It seems almost beneath mention that the Orioles had a comparatively large 4.7% chance of beating the BoSox when Chris Davis came to the plate last night in the ninth with two out and no one on. It would take a statistician of the quality of a Nate Silver to calculate the odds-defying chance that the Red Sox would miss the playoffs and that the Sox and Yanks would both lose last night’s game. If all three of these events were independent of each other (and I don’t think that they are), the odds against what we witnessed last night would be something like 1,750,000-1 – and I haven’t even tried to factor in the odds against what happened this month and last night to the Atlanta Braves.

(YIKES! While I wrote this, Nate Silver did calculate the odds. As I predicted, I got the odds wrong. According to Silver, the odds of what we witnessed last night were actually 278,000,000 to one. Thanks to David in the comments for the correction. Gee, and I thought that my number was off the scale. So I’ll compromise for the moment and post the odds against what we saw last night at 2 hundred million to one against.)

Allow me to state the obvious: two hundred million to one are very long odds. This is not like betting on a longshot to win the Kentucky Derby. It’s more like betting that no horse will finish the race. The odds are much better than you or I will make a double-eagle in golf or be struck by lightning in a given year a given week; even Han Solo thought that Luke Skywalker had a better chance than this to blow up the first Death Star.

Two hundred million to one are the kind of odds that should cause us to wonder about more than the improbability of what we saw last night. It should cause us to wonder about the odds-makers.

I am a sabermetrics kind of guy. I don’t necessarily understand all of the advanced statistics the way I should, but I appreciate that sabermetrics has brought us a depth of understanding how baseball games are won and lost. But we proponents of sabermetrics should not get too arrogant. There is a chaos to the game of baseball that I think is widely underestimated.  If you’re familiar with the concept of the “butterfly effect”, it would seem like the publication of an arrogant headline in a March edition of the Boston Herald can “cause” Carl Crawford to miss a diving effort to catch a Robert Andino line drive in September.

If chaos theory is not your thing, then let’s use a different word to describe what happened last night: luck. When you and I think about luck, we tend to think of a bad break that went against (or in favor of) a particular team, like when Don Denkinger blew the call at first base in game 6 of the 1985 World Series.  But when the numbers guys think about luck, they think differently; they think about any deviation from expected performance, regardless of the cause. And baseball is a highly unpredictable game.

Of course, after the fact the pundits will try to rationally explain what happened to the 2011 Red Sox in terms of cause and effect. You’ll read that the 2011 Red Sox were brought down by injuries to their third baseman and starting pitchers. Read these explanations carefully and critically. Ask yourself how injuries to Dice-K and Buchholz, injuries that occurred months ago, could have caused a swoon effect that did not manifest itself until a few weeks ago.  Also consider another team that suffered injuries this year to its third baseman and starting rotation – your New York Yankees. Finally, ask yourself whether what happened to the Red Sox was so catastrophic that it can explain a collapse that was a two million to one shot. The Red Sox’s injuries were not themselves a two million to one shot. We don’t have explanations for two million to one occurrences in baseball, which is another way of saying that the 2011 Red Sox were an historically unlucky team.

We have a day off from baseball to pause and reflect. The game of baseball, a game that I love, a game in which I have invested a good portion of my life, is a wild and bat-guano crazy game. It is a game where two million to one shots finish first way more often than once in every two million opportunities. You have to be at least a little bit lucky to win, and sometimes (more often than we might think) a good team like the 2011 Red Sox is going to get very unlucky and lose. And that kind of bad luck is coming eventually (probably sooner than we’d expect) to a team that you care about.

Consider this to be your “rational guide” for the upcoming playoffs. For the Yankees to win, they’ll need to be both lucky and good, and to my best understanding, it’s more important to be lucky than good. Keep this in mind when you read mainstream media narratives that focus on a team’s grit, momentum and other such nonsense.

Good luck to you and to whatever team it might be where you’ve made your emotional investment!

28 thoughts on “Chaos

  1. nice piece. nice numbers. since the odds obviously preclude such an event as last night from happening, how 'bout we apply Occam's razor, and try a different explanation…

    Perhaps the "fix" was in?

    Just sayin. I'm pretty sure the NYY/TBR odds didn't figure in the fact that the Yankees wanted TB to win.

    This "once in a lifetime" confluence of events has generated a LOT of buzz re MLB.

    Coincidence? 1/2,780,00 chance occurrence? hmmmm

  2. Didn't Nate say it was 280 million to one? "Multiply those four probabilities together, and you get a combined probability of about one chance in 278 million of all these events coming together in quite this way."

      • Yeah, I was like "I didn't THINK he said 2.78 million to 1" but it's a very easy transpositional error. Also, it should be noted, he admits the number is fudged somewhat due to the events being calculated as if they were independent probabilities and not contingent like they were… but it's still funny as hell. And the NESN article is STILL the gift that keeps on giving…

        • Yes, I also noted that these events are not completely independent. Also, we have to remember that the odds are heavily against the occurrence of ANY particular series of events in baseball — for example, the odds against picking the correct scores of all 15 games on any given Saturday night in July have to be off the charts, but that doesn't mean that we'll see anything unusual in these scores when we read the Sunday paper. But there are probably a considerable number of ways for a baseball season to end that WILL strike us as extraordinary. If our question is, what are the odds of seeing a series of games 162 that will be as crazy as last night's, then we end up with shorter odds.

          • Excellent point, Larry. I was struggling to put this into words, but you did it very well here. You can pose a question about almost anything after the fact and make it seem extraordinary… "What were the odds that Hector Noesi would go 3-0 on a hitter, then 0-2 on the next hitter, then 3-1 on the next hitter, and then 2-2 on the next guy? And give up a single to each one of them? And that it would come the day after Robinson Cano drove in four runs off of three different pitchers? On the road? In a day game? 1,000,000 to 1!!!" But, before that string of events, you'd never actually pose that question because such a series of events doesn't have any meaning or importance attached to it. So, it's sort of a false question. It's the particular string of events that came together tonight — along the long odds that make them so rare — that we really can appreciate.

          • Scott, if I had time this is the area of baseball I'd investigate. There is an intersection of luck and narrative …

  3. Larry, as always a tremendous article. While I can provide explanations why the Red Sox fell apart, I can't pinpoint a specific reason why it all came crashing down. Their collapse (like the Braves) is almost beyond comprehension. Sometimes shit just happens, and it's nearly impossible to truly understand or explain. While I can point to injuries as a reason, I'm no longer sure it was entirely poor luck at play. Certainly the timing of the injuries was luck based, but I feel there may be a problem with the conditioning and medical staffs currently being employed by the team. This is the third consecutive season where the Red Sox have been devastated by late season injuries. At some point, the Red Sox front office needs to put two and two together, and at least make a change at that level. Obviously, that isn't the only change, but it's the first of many.

    • Chip, thanks!

      You know me. I was rooting for this collapse. But at some point last night I felt like I was watching some cosmic convergence of events. You can't explain what happened by looking at the sorts of things we rational saber-oriented guys tend to look at. The odds I've computed are kind of a joke, as is Nate Silver's calculation. When you move to Nate Silver's odds, you're talking about something comparable to winning the lottery with the first ticket you ever buy, or picking a future Catholic saint or POTUS by pointing at a given baby at a maternity ward selected at random.

      We humans are good at spotting patterns … as well as cooking up conspiracy theories. I personally will be skeptical of any theory we might cook up after the fact. You and I both spotted mid-season that the Red Sox were winning games at a terrific rate in spite of the fact that the advanced statistics said that their pitching was mediocre. But they were winning anyway. Then … they weren't. The wheels fell off the bus all at once.

      We're not real good yet at measuring the luck component in baseball. We have things like BABiP and percentage of men left on base. We figure that one run and extra inning games are decided by luck. We look askance at any team that wins more games than their pythagorean calculation would justify. Sure, we'd both figure that with the talent on the Red Sox, their season should never have come down to last night's games … but when the Red Sox go home because of a Dan Johnson two strike home run or a line drive that Crawford catches if it's only hit an inch higher from the ground … you revert to the cliches that the BoSox were snakebit, or that they didn't get the bounces, or that this just wasn't their year.

      I don't know what the true odds were against last night, but they were high. I hate to make comparisons to something much more serious than baseball, but the odds against the recent Japanese nuclear disaster were also very high. However, we can explain that event with a combination of an extraordinary event (an earthquake producing a tsunami) and terrible plant design (not locating the backup generator far away from the plant itself). No doubt that you offer valid explanations for the Sox's collapse, but they don't come close to explaining the severity of the collapse, not to mention the bizarre events that took place last night.

      If I were you, I'd worry more about overreacting to these events, and making changes that hurt more than they help.

  4. I would just like to state that with the new 200 million to 1 odds there is officially betters odds at winning the PowerBall jackpot (1 in 195,249,054) than seeing what we saw yesterday. Crazy!

    There is no sport like baseball!

  5. Larry great article as usual. Nice to see you are out of hiding. Another postseason has come so fast and I can still remember your piece about us being here back. Who knew that the regular season would literally end with a bang. I don't know how the postseason will top game 162. All I know is the red sox being out has had me smiling all day. Sorry Chip.

  6. "If chaos theory is not your thing, then let’s use a different word to describe what happened last night: luck."

    Actually… it's not luck, it's just probability.

    When looking at the distribution of possible events, the improbable, however unlikely, is still an occurrence that is in the mix… even if it only a 0.000000000001% possibility.

    You can't have it both ways.

    It's like when a doctor, who spends his whole life honing his craft, saves someone's life who has a very slim chance of survival… and then rather than praising the doc's skills you call it a "miracle" and ascribe the outcome to a divine nature.

    • Oroboto, you might take a look at the two articles I linked to about luck in baseball. Then we can discuss further.

      • Ha, right on… I didn't bother to read the linked articles. They said exactly what I was getting at, but in a shorter "forum reply" context.

        As an EE w/ a masters in stochastic processes I loathe the use of the word "luck"… it's a colored word that should be replaced by improbable

        Good read, that's why I keep coming back here.

        • It's funny; I learned to play poker from a stats guy who ran MI… so he was like double-numbers guy. It would drive me CRAZY when we'd go to the casino and he's label something as "impossible," so I kept correcting him to "highly statistically-improbable." He always hung his head…

        • Well said. That's why when I use the word "luck" here, I have to define it.

          I don't like the word "improbable" either. That word for me fails in two respects: first, it fails to communicate the importance we place on outcomes. An "improbable" event is outcome neutral; the word "luck" immediately suggests either a good or bad outcome. Second, an "improbable" event can (often does) have a certain cause — the D.C. earthquake may have been highly unlikely but we know what caused it. "Luck" suggests an event without an understood (or even understandable) cause. I can collect all of the suggested causes for the Sox's collapse, but they don't have the cumulative power to explain something this unlikely.

          Yours was a terrific contribution to this discussion! Thanks.Though now I have to go online and find out what makes a process stochastic.

  7. I was in a hotel in Washington, DC for a few days of training. As I took an elevator to my floor of the hotel, there was a television monitor in the hallway that had the fourth game of the 2004 ALCS playing. Even though the Red Sox were down in the series 3-0, after Rivera allowed that stolen base and a base hit tied that game, I knew the Red Sox would win the series. I just knew it somehow. Last night, with the Yankees up 7-0, as soon as those first two batters got on base, I knew the Rays would win the game. It's only happened a few times in life, but Larry's great and wonderful post is dead on. Sometimes things just happen that beat really heavy odds…incredible odds. The Red Sox beat those odds in 2004 and crashed and burned to them in 2011.

    • I know what you mean. I knew weeks ago that the Rays were going to win the wild card. I dared not publish it, of course, but at least two weeks ago it was nearly a foregone conclusion in my mind.

  8. Larry, this is a terrific piece and you have highlighted yet another example of how Life imitates Baseball. In the financial world, for example, George Soros calls it the "Law of Reflexivity" — that markets, which are supposed to be unpredictable and are supposed to be discounting the future, do in fact ALTER the future when they are in a downward spiral because market losses effect confidence, spending patterns, and, therefore, GDP. If this is true, then we as investors should be able to take this into account when we assess markets instead of being so surprised when markets enter a worse downward spiral than traditional odds would suggest likely. In short, the downward momentum is a combination of dominos dropping and, both in baseball and in markets anyway, bad karma getting in our heads as players or as investors. The Red Sox gave plenty of clues that they were hurting. Few of us thought it would turn out this badly for them. But odds of 1 in 278 million? No way. In Baseball, in Markets, and in Life, events are not as random and disconnected as they appear. You will find John Authers' column in today's Financial Times ("Markets" section, "Human factor can make a fool of risk models" a great read and uncanny rendition or your article. You beat him to the punch! If you can't access it let me know and I"ll get a copy your way.