing-eye hits; hanging curves at particular times of the game. In any individual baseball game-as opposed to the season as a whole-the winner is to a significant extent random.

    It’s an interesting study. I always felt that the relative lack of home field advantage made baseball a more interesting and fair game.

  14. Thanks, everybody who has commented so far. Your comments are all really interesting. Let me start by saying that Joey T is exactly where my starting hypothesis was. My going-in hypothesis is that it is overwhelmingly travel-related. And my first set of tabs will include exactly the study he suggests: initial games vs. subsequent games of series. That said, those inital tabs are not going to prove the slam-dunk I’d hoped for, but stay tuned.

    To some of the other comments:
    Adam R: Nice thought getting at the quantification the other way — if the rules advantage comes from last at bat, then we ought to be able to quantify it from extra inning games. That will give us some insight at how big a home-field inherent advantage we’re looking to overcome. Hadn’t thought of that.
    justhank (and to some extent sansho1,jeff Ray and PaulV): momentum may be today’s starting pitcher, but unless it’s today’s starting pitcher on the road, but not at home I don’t see how that helps answer the question. Several of you have noted that baseball games have higher variances. That’s true, but as I hope to explain in a later installment, it is more or less irrelevant to home-road splits. The noise is raised, but we’re trying to look at the signal, and we’ve got plenty of games to estimate the signal.
    Mark Grogan: The Cubs are always an outlier, mostly in terms of success. Bill James once attributed some of their lack of success to an excessive number of sun-baked home games. But if the Cubs are an outlier here, it will be easy to see.
    spike: hmmm. If you’re right, I’m screwed, because I can’t think of a way to isolate that effect. Anybody else?

  15. @19 In NBA starters play well at home and away. Refs give no breaks to bench on the road. No stats, just eyeballing.
    #1 pitchers may get better calls on roads than #5s.

  16. I was surprised by the finding that baseball had the smallest home field advantage because of the variances in ballpark configuration. One would think that 81 games in the home ballpark would give the home team some kind of advantage.

    But Spike @6 has pretty much hit the nail on the head. A great pitcher/hitter is a great player no matter where he plays. The numbers may be skewed by the park effects but the performance is the same.

    But JonathanF please proceed. I look forward to the results. Dang I love this blog.

  17. spike: hmmm. If you’re right, I’m screwed, because I can’t think of a way to isolate that effect. Anybody else?

    Well the obvious thing is to examine league home/road batting splits. If there is an inherent home hitting advantage one would think that would translate to runs and by extension, wins.

    Looking at the last three years of the NL, there is a BaBip advantage of .08/yr, and 9 points of tOPS+, and roughly the same for the AL. Can you translate that to wins, and does it agree with the actual home field advantage? Does the advantage vary over time and does it generally correlate to changes in batting splits?

  18. @19

    The point I was trying to get at (and which Marc @17 probably said more clearly) is that batted-ball luck is a significant factor in which team wins a particular game, and since this factor would tend to favor neither team, it serves as a .500 anchor against those forces which might tend to favor the home team.

  19. @22: Then maybe I didn’t understand your point, spike. I took your point the opposite way. Baseball, to have low home field advantage, must have lower performance differentials home and away than other sports. You attribute that to the individual nature of baseball within the team context. That might well be true. But there’s no way to see that only by looking at baseball statistics, since you’d have to compare the relative performance differentials with other sports. Your method will allow us to separate a pure performance component from a strategic “bats last” component. And that’s probably worth doing once I’ve explored the other stuff I’ve got planned.

    Just to rephrase: I assume that the wins and losses will more or less exactly translate into performance statistics at home and on the road (and separating batting from pitching is an interesting question here). That still doesn’t tell us why the hitting and pitching performances at home and on the road are closer in baseball than, say, football. Your hypothesis, a sort of joint team coordination effect, can’t be measued through baseball stats alone, so it’s not one I can explore through baseball stats alone. (I guess if I had a team chemistry variable, if your hypothesis is right, teams with good chemistry should have higher home/away splits. But I know of no obvious way to measure chemistry.) I guess I could compare the “We Are Family” Pirates with the “Bronx Zoo” Yankees, but I doubt that line of analysis would take us very far.

  20. @24: I don’t think that works. Suppose you had a game with no luck at all. So the best team won every game, the worst team lost every game, the next best team won every game except their games against the best team, and so on. What is the leaguewide homefield advantage in that situation? 0. Sure, one team wins all its home games, but that is balanced by another team that loses all its home games.

    On the other hand, assume every game is totally random. then there won’t be a homefield advantage there, either. The math goes through to every intermediate case. Home field advantage, so long as every team plays the same number of home and road games must, in the aggregate, be independent of all luck factors which are uncorrelated with who is home and who is on the road. So it doesn’t matter if those effects are big or small, except for the noise it puts in the estimates.

  21. @23 Smitty
    I agree, with my high-ranked Hoosiers taking a black eye in Wisconsin this week. We haven’t won there in 11 years.

    JonathanF, you’re the man for the job. Can’t wait to see your results. My question:

    We’ve heard how the flight to Seattle is loathed by most ballplayers. We’ll see how that translates for the Mariners’ record.
    But it used to be an easy buck betting against the loser of the Monday Night Football game the next Sunday. Can I bet against an MLB team flying into/back from Seattle with the same confidence?

  22. @25, I was proposing a method to test my initial assertion. If you can correlate a home hitting advantage to home winning percentage, it sort of invalidates my #6, if it’s by a persistent non-trivial amount. If it’s a demenimus advantage, it may just be the result of reps in a particular ballpark, regardless of whether it was one’s home or not.

    Or not. That’s why I am no statistician.

  23. OK, fair enough. I’ll probably take the question up again once you’ve begun posting your findings, and I’d urge you to consider the idea that whatever factors result in baseball being the most competitively balanced team sport overall might also affect the strength of home park effects. Regardless, whenever someone posts original research on the board, I’m digging it hard.

  24. Of course, baseball has less of a home field advantage.

    I think it has to do with the great effect of randomness on the outcome of baseball games. If the home field factor could be isolated and the effect of randomness removed, the rules and ball park differences would most likely show the greatest home field advatage in the MLB.

  25. I’m unconvinced that home field is entirely uncorrelated with BABIP. For example, in a park with really quirky dimensions, the away fielders may be more likely to misplay a batted ball than the home fielders. What’s more, teams used to have their grounds crews mess with the field in all kinds of creative ways, such as overwatering the infield dirt to slow down Maury Wills on the bases. In other words, on a game to game basis, there may be ways that a home team can take advantage of their home park. They may be vanishingly small, but I don’t know.

  26. I seem to remember a presentation at a SABR meeting, maybe 2009, about home field advantage and travel. The short answer is that the longer the series, the less apparent a home field advantage existed. I don’t remember if the presentation just looked at cross-country trips or all, but the my take away was that the home team won far more often in the first game of a series with advantage appearing to dwindle the longer the series lasted.
    Travel is an obvious factor.
    I’d be curious to analyze the results of truly poor teams. The old saying was everyone (even the bad Braves of the late 70s and late 80s) wins 60 and loses 60 games. The results of the remaining 42 games differentiates the winners from the losers.

  27. 31 – Along those lines, it seems like there are so many different variables to account for, but in the end they may be “vanishingly small.”


    Y’all read this DOB story yesterday? To me the big news is that the Horrible TV Deal is only 14 more years, not 19 more as I had previously thought. So that’s… something. Like the sentencing review board decided to lop a couple years off the end of our armed robbery conviction, or something.

    Also, if you’re state media and you’re trying to write a story about your team’s TV deal being crippling, you pretty much have to title it “Braves CEO Says TV Deal Isn’t Crippling.” When everyone knows how the Xinhua News Agency game is played, it can be lots of fun and even informative.

  29. @27 – that game was in Bloomington, I believe.

    Not crippling, my ass. Has he noticed what the price of even average talent is these days? And it’s only going to get worse.

  30. @ 19,
    To your last question: perhaps comparing the varience home/away defensive stats (which are somewhat cooperative and largely skill based), to the varience home/away batting or pitching stats (which are individual and somewhat luck based)? Of course, defensive metrics are so weird that may be no help.

    I certainly think the fielders get an advantage at home, as suggested @31. I have watched a lot of games at Coors Field, and I have seen many visiting outfielders misplay fly balls that carry over their heads. Coors is an outlier of course, but I would wager that it has one of the biggest homefield advantages.

    Maybe the home field advantage is muted in baseball because it only applies to one side of the ball.

  31. Does one get more accustomed to a particular batter’s eye or are they all pretty much the same?

  32. @37 There may be bigger disadvantage playing away from Coors. Curves break and pitchers have to relearn how to pitch. Coors destroys pitchers’ confidence.

  33. The nature and scope of scoring may be a factor as well. In football, there is no obvious reason for a homefield advantage (other than noise), but one bad pass interference call may result in 7 points.

    In soccer not only does 1 goal often win the game, but one must also consider the fact that the penalty/non-penalty call is often among the most controversial in sports and happens nearly once a game. Oh, and home teams are nearly twice as likely as visitors in european soccer to get a penalty call their way…

    All of this is a long-winded way of saying that the emotional stability of officials may be the reason the other sports have so large a homefield advantage. It’s not that baseball has an abnormally small advantage; rather, the refs give the other sports an abnormally large one.

  34. @39 – Same for me. The worst part about this silly story is that we have to read yet more about Notre Dame football. I was hoping we’d be done for a couple of months.

  35. I actually saw 1 hour of sunshine today. We havent seen that in Birmingham for 10 days. No lie, 10 straight rainy/gloomy days. Awful

  36. @46 Come to Michigan, it is like that all the time in the winter. Today was very sunny though, but like 25 degrees. Makes opening day seem so far away!

  37. #47 – yeah no thanks. I love the cold, but I hate rain and I’m not a huge fan of snow. One or two days a year with snow is plenty

  38. @42 Replacement umps who screwed the infield fly rule up in wild card game is the exception that proves rule?

  39. How would you compare the role of the officials in baseball as compared to other sports?

    I don’t watch basketball or football, but from what I see, if you were calling by the rule book, you could blow a whistle on about 90% of plays if you wanted to. It might be that the discretion of the officials has more effect in those sports, therefor, more homefield advantage.

    Another thought, since the majority of homefield advantage, in baseball, revolves around the last at-bat thing… Maybe the nature of baseball’s scoring (no way to “turn over,” it’s my turn then it’s yours,) means that more games are more or less put away before the “last at-bat” advantage really comes in to play.

  40. I’ve had the misfortune of being in Iowa for six months, and there ain’t no sunshine here!

  41. Also, Eric Gregg is the only person for whom my sports-hate ever crossed over in to real-hate. I real-hate Eric Gregg. I remember wishing he were dead. And I don’t feel bad that he actually is.

  42. How about called strike charts for home teams and away teams? Balls and strikes have to be the biggest influence umpires have, so maybe that would tell us something about the impact of the officials.

  43. Can you download and separate the data between the regular season and playoffs? If crowd noise, or lack thereof, is a factor, I’d think there would be a fairly large difference.

  44. Despite attempts by the media to paint Eric Gregg as someone we should have compassion for, I never did. Hate is a strong word but I was glad that MLB never saw fit to reinstate him. He was bad at his job and I never wanted to see him in an umpire’s uniform again.

  45. Anyone think we should move the RF fence in for McCann (and, to a lesser extent, Jayson, Freddie, Constanza …)?

  46. The Braves have no Jaysons, and the only Jaysons in MLB are right-handed…you just wanting to taunt them when they come to town?

  47. Anyone think we should move the RF fence in for McCann (and, to a lesser extent, Jayson, Freddie, Constanza …)?

    Absolutely not. The Braves primary organizational talent is finding and developing pitching. You don’t make your park easier to hit in when you’re best competitive advantage is developing pitching.

  48. “Also, Eric Gregg is the only person for whom my sports-hate ever crossed over in to real-hate. I real-hate Eric Gregg. I remember wishing he were dead. And I don’t feel bad that he actually is.”

    That really is asinine and despicable. You need to grow up or do something to get some perspective. It’s just a baseball game.

  49. @57: Playoffs present a problem because you have to control for the fact that better teams get more home games. The failure to recognize this bedevils lots of calculations of home field advantage in lots of sports. The advantage of regular season play is that good and bad teams are equally likely to play home games. We can control for attendance, and even percentage of stadium occupied though, and some people have tried to do that in the past.

  50. A couple of other ideas. Both of these are predicated on the idea that it’s easier to look within baseball to start (since you already have the data loaded).

    You could look at competitive balance by year and compare that with the home field advantage for that year. In broad eras, it looks like the time between the introduction of free agency (early 70s) and the massive revenue imbalances (early 90s) is the time with the least home field advantage. If that’s true within baseball, you can start comparing with other sports.

    Also, you might want to look at the first game of an away team at each ballpark each season just to see if familiarity has a big impact. In fact, if you get any results by looking at the first game of a series for your rest thesis, it might mask a familiarity effect that could be somewhat isolated by only looking at the first game in a park of the entire season.

  51. Is there a theory about breaking even on road and winning bulk of home games or is it breaking even with good teams and winning bulk against weak teams?

  52. #40

    Obvious bias here, but I thought the fangraphs/Gregg article was pretty lousy (other than the line about the lamp), basically trying to explain away the horrendous zone despite the incontrovertible video evidence. Don’t see how anyone could look at those GIFs and not be astonished how bad the calls were.

  53. So… here’s Eric Gregg, in 1993, talking about how his serious alcohol problem contributed to his serious weight problem.

    I know what the problem is. I used to tell them, `Hey, I’ve only had one sandwich all day.’ And they’d say, `Yeah, but you had seven or eight beers.’
    You simply can’t have four or five beers after a ballgame. You can’t go out with the guys to dinner and drink wine.
    Some guys can do it, big guys can’t. I learned that much. Alcohol slows your metabolism down. It won’t let you burn up the calories.
    No more tossing a couple of beers in the (duffel) bag for the trip home. No more beer in the fridge at home.
    It’s the road that’s tough. You get a little lonely. You’re tired. There’s the pressures of the job.
    But now, every time I’m tempted, I’m gonna think about what I had to do to get my job back.

  54. Urgent!! Avilan the Untouchable just tweeted: ‘Dandole durisimo al gym’

    I hope that’s good.

  55. Translation website yields: “Giving hard at the gym”

    To which the high school coach permanently embedded in my brain responds, “If you have time to tweet about it, you could stand to give a little harder, dumbshit.”

  56. I agree with #68. There seemed to be waaaay too much rationalizing going on there. I get that he was trying to approach it from a detached/academic perspective, but looking at this gifs, I don’t know how you can do anything but laugh or cringe. It’s just so comically bad!

    As for the home field advantage thing, my instinct is that the reason its appears to matter so little in baseball is that baseball is a relatively “noisy” game. The best teams have a fairly good chance (gotta be at least 25%) to lose to the worst team on any given day, and this is simply not the case in other games like football or basketball. There just aren’t ANY factors at all that strongly impact the probability of winning a particular game, with the possible exception of an elite starting pitcher.

    I think the more interesting question is how big the effect of home field advantage in a sport is relative to the size of the effect of upgrading your roster from, say, an average one to the best in the league. My instinct is that the relative magnitude of the effect in baseball is actually similar to the magnitude of the effect in other sports. Possibly even larger.

  57. Penn’s stupid motto is “Laws without morals are useless.” Shows you how much fun I had in college.

  58. Huh, Georgia Tech’s is apparently “Progress and Service.” I honestly had no idea we even had a motto.

  59. BYU’s motto: No offical motto.
    But we have 3 unofficial ones!

    UVA: can’t find an official one

    Wisconsin: Numen Lumen (certainly not what I expected)

  60. UNC motto: Lux libertas. Light and Liberty.

    Borrrring – how about ‘NC State sucks, but dook swallows.’?

  61. I went to New College of Florida. From all the signs around campus, you’d think our motto was, “There is only one New College”, which is dumb, because there are at least three schools in the US called, “New College”. I prefer the motto from our student alliance which is, “There is more to running a starship than answering a bunch of damn fool questions.”

  62. Medlen $2.6
    Jhey $3.65
    Venters $1.625
    EOF $4.32 + award bonuses
    LISP no figures yet
    Martin no agreement yet

  63. Answered my own question… we’re $1.5m above the estimate most people have been using, and that’s before we see Martin or Lisp.

  64. Morehead State’s motto is, er, never mind.

    That list may comprise the most value for the least cost of anything ever.

  65. Except for: Career to date (may be incomplete) $2,118,500 for 755 home runs. I think the Braves got their money’s worth, even inflaton adjusted. Thanks to

  66. How on earth could they not agree if they are only .4m apart? Unless one side or the other was trying to leverage for a multi year deal.

  67. Amherst is “Terras Irradient” – “They enlighten the Earth.” I think we think a little highly of ourselves.

  68. I’m prepared for Constanza/Francisco. Fully expect lots of “they’re tan, rested and ready to produce” articles soon, just as we saw with Reitsma before the 2006 season.

  69. how much cbd gummies should i take for sleep

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