Home-Field Advantage Does Not Exist in the Postseason

The Royals played well at home, but lost Game Seven of the World Series there. (via Jim Chou)

The Royals played well at home, but lost Game Seven of the World Series there. (via Jim Chou)

Plenty has been written about “home-field advantage” in baseball. Historically speaking, the home team wins approximately 54 percent of the time. Recently, The Washington Post posited that “home-field advantage” in the playoffs was worth one extra win. The value of home-field advantage, however, when applied to the postseason, is grossly overstated, and the application of the “home-field advantage” argument usually is flawed.

In a vacuum this assertion might be correct, assuming athletes are not merely, cold, calculated, metal machines with no hearts or souls, built solely upon repetitions and probabilities. However, in the real world there are issues even beyond this assumption. Even if you:

  • throw out the issue of sample sizes and assume the effect of home-field advantage is equally distributable,
  • assume team match-ups are equal even though the postseason is structured so teams with better records play teams with worse records
  • allow for the presumption that the effect of home-field advantage is largely mental and transferable, rather than being based on team play that is tailored to home ballpark factors

the structure of the postseason schedule and likelihood of the advantage ever coming into play for the team that “gets” home-field advantage in the postseason largely negate its utility to that team.

First let’s look at the raw numbers, assuming a 54 percent chance win expectancy of two otherwise equally matched teams. Under these conditions, ignoring all other variables, in a seven-game series, the team with home-field advantage is expected to win 51.25 percent of the time based on all possible best-of-seven-game-series outcomes. Why is this number so low? Because the team with home-field advantage does not play all its games at home. A 1.25 percent advantage is pretty marginal, and not only is it based on an assumption of parity, but applying it also hinges on an assumption that the series will last seven games.

To assume parity in the postseason is itself a bit bold. Despite being a “best-of-the-best”-type tournament, the small sample sizes of the postseason make anything possible. This means inferior teams are more likely to play over their heads than they would be over the course of a 162-game season, and even the invincible Clayton Kershaw could get hit around. Anecdotally, seven of the last 10 World Series lasted five games or fewer.

More importantly, however, applying the home-field advantage argument in the postseason assumes the series lasts long enough for that advantage to matter, even assuming that a 1.25-percent statistical advantage is meaningful in a small sample size that is no larger than seven events.

The structure of later-round postseason play in baseball is established in a 2-3-2 sequence. For the team with home-field advantage in the Championship Series and World Series to realize its 1.25-percent advantage, the series must go a full seven games. This Giants-Royals World Series, however, was only the second time since the winner of the All-Star Game began to “matter” — determining whether the American League or National League gets home-field advantage in World Series — that the World Series has lasted a full seven games.

Since 1987 (my lifetime), the World Series has had a Game Seven only five other times. In fact, this is only the 39th time in World Series history (not including the 1903 World Series, which was a privately organized best-of-nine competition) that the World Series has lasted seven games. In other words, historically speaking, the World Series has been twice as likely not to have a Game Seven as it is to have a Game Seven.

Let’s look at this in another way. If the Championship Series or World Series is a sweep, then, ignoring all other variables, the value of home-field advantage is null; both teams get to play two games at home. Arguably, the same can be said about a six-game series (more about that shortly). However, if the series lasts five games, then the value of home-field advantage inures to the team without “home-field advantage” in the series (let’s call this team the “Visitor”). Whereas the Visitor has a 19.7 percent chance of winning a best-of-seven game series in five games, the non-Visitor (let’s call this the “Home Team”) only has a 17.7 percent chance of winning the same series in five games (a two-percentage-point difference here equates to an 11.3-percent greater relative probability).

In fact, provided the series does not last a full seven games, the Visitor has a neutral or better advantage based on the effect of “home-field advantage,” and thus the Visitor’s realization of the value of the home-field advantage is more immediately realizable than it is for the Home Team.

Based on a 54-percent home-field advantage, one would expect the binomial probability distribution of outcomes to be as follows, depending on how many games the series runs:

Seven-Game Series Win Probabilities
Team 4-Game Win Probability 5-Game Win Probability 6-Game Win Probability 7-Game Win Probability
Home Team 6.17% 11.50% 16.64% 16.94%
Visitor 6.17% 13.50% 14.64% 14.43%

(Please note, the numbers do not add up to 100 percent due to rounding. Also, please keep in mind this distribution assumes the probability of any series length is equal).

Let’s revisit the notion that the home-field advantage effect in a six-game series is neutral. Without looking at any context, the likelihood of either team winning is 34.3 percent. However, for the series to run six games, the head-to-head record of the two teams must be three wins to two. The Visitor would experience the benefits of home-field advantage over the first five games. And because the effect of one extra home game would be greater over a five-game sample with four collectively neutral sites than it would be in a seven-game sample with six neutral sites skewing the probabilities toward 50 percent, the Visitor team is more likely to be the team that has the one-game lead as the site switches for Game Six.

Being in such a position would give the Visitor a substantial advantage. A Visitor team that heads into Game Six with the 3-2 series advantage would be expected to win the series seven out of every 10 occurrences (a greater than double relative probability of outcomes). This is not shocking since, even though the odds would be slightly skewed in favor of the Home Team in Games Six and Seven, the outcome is still largely a coin-flip. And the Visitor is more likely to get two bites at that apple (and maintain more roster and usage flexibility) based solely on the impact of the asserted home-field advantage effect.

All of this is to say that the sequence in which games are played at home in the baseball postseason causes the value of home-field advantage to work to the disadvantage of the team that baseball allegedly awards with such. The likelihood of a Game Seven occurring is much less likely than the series ending in four to six games, and in games four through six, the Visitor has either an advantage or a situation that is better. In other words, if home-field advantage matters, it inures to the benefit of the Visitor and not the Home Team!

Obviously, much of this analysis (like most other postseason home-field advantage analysis) is based on flawed assumptions. In the Championship Series, the team with the better record gets home-field advantage, and being the “better” team might have more of an impact than playing one extra game at home. Additionally, much of what we observe as home-field advantage might, in fact, be more of an observation of ballpark factors and the home team tailoring its roster construction around such factors, while the Visitor team would not be similarly situated.

Moreover, anything can happen in seven games, and even moreso in subsets of those seven games when you try to analyze the impact of where one possible extra game might be played. The value of home-field advantage might be realizable and real over the course of 81 home games, but, my affinity for baseball gambling aside, it is foolish to think that such value is evenly distributable across each game or predictably impactful in any singular or short-term instance.

At most, I am willing to concede that home-field advantage is another probability in a complex postseason-outcomes calculation. This calculation must take into consideration the likelihood of there being a Game Seven and the converse advantage the visitor gets in a five- or six-game series.

If baseball truly wanted to make home-field advantage matter for the home team in the postseason, it would have to structure the postseason more like hockey or basketball and sequence the series with a 2-2-1-1-1 structure. However, the expense and exhaustion of travel (not to mention a long season made longer due to the need for more travel days) probably makes that impractical.

Bottom line: Let’s stop talking about home-field advantage as if it means something in the Championship Series or World Series (or at least change the #narrative, if we want to fixate on marginal topics).

References & Resources

  • Thank you to my favorite math teacher, Tim McCormick, who was instrumental in my getting the math in this article correct.


Jeffrey Gross is an attorney who periodically moonlights as a (fantasy) baseball analyst. He also responsibly enjoys tasty adult beverages. You can read about those adventures at his blog and/or follow him on Twitter @saBEERmetrics.
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Steaming Deuce
7 years ago

This is by far the worst article I’ve ever seen on THT. It’s dumber than YouTube comments. You start with a model (home 54% every game) calculate that HFA exists for the series in this model (HFA team wins 51.25% of series), and then spend the entire article arguing that HFA doesn’t exist or is sometimes reversed or whatever other brain vomit made it online that i forgot to mention. What. The. Deuce. Who edited/approved this?

Jeff Gross
7 years ago
Reply to  Steaming Deuce

Thank you for your reasoned, thoughtful insight.

Steaming Deuce
7 years ago
Reply to  Jeff Gross

You’re welcome. Since Mr. Clayton below brought it up, I guess it needs to be specifically addressed that in your model (home team is always 54%), the order of the home and away games is completely irrelevant to HFA. 2-3-2, 2-2-1-1-1, or even 4-3 or 3-4 all grade out the same 51.25% series win.

Jon Clayton
7 years ago

I’m a little puzzled by the approach too, though not so venomously. What I get out of the article is that even if teams are more likely to win at home, the 2-3-2 series format makes the impact of that “advantage” rather small, largely because it is a small sample. A separate observation is that the “better” team gets home field advantage, and being “better” may matter more than having home field.

But I really don’t see why an article on this topic wouldn’t look at actual data at the game by game level. It’s really interesting to me that in World Series games since the introduction of the “DH at AL stadium” rule, home teams have won more than 60% of the time, while prior to that there really appears to be little if any home field advantage in the World Series. This would support the notion that if home teams win more often than visitors, it’s not because they were at home, but because in the LDS and LCS they are the “better” team based on regular season record, and in the WS they have a structural advantage because they are playing with/without a DH as they did during the regular season.

Jeff Gross
7 years ago
Reply to  Jon Clayton

I think that’s an interesting question. Definitely something to consider. I’ve often thought about looking at the DH impact and the home-away split impact, but it is not something I have gotten around to.

Marc Schneider
7 years ago
Reply to  Jon Clayton

I’m not sure why it matters whether it’s the “structural issue” or home field. Since having the home field gives one team a structural advantage, it’s still a home team advantage. It’s just not this mystical “we play better at home because of the crowd” type of advantage. But it seems to me-not a statistician by any means-that the author is correct that the trend of teams winning Game 7 is largely a statistical fluke. At one point during the 50s/60s (when 7-game World Series were much more common) the home team lost 12 of 15 Game 7s. I don’t think anyone would say there was a home field diasdvantage. And, given the fact that there have been few Game 7s in the last 35 years (9) and they have been largely spread out, it strikes me that it’s more a statistical blip, akin to flipping a coin 9 times over a course of time and getting heads every time.

That said, the advent of having different DH/non-DH rules in home parks presumably has some effect on the outcome. But I don’t think looking at Game 7s really tells you much because, as the author points out, most World Series these days don’t go long and, therefore, there is no deciding game affected by home field advantage, is whether the playoff format contributes to home teams winning more often. In other words, you more often have teams that are not necessarily the “best” teams, at least in terms of regular season record, playing in the World Series. Would having lesser teams playing in the World Series (at least compared to the pre-Division era where the “best” teams always played) make it more likely that the home team would win, especially given the structural advantage?

One other thing, I’m wondering with respect to the supposed home field, is

Jeff Gross
7 years ago
Reply to  Marc Schneider

I think we should be able to calculate, to some degree, the impact of the DH. I would be interested to see how it impacts your average AL/NL team. One would hypothesize that the NL team is built less around “the 9th hitter” and more around depth beyond the “8th hitter” due to the rules of the league, whereas the AL has a stronger incentive to forgo the depth beyond the 9th hitter to concentrate value in the 9th hitter, since that specific 9th hitter would be used with more frequency in the AL. I do think that this impact of the DH would have some effect — though what impact, I do not know. I would guess it is more impact than the number of home versus away shouters in the stands, but who knows what degree of impact “the mental” part of the game has — its not as quantifiable per se.

Tess
7 years ago

This article makes no mention of the DH and fails to shows what has happened throughout history. First it starts talking about “post-season” home-advantage but then it just dwells on the world series. I might be going off a limb here but I would guess if you take every play off game in the last 20 years and calculate the percentage of wins for the home team regardless of situation or series I would say it should be around the 54%.

Ask any person that has ever played a competitive sport and ask them if home advantage matter in a post-season and I am sure you will get a unanimous “YES” as an answer. Sometimes we have to look past the numbers

Jeff Gross
7 years ago
Reply to  Tess

Tess:

I think fans of the game are aware of the differences between the AL and NL in terms of DH/no DH, but my point was not to focus on the DH impact or park dimensions impact or otherwise of who is the “home team”, but simply to look at the recurring blank statement that being the home team matters, and to what degree it matters. These other factors (DH, park dimensions, altitude/weather of different climates, etc) certain impact the game and so in that regard, where each game matters, but that’s more of a nuanced analysis rather than a blanket “I am the home team” intangible effect. I simply intended here to show the negligible impact of that blanket argument in a short series, and to also show, contrary to what the league intended, that the established sequencing of home field/away field in the post season is not conducive to truly imparting the effect of home field upon the winning league of the ASG. If it was sequenced 2-2-1-1-1, perhaps things would be different, but the confluence of the negligible impact and more likely reverse application of home field advantage in the postseason warrants criticizing the assertion of “being the home team” is important — what is probably more important is playing more games in a field that tailors to the team’s design of play in my estimation.

Jeff Gross
7 years ago
Reply to  Jeff Gross

*certainly impacts

*where each game is played matters

Steaming Deuce
7 years ago
Reply to  Jeff Gross

Will you please stop tarding off about reverse series HFA because of 2-3-2? Jesus Christ on a crutch.

Just because the away team in a random mlb game is more likely to score first doesn’t mean that HFA doesn’t exist in that game, and you’re making an even dumber version of that argument about a 232 series.

Jeff Gross
7 years ago
Reply to  Jeff Gross

Disagree.

Steaming Deuce
7 years ago
Reply to  Jeff Gross

OK, let’s try to narrow it down to see if your problem is the result of bad math or the result of breathing the air in your transverse colon.

Keep your model that the home team wins 54% of the time. Pretend that the series is the ASG winner greeting 4 home games followed by 3 road games (if necessary, blah blah). How often does the ASG winner win the series under that schedule? Now pretend it’s 3 road games followed by 4 home games. How often does the ASG winner win the series under that schedule?

What do those numbers, plus your article number, tell you about how series HFA relates to the scheduling?

Marc Schneider
7 years ago
Reply to  Tess

Then how do you explain the period from 1955 through 1979 when the visiting team won 12 of 15 Game 7s?

It’s certainly better to have the home field than not, but the point is that, relative to other sports (NFL/NBA) the HFA in baseball is much smaller. I don’t think anyone can doubt that. Obviously, you would rather be playing at home than on the road, but, even saying there is a 54-46 home/road split isn’t really all that large.

Brian Oakchunas
7 years ago

I am somewhat amazed that no one else mentioned this, but a team that wins 51.25% of the time does not have a 1.25% advantage. They have a 2.5% advantage because the other team is winning only 48.75% of the time, not 50% of the time. That is like saying a team that wins 100% of the time has a 50% advantage.

Also, you spend a lot of time arguing what should happen and never mention what *does* happen. Why would you not state what percentage of the time a team that has home field advantage actually wins the series? Does it go against your conclusion?

Jeff Gross
7 years ago

*Relative* advantage to a 50/50 split. The incremental “gain” is 1.25%

Brian Oakchunas
7 years ago
Reply to  Jeff Gross

I don’t get that. You’re talking about home field advantage versus the other team, not versus a 50/50 split. For the purposes of your article, they are 2.5% more likely to beat the other team (according to your numbers, which are completely untested against what actually happens).

evo34
7 years ago

I agree. This article is 100% buildup, with no actual results. Very curious. By the way, the obvious way to test HFA (when faced with a small sample of games) is to look at runs/inning differentials, not game outcomes.

evo34
7 years ago
Reply to  evo34

Also, you’d think an article with an incredibly provocative title would actually bother to *test* its own aggressive assertion. Apparently not. A better title for the piece would be, “I’m Just Not Sure How to Measure Home-Field Advantage in the Post-season”

Tangotiger
7 years ago

It seems semantical with regards to the 1.25% or 2.50% discussion.

When you have two even teams playing at a neutral park, they are 50/50. If you play at a home park, they are 54/46. Mathematically, you’d say that it turns the home team from a 50% team to a 52% team, and it turns the away team from a 50% team to a 48% team. And so when you have 52/48 matchup it results in a 54/46 outcome.

***

I think the structural discussion is interesting in seeing how the home advantage… progresses (for lack of a better word)… as the series goes on. But the structure will have no net effect.

***

And I agree, empirical results would have helped.

***

Some of the comments above are abusive or personal attacks. Regardless of whatever merit exists in part of the comments, the delivery of the comments deserve no response.

Brian Oakchunas
7 years ago
Reply to  Tangotiger

I agree that there is no place for the despicable attacks and I would not respond to them. While I have issues with the article, I’m trying to contribute to the discussion–not ruin it.

Jianadaren
7 years ago

6.17+11.5+16.34+16.94 = 50.95 > 50
6.17+13.5+14.64+14.43 = 48.74 < 50

Even your binomial model shows home-field advantage. Going 2-2-1-1-1 would not even help the home team: it would just swap Game 6 with Game 5. You might expect to see more home teams win 5 game series, fewer away teams winning 5 game series, fewer home teams winning 6 game series, more away teams winning 6 game series, but overall home vs away series win probability remaining unchanged (unless you believe in momentum or something).

You see this in hockey:

Andy
7 years ago

Though this may not shed any light on the HFA question, thought I’d throw it out. As is well known, in a 50/50 or coin flip situation, these are the odds that a best of seven series goes 4, 5, 6 or 7 games:

4 – 12.5%
5 – 25.0%
6 – 31.25%
7 – 31.25%

There have been to date 101 best of seven WS, not including those in which tie games were recorded. There have also been 29 best of seven AL championship series, and 29 best of seven NLCS, for a total sample of 159 best of seven series in MLB history.

Here is the actual distribution:

4 – 26 16.4%
5 – 39 24.5%
6 – 44 27.7%
7 – 50 31.4%

Though this distribution is surprisingly close to that expected for coin flips, there are a couple of interesting deviations. First, the proportion of 4 game sweeps is higher than predicted by 50/50 chance, and is significant at at least the 95% confidence level for a dataset this large. One might explain it by assuming one team is usually significantly stronger than the other, but if that were the case, the proportion of 5 and 6 game series should also be higher than predicted, and they aren’t. I speculate that maybe when a team goes up 3-0 it has a psychological advantage, that the trailing team gives up to some extent. I wonder if there is even an advantage just in playing the first two games at home, and being more likely to go up 2-0. It wasn’t until 1955 that a team that lost the first two games of the WS won the series. And IIRC, didn’t they change the format of 5 game series from 2-3 to 2-2-1, because they thought it was unfair of the team with HFA to play the first two games on the road and maybe be down 0-2 before playing at home?

The other interesting deviation is that the proportion of 7 game series is higher than that of 6 game series. An earlier analysis of just WS from about 1950-2000 came to a similar conclusion, and suggested it was because the team trailing 3-2 after 5 games was more likely to play game 6 in its home park, but did not show any data to back that up.

Mr Punch
7 years ago

The first year in this study, 1987, is I’m afraid the fact that undermines the theory. Let’s say there were a team that was terrible on the road but almost unbeatable at home, finishing only slightly above .500 but winning a weak division; and let’s say it had home field advantage through the postseason. That’s what happened with the Twins. So yes, sometimes, for some teams, home field is a huge advantage.

MGL
7 years ago

I’m not really understanding the discussion in the article or in the comment section.

If one team has an extra home game in a 7-game series, regardless of the order of the series, and the home team gets an extra 4% in WE, and both teams are the same talent (their chance of winning in a neutral field is .5), then their chances of winning the series is indeed 51.25%. The order of the games makes no difference!

The 1.25% advantage for the extra home game starts to decrease a little as the talent difference between the two teams increases, but that decreases slowly until you get to the extremes. If one team is a 55% fave in a neutral park, then they will win a 7 game series in a neutral setting 60.8% of the time and if they have an extra home game in a normal 7-game series, they also will win around an extra 1.2% of the time, assuming an extra 4% per game for HFA.

If one team is a 70% favorite in a neutral field, then the value of the extra home game is only around .8%. At 90%, it is only .1%. At 60%, it is 1.1%. Again, the order of the games makes no difference.

Now, whether the AL or NL has a different HFA than then normally do because of the DH and pitchers hitting is another matter. In the regular season, IIRC, the home team in IL games has a slightly higher HFA, as you would expect, and the AL has a slightly higher HFA than the NL (in IL games).

I don’t know what else there is to write or discuss.

MGL
7 years ago

As far as history goes, obviously you have a limited sample size so that you are not going to be able to draw any conclusions independent of the theoretical numbers.

There are things that happen in real life though that are not necessarily reflected in a generic model.

There is a spread in “true” HFA among teams (not their HFA during that season, which means almost nothing for the post-season). For example, Rockies have an enormous HFA and large road field disadvantage. Boston has a larger than average HFA. So did the Twins in the Metrodome and the Astros in the Astrodome. Quirky parks have an extra HFA, while cookie cutter parks have a lower one, etc.

When teams are facing elimination, they tend to win more often than “expected,” I think, because they use strategies which increase their WE for that game (and presumably cost some WE for future games in the series), like using the bullpen more aggressively, pitching a good starter in relief, throwing a good starter on short rest, etc.

Yehoshua Friedman
7 years ago

First, I wish to protest the abusiveness of one commenter. What crawled up him and died? Second, I propose for the WS and all interleague play, and maybe for all games, a coin toss at home plate for the choice of DH/NODH. If you have a Greinke or a MadBum pitching, you will choose NODH. If the other team has Bartolo Colon pitching, you will choose NODH. This will make the structural difference in AL and NL rosters even out. Teams will build their WS rosters with the expectation of using DH about half the time. The suspense at the beginning of the game will also be greater because the two managers will have to show up at HP with two potential lineups. This might be the answer to standardization of the NL and AL regarding the DH rule.

Barry Fagin
7 years ago

It’s incorrect to assume the possible length of a series are equally likely. That in turn significantly changes the conclusion of the article. See http://excessivelylogical.blogspot.com/2014/11/yes-of-course-home-field-advantage.html for details.

(Not my blog, but the math is correct)

–BF

Barry Fagin
7 years ago
Reply to  Barry Fagin

Nuts. Possible “lengths” of a series …