THE BOOK--Playing The Percentages In Baseball

Has it ever actually been tested whether teams tend to split double headers, or does the best team win more often?

#1, I wouldn’t waste my time.  I suppose that since a lot of regulars get rested in one of the games, that good teams get hurt a little, but other than that…

I’m almost positive I’ve read a study somewhere that debunked this piece of conventional wisdom, but I’m having a hell of a time remembering when or where.

I’m sure there’s a grain of truth to it. I mean, on average both of the teams in a double header should be… average, right? And on average, two average teams should play about .500 ball versus each other, right? (I’m oversimplifying here - obviously there’s home field advantage to account for here.) So a split should be the most common outcome for a double header, shouldn’t it?

Now, that’s really no different if they played the games on seperate nights - the problem is thinking that the double header CAUSES the split.

Only way to tell is with empirical data and taking into account the odds of each team winning each game (Vegas odds).

But I must admit that it’s rather entertaining to come up with hypothesis as to why there may be more splits than usual.  Splits should occur no more than 50% of the time, and that is with two perfectly even teams (50% win probability for both games).

WW = (.5)(.5) = .25
WL = (.5)(.5) = .25
LW = (.5)(.5) = .25
LL = (.5)(.5) = .25

So if the empirical data shows anything 1 SD above 50% of the games being split, then my interest would be perked.  Then to dig deeper, you’d need to know the win probability for each game.

I wouldn’t call the talking heads “dumb” without having the data to back it up.

vr, Xei

Colin:  With the home team at .540, the chances of a sweep are 50.3% and the chance of a split is 49.7%.  So I’d guess it’s not even true that a majority of double-headers are splits.  If it is, I’m sure it’s barely over 50%.

I’m old enough to remember the 1966 Tigers, who had three managers, two of whom (Chuck Dressen and Bob Swift) died.  Anyway, when Dressen was sick at the start of the year, the Tigers didn’t win a single game in a single doubleheader the whole time he was away.  He came back and they immediately split their first doubleheader, which was big news.

Point is, there was a time when you played at least one doubleheader every week, nearly always on Sunday.  Now, there are no doubleheaders scheduled and only the odd makeup games here and there.  Small sample size will never be overcome.

Just checked the Retrosheet game logs, and a doubleheader is swept 51.8% of the times.

Guess I was wrong there.

Colin, 51.8% is definitely higher than what it should be.  Should never be higher than 50% and that’s the highest it should ever be with two teams with a 50% win probability for both games of the double header.  Chances are it should be somewhere between 48.5% and 49.5% and it came out 51.8%.  Now we need to see how many standard deviations that 51.8% is from whatever the odds of a split should be.  How big is your sample size?
vr, Xei

I shouldn’t say “never” above 50%.  Just that 50% is the max that it should be.  Anything over 50% raises an eyebrow and needs to be looked into.
vr, Xei

Xeifrank - Guy helpfully pointed out the effect of HFA. And whichever team wins the first game should probably be more likely to win the second game, since the better team should probably win the first game. Now that I look at the data I’m not too surprised.

Colin, I read the 51.8% number as splits not swept, so I made a mistake and take full responsibility for it (no excuses).  My bad.  Looks like the numbers are in line.
vr, Xei

I can’t believe all this time spent on seeing whether there was some “magic” to a DH.  It’s just two games that happen to occur on the same day.

Anyway, I am pretty sure that Kay was vaguely aware that splits occurred about half the time.  What he meant was that teams split a DH a lot more than they sweep, which is true of course.  In his small mind, he assumed that somehow a team wins back to back games more often than they sweep a DH.  And since he said that “The Twins were upset...,” someone from the Twins team must have echoed the same sentiment and the same thought(less) process to him…

It’s also interesting that Kay seems to completely ignore the third possible outcome of the DH where the Twins get swept (which is a more likely outcome than them sweeping the home team anyway.) Using the exact same faulty logic, he could also claim that the Twins should be happy about the rainout, as it reduces the risk of them being swept and having their playoff chances virtually eliminated.

you could argue entirely logically that teams with deep bullpens will tend to do better in doubleheaders, or that AL teams who have great offensive catchers and great DHs will do worse, but--arguing for the split theory implies a factor that will tend to equalize the teams.  How could such a factor even exist?  It just seems like fertile ground for bullshit “psychological” speculations....

MGL:

“
I can’t believe all this time spent on seeing whether there was some “magic” to a DH.  It’s just two games that happen to occur on the same day.
“

Right. Which influences roster management and pitcher usage and all sorts of other things. Plus, believe it or not, some people enjoy looking up baseball statistics for the hell of it, and playing around with numbers looking for useless info. Particularly when someone known for being abrasive calls someone else an idiot and then does nothing at all to back that up.

I would also think a sweep is more likely, due to bullpen issues. If you have a few relievers get lit up in game 1, you may not have as many available in game 2.

Is there also a bias to the end of the season?  These days, I could imagine more DHs take place later in the year when many teams have washed out and are scrubbed up - so they aren’t 50-50 teams, but .600 vs .400.  Which could contribute to the tilt towards sweeps.

"I can’t believe all this time spent on seeing whether there was some “magic” to a DH.  It’s just two games that happen to occur on the same day. “

And you sometimes wonder why I frequently use the term “idiot” when talking about baseball insiders/outsiders?

Kudos to nick, Fly, and Mike for pointing out the subtle differences between two games on two consecutive days and two games in one day. 

And from my experience playing dozens of seasons with Diamond Mind baseball, especially seasons with 22 DHs scheduled per team, I have noticed quite a difference in strategy with a DH—I do not use my starting catcher in both games, I’m careful with my relievers, a small injury to a player in the first game prevents him from playing in the second game as well (this is a DMB issue, though, in real-life, he -might- return for the 2nd game). 

Another real-life issue—the road team might have just arrived the night before, perhaps exhausted, and now they have to play TWO games on little sleep?  I can see that adding to the 51.8% of the time a DH is swept—assuming it’s the home team that is doing more of the sweeping.  Otherwise, this theory FAILS. 

Therefore, -some- teams -might- have an advantage to DHs vs. other teams.

And I second Fly’s remark about how some people might enjoy conducting “pointless” research.  And, AND, they might actually come upon a useful nugget of information that otherwise would have been overlooked. 

Yes, Kay’s COMMENT was idiotic, but other comments here have been idiotic (and arrogant) as well (perhaps even including some of mine—GASP!).

One possible way that the double-header could have hurt the Twins would be if they didn’t want Mauer to catch both ends of the DH. But since he did play both games, it wasn’t that big a deal.

Or, if the Twins had a really shallow bullpen and had to use all their good relievers in Game 1, leaving them short-handed for Game 2. But as it turns out, the Twins have a good, deep bullpen. so, that shouldn’t have affected them much either.

Unless the Twins were mentally unfocused because they believe that “doubleheaders are usually splits”, the Twins shouldn’t have been significantly more affected than the Tigers were

Chance of a sweep of a double-header, by home team’s chance of winning one game:

HomeTeam / DH sweep
0.660 55.1%
0.620 52.9%
0.580 51.3%
0.540 50.3%
0.500 50.0%
0.460 50.3%
0.420 51.3%

The first line says: if the home team has a 66% chance of winning one game, then there’s a 55.1% chance that there will be a sweep (43.6% for the home team and 11.6% for the away team).

As you can see, the chance of sweeping a double-header will be above .500. 

Colin is reporting 51.8% which seems fairly unsurprising.  Even if it is “statistically significant” from whatever our expectations should be (you’d have to figure out the expected win% for each game first, and apply the numbers from the table above, so you have the proper weighting), we’d be talking about a tiny difference, if any.

No one’s going to make a big deal out of an actual 51.8% if the expected is 51.2% or something, are they?

Colin: if you’ve got it handy to do, what are the sweep rates of 2-game series (excluding DH).  That is, ignore the 3-game and 4-game series, and just look at 2-game series.  What’s the sweep rate?

Actually, Matt S. should have this pretty handy already, if he’s around…

Rather than take the overall chance of winning both games, couldn’t you compare the odds of winning Game 2, given they won game 1 and compare that to the odds of winning tonight, given they that won last night?  Control for the same opponent, game # in the series, HFA, differences in talent levels, etc.  I suspect the result is not really much different, but it would be a more powerful ‘quasi-experimental’ (sorry for the use of that awful term) approach to claim nothing changes based on the implementation of a doubleheader. 

Are we sure that the reduced time period between games doesn’t reduce the Markov assumption of the probability of winning?  While it may not be a large change, I don’t think it’s completely out of the realm of possibility for a psychological carryover effect.  I’m not convinced that effect would be detectable if it exists, either.  But I think it’s possible enough at least to the point of not writing it off as ‘idiotic’.

Bah!  You beat me to it, Tango.  I think it’s at least a useful exercise there.

Kay’s statement was idiotic.  “Everyone” and “usually”?  What does that mean?  90% of people know that there is a sweep 70% of the time?

Had he said “60% of the people know that there is a sweep 50-52% of the time”, then we really have no issue here.  That could not be what “everyone” and “usually” means, is it?

***

“When I’m right 52% of the time, this means I’m wrong 48% of the time.”

“D’oh”.

Fair enough to feel he’s imprecise or incorrect.  I’d agree that the ‘everyone knows’ comment was a quyite far-reaching.  But simply calling someone an idiot without any sort of retort to the claim is just calling the kettle black.  That’s something you preach here over and over, and why I continue to come here.  And do you really expect an announcer to talk in that way?  I’m not here to agree with what he said, but I’m unsure why MGL finds these things so terribly offensive, that’s all.

I’m sure Kay would wonder what all the fuss was about if we are talking 52%. That would prove his point as far as he was concerned.

Millsy: I won’t speak for MGL. 

Plus, I took a vow a few weeks ago to no longer waste my time responding directly to every inane comment made by self-appointed experts, be it broadcasters, writers, players, or execs. 

The best we can do with these people is to use their idiocies (or lapse in judgements) as “teachable moments”.  Colin’s already done that, by giving us the 51.8% data.  And once Guy mentioned the home field advantage, and I provided the chart, really, the teachable moment has been made.  Context has been provided. 

Anything more that we do will simply do nothing more to advance our knowledge.  I do encourage time-wasting if it’s research-related, if only because it’s keeps you sharp (like taking the stairs instead of the escalator).  But, that’s pretty much it.

If we assume the two games are independent, then Colin’s numbers suggest that on average the true talent disparity (including HFA) between two teams is about .595 vs. .405.  That can’t be true.  So it looks like there may be a small DH effect in the opposite direction that Kay was thinking. 

Colin:  can you tell us how often the home team sweeps?  I’m thinking maybe HFA is a little bigger in DHs, which would be interesting.  And how many years/DHs did you look at?

Guy - All Retroyears. I’m at work so I can’t break the data down any more right now.

You don’t work for us?  :>)

Thanks....

Sean Foreman posted this data over at BTF:

For double-headers:
+------+------------+--------+-----------+
| DHs | home_sweep | split | vis_sweep |
+------+------------+--------+-----------+
| 1286 | 0.3095 | 0.4883 | 0.2022 |
+------+------------+--------+-----------+

Now I look at all cases where two teams played on date N and date N+1. This will include a four-game series on consecutive days 3 separate times. b2b = Back-to-back
+--------------+----------+--------+---------+
| consec_dates | home_b2b | split | vis_b2b |
+--------------+----------+--------+---------+
| 41046 | 0.2955 | 0.4885 | 0.2160 |
+--------------+----------+--------+---------+

It’s interesting the HFA increases from .540 to .554 in DHs.

"It’s interesting the HFA increases from .540 to .554 in DHs. “

More time in the nicer home clubhouse?

As I noted in the BTF thread, this is 1.4 SD difference, and if you look at the year-to-year home win% for all games (see my post at BTF), it’s pretty uneventful.

Sean posted his data on his blog:
http://www.baseball-reference.com/blog/archives/2746

But but but...what about triple headers?

I wonder how the Cubs performed in double headers while Ernie Banks was employed.

This thread is why I love baseball (and this blog.) A stupid, seemingly meaningless comment by someone I never heard of led to an entertaining and educational 34 post thread. Sorry I had to break the streak.

BTW, I REALLY paraphrased what Kay said.  Basically he was just remarking that somehow it is harder to sweep a double header than win back to back games, and I doubt he was talking about 51% to 52% or something like that.  He also said, “I don’t care what the stats say,” but I don’t know what he meant by that.  Maybe someone can check the broadcast.  I forgot what inning it was.

Yeah, it is instance 1,487,221 of a broadcaster saying something stupid, but it gave me a chuckle since someone from the Twins had to have initiated the thought (apparently). 

And I take back what I said about it being not worth investigating.

Typical MGL post.

Thank you.  I assume you mean, enlightening, insightful, and entertaining, otherwise why would you read it or even come to this site.

#38 - MLB does not play 7 inning games (except of course for rainouts)- There are few DH compared to 30-40 years ago

I flunked my 1st eye test and am now in bifocals, but read #38