Nationals Baseball: The failing fallacy

Wednesday, August 17, 2016

The failing fallacy

Commenter Donald brings up some points about calling it now that I'm sure are echoed by every one still worried about how the next ~45 games are going to play out. We've seen teams lose 3-4 in a row and win 3-4 in a row all year long. If the Nats were to do something like the former and the Marlins like the latter, and the Nats were only up by 5, 5 games from now, surely I wouldn't call it then.

He's right. I wouldn't. Not with six head to head games left. But there's something at play here that we need to address. Just because we've seen teams win and lose in streaks like that does not make it likely. It just makes it possible. How possible is what drives "calling it". If that wasn't the case, you'd never call it before mathematical elimination.

So how possible is the scenario described above? Well both teams play 5 games in 5 days and the Marlins are 8.5 games out so technically 5 games out at the end isn't possible. But let's give the Marlins a rain out. Let's make the Nats go 1-4 and the Marlins 4-0.  That would do it. Those don't seem that crazy do they?

Well let's look at how many times these two teams have actually hit those marks in a 5/4 game stretch this season. We'll include overlapping streaks because well, they count too.

The Marlins have had 116 four game stretches (from games 1-4, 2-5... all the way through games 116-119) They have won all four games in those stretches 6 times. The Nats have had 114 five game stretches. They have lost four or more games 11 times. So if we take these things to be completely random you'd figure the chances of the Marlins having a 4-0 streak right now while the Nats were to have a 1-4 streak to be 6/116 * 11/114. That would be 66/13224 or real close to 0.5%.

That's not 5%, that's 0.5%, meaning there would be a 99.5% chance of that NOT happening.

But why does it feel like it could? Well part of the reason is that you aren't just following your team generally. You are following your team, and the teams that they are playing now, and probably playing next, and their divisional opponents, and maybe a couple other teams of interest.  All in all at any point in the season you may know how, let's say 8, different teams are doing.  Let's say they all have the same chances of winning 4 in a row as the Marlins. (probably not bc the Marlins are in the top half of the league but bear with me here).  The chances that any one of them are on a 4-0 streak at any given time is the inverse of the chances that all of them are not (the latter is easier to calculate and then we can just subtract from one). At any given point the chances of one of them being 4-0 is like a 1/3.  Let's say the chances of 0-4 are the same* and thus you have a 1/3 chance of one of the eight being on that streak at any moment too. The end result is that you have a pretty good shot at any one time, about 2/3rds, to find one of the teams you follow on a winning or losing streak of 4 games (or more)

It may not seem right but it is. If you are watching a bunch of teams, chances are someone is streaking. It's almost certain in fact if you are paying attention to half the league or more. If you are an AL fan Boston's won 5 in a row, LA has lost 4. Three other teams are on 3 game streaks. In the NL San Diego has lost 4 in a row and 4 other teams are on 3 game streaks. However the chances of any one specific team streaking in a certain direction and another specific team streaking in another direction at the same time are very low. They get even lower if they are going against what they have done all year.

This is just one part of why calling it makes sense though. Here's what simple logic tells us. The Nats are better than the Marlins. Therefore the chances the Nats gain a game in the standings is better than the chances they lose a game in the standings. It is more likely that we find the Nats 9.5 games up tomorrow than 7.5 games up (making a lot of assumptions - yes). Starting from this point it is more likely the Nats will be 12 up than 5 up after 5 games.  The streak analysis doesn't necessarily have to hold for this latter claim, teams can differ in how streaky they are, but it usually will, and in fact it does here. The Nats are pretty much exactly as likely to go 5-0 as the Marlins were to go 4-0, but the Marlins are way more likely to go 1-3 (or worse) than the Nats were to go 1-4. The end result is a 1.2% chance of the Nats expanding their lead to 12 games by this imperfect analysis.

By asking if the Nats are 5 games out a week or less from now would I have picked them at that point is essentially asking, "If you were to know an extremely rare and bad event would happen to the Nats in the next week, would you pick them" I might say no. But from this point I'll take the very very good odds that that extremely rare and bad event doesn't happen. Also note that when I made the call the Nats were in the beginning of a longish stretch against bad competition. The Marlins had just lost Stanton for the year. I didn't include that in any of the scenarios above but it is in there affecting all those odds in the Nats favor.

Donald also asks if maybe the Nats are not this good just on a hot streak now (and he doesn't ask but conversely let's go with the Marlins are better than this and are just cold) maybe they will streak to balance it out? He's right on the first points - though 120 games is a pretty good indicator, we don't really know the Nats true level. Part of that is just because that's a shifting target, with injuries, development, etc. But maybe they are a 92 win team instead of the 96 win team they are on pace for. (or the 102 win team RS/RA suggest or any other such projection) Who can say? And the Marlins could be better.

The problem is, for this worry, is that the "streak to even out" is not very likely. It doesn't work that way. Regression to the mean doesn't mean if you are a .500 team and you go 5-0 that you'll go 0-5 to get back to .500. It means that you'll play around .500 ball the more games you play and that winning percentage will drift back down to .500. 5-0 and a 1.000 winning percentage becomes 10-5 and 0.667, 20-15 and .571, 55-50 and .524.  If the Nats are worse and the Marlins are better, even if the Marlins are better than the Nats, it's hard for them to catch them because the most likely scenario over 20 games puts the Nats going say 11-9 and the Marlins 12-8, with the chances of different levels of success and failure rapidly diminishing from these central points. It's is very unlikely for a team, even if they are better to make up more than a few games over the course of a time frame even as long as a month.

Take the Nats - how have they done in a month? They've gained 1.5 games on the Marlins, 3.5 on the Mets, lost 2 games to the Phillies, and gained two on the Braves.  The Cubs have gone 20-8. That's huge! Back to their "maybe a top season of all-time pace" But even they didn't expand their lead by more than 4.5 games for three of the four teams behind them.

I called the Nats because it is simply very very unlikely for a Nats team that is better than the Marlins to find themselves losing all this ground in what remains of the season. Even if you don't think that the Nats are better, it's still very unlikely. Hell, even if you thought the Marlins were the best team in baseball and the Nats the worst, an 8.5 game lead over 45 games is pretty safe. It's over.

*This isn't the case, especially if you are looking at teams like the Marlins who are better than .500 but we're just spitballing here.


PotomacFan said...

Why are we talking about this? Why aren't we talking about Oliver Perez and how the Nats need to replace him soon.

G Cracka X said...

Two comments:

1) I think it may just be easier to point to Fangraphs' Cool Standings. It gives the Nats a 99.3% chance of winning the division. That is very safe 'calling it' territory. Anything much more than that, and there is basically no point in 'calling it'.

2) However, I would like to hear your thoughts from Boswell's Monday chat. He talked about black swan events that happen every now and then - a team gets jittery, panics, and does much more poorly than expected. He said something like statisticians always think these type of gross statistical anomolies happen once every 50 years, but in his opinion they are often more common than that.

Fries said...

Agreeing with PotomacFan, Nats have it all but in the bag, the playoffs are pretty much a forgone conclusion.

But the bullpen...While I don't quite agree with the Doom and Gloom he is professing, Buster Olney definitely has a point in that the Nats bullpen is still the weakest link and does not lend itself to a ton of confidence come playoff time. I'm excited that Rizzo is bringing up Koda today since he's had flashes of brilliance, but it's been 2 INNINGS. Expecting him to contribute in the playoffs is ridiculous. Solis is the only serviceable lefty, Kelley/Melancon/Belisle aren't quite as lights out as you'd want in a playoff scenario, Treinen is still wild.

I just hope we can expect all the starters to go 7 innings and then turn it over to Kelley/Melancon, but we can't really expect that. Here's hoping Koda is the second coming of Mariano

Andrew said...

@GCX on point #2:

I'm relying on your description, but it sounds like Boswell is going into full self-parody here. A black swan event means something that was not and could not have been foreseen so talking about it happening more often that we expect is ludicrous. And if the numbers show something happening every 50 years, it doesn't really matter his opinion about how often they are. He may be committing a logical fallacy in thinking that "50-year" events seem to happen all the time so they aren't really that rare. Sure, you could have 5 different 50-year events happen this week, but each individually still could be that rare. Or maybe a certain 50-year event repeated after 10 years last time, but it could still be 50 or 150 years before it happens again.

I think Harper's larger point holds that sure, there's the very low probability case that the Nationals fall apart down the stretch. But that's not more likely than the Marlins completely falling apart. In fact, given that the Nats were already a better team BEFORE the Marlins lost their best hitter for the year I'd say it's less likely.

DezoPenguin said...

I'm a lot less jittery about the Nats blowing the division to the Mets and/or Marlins (which would basically require a historic collapse, probably fueled by crippling injuries to multiple key players) than I am about playing SF, LA, St.L, Pittsburgh, or, yes, the Mets and Marlins in a small-sample-size five-game series where basically anything could happen and even being historically good is no promise of anything. So I'll save the anxiety for October at this point and focus on being nervous over the Blue Jays instead.

JE34 said...

@Fries: Blake Treinen's results have been pretty darn good, aside from last night. Just one earned run allowed in June, and one earned run in July. He's inducing double plays in big spots lately. There's reason for concern in the pen, but I don't think Treinen is among the issues.

Perez is definitely worrisome, as he's had a bunch of bad appearances lately, in a short space of time.

Harper said...

Potomac - because soon enough rosters expand and Perez can be lost to a gaggle of AAA and AA arms.

GC X - I think it probably does happen more often than would be expected by random chance but not that much difference. Look at the teams now - there are 6 teams trailing by 5-10 games (the rest are too close and I'll go 10+ being too far at this point). Last year on 8/15 - 6. 2014 - 7. Let's say 6 is typical. The Nats Marlins is a pretty extreme example (bigger lead, obv talent diff) so let's say the chances statistically are more like 1% from that range of lead. Well if a "swan" event happened once every 4 years that would be like < 5%, once every 6 years that would be like < 3%. Not too big a difference.

What is discounted is that the division and WC have really opened up the potential for events. So many more chances. So it may in fact happen once every 5 years (I'll od my Boz diliegence here and not look anything up) to SOME team. But just some team and more likely a bad lucky team being caught by a good unlucky team and or injury related etc. Of course we forget the circumstances and the say 29 times it DIDN'T happen.

Fries - its a pen that has holes but Dusty has worked around it but you're right playoffs are a different beast usually calling for earlier impt pen usage. It'll be interesting to see if an arm emergence after call-ups

Jay said...

Don't forget there is recall bias as well. I was shocked two nights ago when I saw the Nats were 8-3 in August at that time. They are now 9-4 in August. I felt like the would be very close to .500 since as a fan, I feel they win one and then lose one (like they have against Colorado - confirming my recall bias). I forget the fact that the swept the D'backs. I also forget they took 2/3 from the Giants. My recall bias made the Giants series feel like a split - like the Indians 2 game series. Anyway, here we are over half way through the month, and I feel like the Nats have been playing .500 since the end of April.

Meanwhile, the Marlins are surely a threat in my anxious fan mind. Surely, they can make up a deficit of 8.5 games in 6 weeks. We're lucky they haven't shaved off 2-3 games in August. Reality shows me the Marlins have been 5-9 in August. Part of the reason the Nats are so far ahead is bc the Marlins have lost 4.5 games in the standings in August.

In fact, when I check standings for August - the Nats have the 2nd best August W-L record in the NL behind the Cubs (12-2) and third best in MLB in August behind the Cubs and Seattle (11-4) and tied with KC (10-5). Doesn't sound like a team that is fading does it? And I agree with Boswell that black swan events can occur, but the likelihood of that occurring in the regular season the Nats and Dusty Baker is pretty small. Baker and the Nats know how to "close" in the regular season. The post season...that is another story... but we'll save the fan anxiety for closer to October.

Dr Trea (formerly #werthquake) said...

Phillies - Mets 2007 is just entrenched in many of our heads I guess

Kevin Rusch said...

I'm not too worried about making the playoffs, and honestly, my biggest worry is using guys that I don't consider likely to contribute because they have "experience". If Zimmerman's not being productive, then don't use him. Perez looks bad right now. If he's hurt, DL him. If he's done, then the nats need to find another LOOGY. (If only they hadn't traded away a young hard-throwing lefty) Is there a starter in the minors who they can get to be a LOOGY?

What's the bench look like? Can Difo contribute? Drew? MAT is hitting better in AAA - maybe he's figured something out.

Those are the things that worry me.

Mythra said...

Only one thing about Perez and the roster expansion.

This helps if Perez is tired, overworked, dead armed, etc. But I am fairly certain that playoff rosters are limited to those who are on the roster before expansion. This stops a team from just replacing 25-man roster slots with someone having a hot September call up.

Glover coming up now might be to see if they can swing with just Solis in must-have lefty matchups and have Glover/Kelley/Melancon for the 7-8-9th.

The roster expansion does help Murphy, Werth and Ramos, though. They can get off their legs and let Goodwin, Difo, and Severino get some playing time and give them some needed rest.

PotomacFan said...

From SB Nation:

So here is a breakdown of the eligibility rules for playoff rosters.

The first part is easy. Any player who is either
- on the 25 man major league roster, or
- on the disabled list (7, 15, or 60 day DL), or
- on the suspended list, or
- on bereavement leave, or
- on military active duty

as of midnight on August 31st, just before major league rosters expand, is automatically eligible to be on the club’s post season roster.

In addition, a club can replace any player who is injured at the time that playoff rosters are submitted. So, for every injured player, the club can add a player who was not on the major league roster, or any of the above eligibility lists at the end of August.

In order to be eligible to be added in place of an injured player, one need not be on the 25 man roster, nor even the 40 man roster as of August 31. Any player in the organization as of August 31 can be used to replace an injured player, with permission from the commissioner’s office.

ntr realDonaldTrump said...

Why are you misquoting me? I never said any of those things.

Ben said...

This is an absolutely superb article. A pleasure to read.

JE34 said...

Hopefully with the roster expansion, Stras will get some time to get himself right. He's in the midst of his third straight crappy start. Ugh.

Anonymous said...

For maybe the first time since his debut, I was really starting to believe he might actually live up to all the crazy hype. Then this happens.

I promise you, I'm never making that mistake again the rest of his career, ever.

mike k said...

What mistake? That he'll never have 3 subpar starts in a row? Man are you going to be disappointed in life.

I know, I know, I shouldn't take the bait...

Sammy Kent said...

Nothing is in the bag in August. Nothing. It is beyond stupid to be talking about the post season at all at this point, much less talking about it as if it is a foregone conclusion.

Froggy said...

Calling it is purely an ego thing. People 'Call it' so they can say: 'I called it first...see, I was right'. Justified after the season is over of course.

I remind folks of 2011 where the Braves had an 8.5 game lead in early Sep and the Red Sox had a 9 game lead on Labor Day weekend only to choke it away through epic September collapses and last day of the season losses.

I agree with Robot, JE34 and Potomac Fan, one of the Anons, to name a few that we should NOT be talking about calling it and instead should be appeasing the baseball gods and focusing on the day to day shortfalls that need to be addressed. Oliver Perez, the rest of the pen minus Belisle and Melancon, the Revpinsosa offense hole, dead arms in the starting rotation, whether Ross will be the savior, does Roark end up with the Cy Young, will BRYCE come back, etc, etc.

JE34 said...


...AND banning baseball in the thin air of Colorado.

Last night I was trying to explain to my son about the difference the thin air makes. Using, I took random samples of home/away splits over the careers of various players over various lengths of time. Home/away splits in my random sampling were nothing to write home about... 10-20 points better at home, here and there. Not seriously scientific, but informative. Comparatively, the home/away splits for Rockies players are downright hilarious.

Just for fun, I looked back at Larry Walker's career. Pretty consistent year to year as an Expo, then with his new home at Coors, he's 100+ points better at home, almost every year. In 1999, he hit .286 on the road, and a bonkers .461 at home! 1.410 OPS! Good gravy.

Jay said...

I agree with JE34. I hate Colorado. The only other stadium I that comes close is the band box in Cincinnati. Hopefully, they can get back on track against the Braves.

PJI said...

Oliver Perez is a bad pitcher. He was booed out of New York. Dusty Baker has way too much confidence in him. I rather see them use the right handed pitchers against lefty batters than let Perez pitch. No confidence in him. Worried Zim will come back and do absolutely nothing. Time to bag him and use DM at 1st base.

Froggy said...

I also think fastball / power pitchers and Coors stadium don't mix well. (see Scherzer and Strasburg) As a batter you guess heater and it's going out of that place pronto. (see Werth hitting a 447 foot bomb onto the concourse in LF) You're better off putting your junk ball pitchers out there and playing for the contact out. But it's a moot point now as I think we are done with playing in Colorado for the season.

Sammy Kent said...


I agree with you about both Oliver and Zim. I like Oliver and think the throwback Lius Tiant style is cool, but you gotta have results and he ain't getting it done. BTW, Matt Thornton was released by the Padres a few days ago. I know he hasn't looked that good this year, but he was a pretty darn good LOOGY for us and Rizzo can pick him up cheap. If nothing else, sign him to a 10 day deal and see if he can get a guy out. Perez right now isn't even LOOGY material. He throws the ball and they hit the ball until Dusty comes to get him, then he does his little prance over the foul line like it's just a joke. It doesn't appear to bother him at all that he's just stunk up the joint again.

But honestly, there is something really different about the entire bullpen now compared to early in the season. Those guys were darn near unhittable in May and June, and we were all doing backflips over Mike Maddux. Now the pitching, both starting and relief, is showing some serious red flags, and it's making me nervous.

Booyah Suckah! said...

Man, I used to love reading the comments section of this blog ALMOST as much as I liked reading the blog itself. But it's just way too doom-and-gloom old-school woe-is-us our-team-is-the-worst fan nonsense for me now.

1. I love when people bring up the 2011 Braves/Red Sox collapses as though that proves the point. The reason we're still talking about it is because A) they were relatively recent, and B) they were so unbelievable that it proves exactly the point Harper is making. If that stuff happened all the time, we wouldn't still be talking about two collapses from six seasons ago. What about the dozens of playoff races that DIDN'T go that way since then?

2. Sammy, say one positive thing. Just one. I'm worried about you.

3. Kevin, now we're supposed to be upset that we got rid of a "young, hard-throwing lefty" in return for Melancon? I'll make that deal twice a day, every day. His stats were arguably some of the worst in the pen. But I get it. We're fans, and now that he's gone, he must've been the second-coming of Rivera. Because our team is the worst!

4. Fries, "Kelley/Melancon/Belisle aren't quite as lights out as you'd want in a playoff scenario"? Then who would you like to have? Seriously? Barring some sort of historic fantasy baseball situation, where are we supposed to go? Are those the greatest three relievers in baseball? No, probably not. But Miller hasn't exactly been killing it since the trade. The Cubs got Chapman precisely because they didn't like what they had. The Royals pen hasn't exactly gotten them back into WS contention. Seriously, pick a 7-8-9 combo out there that you would trade whole-hog for our 7-8-9 combo in a playoff situation. Not saying ours is the best, but it's not even remotely close to being the worst. But again, it's "our" team, so it must be doom and gloom.

5. Sammy (again), Thornton isn't a LOOGY. Actually, his stats this year were better against righties, and he faced more of them. Last year he was a little better against lefties, but certainly not into LOOGY territory. For the record, I really like Thornton. But the guy has a .848 OPS against him this year. That's over 100 points worse than Perez for the year, FYI, whom everyone wants to release. But he doesn't play here!

Anyway, sorry for the rant. I had some time to kill. My point is, I've always liked to commenters here because we tend to stick to facts and dispassionate analysis and save the sky-is-falling nonsense for the Mets blogs. Especially when we're up by 8.5 games. But I might have to just start clicking away after reading the post. Yeesh.

Rob said...

I'm glad there are no more games in Coors Field this year....yikes!

Froggy said...

Booyah, I agree that it is not all doom and gloom, but disagree somewhat that citing previous MLB meltdowns predicts the same fate upon the Nationals. I just think 'calling it' with 25% of the season remaining to be played is literally premature and lends itself just as validly to considering the possibility of an opposite outcome. It also is an arrogant distractor and somewhat disrespectful to the game IMO.

The thing I love about this blog is how consistently Harper produces in depth analytics based opinion pieces that stimulate lively discussions from the largely loyal Nats fan base and it all remains passionate without devolving into ad hominem comments. It's very similar discusdiins to what I experience throughout the season with fellow season ticket holders at the park.

JE34 said...

@Booyah - THAT...was awesome. I recognize the absurdity of thinking that somehow, having us talk about "calling" the division will somehow affect the outcome... and how we tend to focus on what's wrong, even with a comfortable lead over the nearest division rivals who themselves have very serious problems. But alas, human nature. When we watch something every day, especially a game that is a collection of little failures, happily interrupted by bursts of awesomeness (like a Trea Turner triple, which is a weekly occurrence now?), we obsess over the bad. I remember in 2014, (IIRC) when the Nats clinched a trip to the postseason on a day they lost, I thought to myself, "Meh... that's kinda lame to be spraying champagne after losing." I then caught myself being crazy and said, "JE34, what is your major malfunction? We're in the playoffs, you idiot!" It's a constant battle.

Booyah Suckah! said...

JE34, I completely agree. I actually caught myself having a shi**y attitude with my kids yesterday because of the pounding the Nats were taking right before I went to pick them up from school. And then I'm like, oh right, it's just a game, and also, we're still cruising. Let's step back off the ledge.

There are fans of probably 25 teams who have far more legitimate reasons to be worried about their team than we do. And really only fans of 1 team who have less reason.

Froggy, I see your point, but disagree philosophically. The whole point of "calling it" is that there's still a mathematical doubt. If there wasn't, you're not calling it, you're just stating a fact.

That being said, I'll bask in the fact that we're even able to have a conversation about whether we're calling it too early, instead of the conversations of past years about whether we can come back from 8 down, or which call-ups will be interesting to watch for future seasons.

Anyway, I stand by the act of calling it. Not one single person in this comment section would have said in April that the Marlins were 9 games better than the Nats over a full 162 game season. I can't imagine why we would now think they could be 9 games better over 44.

John C. said...

Booyah - well done. 100% in agreement there.

Kevin - "If only they hadn't traded away a young hard-throwing lefty"

Two points: (1) they had to trade something to get Melancon. Unless you would rather have Papelbon still closing? and (2) For whatever reason, Rivero has sucked against LH batters this year: .324/.427/.432/.859 vs. lefties. Ouch. Just imagine how we would fry Rizzo if he had KEPT Rivero and Rivero got tattooed (again) by lefties in a crucial situation in the pennant race or playoffs.

Froggy said...

Booyah I guess my opinion is admittedly based more on superstition than statistically probably outcomes. Regardless, Harper's piece was most excellent, and I should have led my comments with acknowledging those points first instead of taking the counter superstitious counter position.

As for Rivero for Melancon, I agree with JC, I don't see how you don't do that trade. I for one am super glad that Papelbomb is gone, regardless of what a 'great teammate' he might be.

Sammy Kent said...

Booyah: I said Thornton was a pretty good LOOGY for US. In both 2014 and 2015 Matt used him almost exclusively for left-handed batters in late game situations. San Diego used him differently. I realize, and said that his numbers were less than stellar this season, but I believe he could be very effective back in a Nats uni being used as Matt used him. I don't think he could possibly hurt us any worse than the current lefties we have in the bullpen (one of whom is now on the DL and in no position to hurt OR help).

Thank you for your concern, but don't worry about me. I realize my posts often sound excessively critical, but I am just as happy when the Nats play good baseball or management does something creative and helpful as I am testy when they do stupid stuff or play like crud. When they do exceptionally well, you'll hear it from me.


Dusty's Toothpick said...

Harper your logic is soothing to the soul, keep it coming!