The Null Hypodermic

Introduction

Apparently, I like doing sports forensic analysis. I must, since I'm clearly not doing it for the money. So here's a third installment, after my look at Derek Fisher's 0.4 shot and Mookie Betts's encounter with Houston's right field fans. This makes it two for three on forensic analyses done many many years after the fact, haha.

Let's set the stage: It's October 29, 2014. The San Francisco Giants and the Kansas City Royals are locked in a tightly contested winner-take-all Game 7 of the World Series. Both starting pitchers have long since been knocked out, and the Giants are clinging to a 3–2 lead in the bottom of the ninth. Giants ace pitcher Madison Bumgarner entered the game in the bottom of the fifth inning and hasn't left. He gave up a sharply rapped single to right to Omar Infante, then subsequently mowed down twelve straight batters.

Here, in the bottom of the ninth, he strikes out Eric Hosmer for the first out and gets Billy Butler to foul out weakly to first base for the second out. Bumgarner has now retired fourteen straight batters and needs just one more to record a five-inning save and earn the Giants their third title in five seasons.

But Alex Gordon, after fouling off the first pitch, cues a tailing liner into left center that dies just in front of the hard-charging center fielder Gregor Blanco, then bounces by him toward the wall in left center. He pulls up as it appears clear that left fielder Juan Pérez is going to beat him to the ball.

Pérez boots the ball as he rushes to pick it up, though, and a tense couple of seconds pass before he succeeds and finally gets the ball back to shortstop Brandon Crawford in shallow left. By the time he does so, Gordon is pulling into third base on a single plus two-base error, having gotten the stop sign from third base coach Mike Jirschele. Crawford checks to make sure that Gordon doesn't keep running, then throws routinely to first baseman Brandon Belt near the pitcher's mound.

Salvador Pérez (hereafter "Salvy," his nickname, to avoid confusion with Juan Pérez) now comes to bat, and there follow six specimens of what writer Wade Kapszukiewicz calls "Golden Pitches": pitches whose end result could potentially win the World Series for either team. Such pitches can only occur in the bottom of the ninth or any later inning of Game 7. If Salvy hits a home run, the Royals win the World Series. If he makes an out without first driving in Gordon, the Giants win the World Series.

Bumgarner goes to a tactic that has been successful all game for him: climbing the ladder on his high fastball and daring the Royals to hit it. Salvy swings repeatedly at pitches that are nearly neck high, and on the sixth pitch of the at-bat (and the 68th pitch of Bumgarner's appearance), he finally fouls out meekly to third baseman Pablo Sandoval, Gordon is stranded at third, and the Giants win.

In the aftermath of the game, and indeed all throughout the offseason, Jirschele and Royals manager Ned Yost were repeatedly asked whether they could have or should have sent Gordon home on that second-to-last play. Both were adamant that they made the right decision to hold Gordon, but the fact that Salvy never seemed to be able to contend on an equal footing against Bumgarner in this final at-bat sustained the fervent wish that Gordon had gone home.

But should he have? The question is a tantalizing one and touches on many notions of tactics and strategy. In this post, I'll analyze the game footage and other media and create a framework for deciding whether the Royals would have been better off sending Gordon home.

Technology and Stuff

The first order of business is to establish the basic facts of the play. How long after the crack of the bat did Gordon take to reach first base, second base, third base? When did Crawford field the throw from Pérez in left field? How far was he from home plate at that time? And how long would it take him to deliver the ball to catcher Buster Posey at home, if Gordon were to run home?

The play's timing can be determined by counting frames of the MLB video of the play and its various live-speed replays. Here's the play on YouTube; this video is encoded at 30 frames per second, so by counting frames from the initial contact with the bat and dividing by 30 frames per second, we can construct a timeline of the play:

• 0.00 s: crack of bat
• 2.97 s: ball falls in front of Blanco
• 4.00 s: ball bounces a second time, then rolls to fence
• 4.73 s: Gordon touches first base
• 6.63 s: ball reaches the fence
• 7.80 s: Pérez boots ball along fence
• 8.43 s: Gordon touches second base
• 10.00 s: Gordon turns to look at the play in the outfield (approx)
  
• 10.17 s: Pérez throws ball to cutoff
• 10.67 s: Jirschele begins raising his hands (approx)
• 11.17 s: Jirschele's hands are now up to hold Gordon (approx)
• 11.77 s: Crawford fields ball (about 212 feet from home plate)
• 12.17 s: Gordon stops at third base
• 13.53 s: Crawford throws to Belt
• 14.93 s: Belt fields ball and time is called
  

For some of these events, I also used, as secondary event and time sources, this MLB Statcast video, this fan video from just above the Giants' dugout, and this other fan video from the left field stands, all encoded at 30 frames per second. None of these times are accurate to any better than 1/30 of a second, therefore, though they've been rounded to the nearest hundredth to simplify the arithmetic. I estimate these times have an error of about ±0.05 seconds.

Incidentally, ESPN also analyzed the MLB video, and somehow got 8.30 seconds for Gordon to touch second. I've measured it a few times, and I don't see how they get that. The rest of our times are within my ±0.05 second error bar, including notably the time it took for Gordon to reach third base, which makes that 0.13 second discrepancy even odder. I'll use my figure of 8.43 seconds, to keep the methodology consistent.

Next, how far was Crawford as he fielded the throw and prepared to throw home if necessary? For this analysis, as a reference frame for determining event locations, I used the special groundskeeping design for the World Series games at Kauffman Field in Kansas City, which is depicted here (click to enlarge):

Gorgeous setting, by the way. This photo is from before Game 1, but I don't think the pattern changed for Game 7. As you can see, left field (and right field, but we're focusing on left field) is criss-crossed with a lattice of intersecting light and dark bands, which will serve as a grid for us to identify the locations of players and events during the play. We'll need to fix this grid on a diagram of Kauffman Field, which we create from Google Maps's satellite view (click to enlarge):

North is up. This groundskeeping pattern is not the one from the 2014 World Series, so we can't simply use the satellite image as is. Rather, by comparing the two images, we create an overlay for the World Series groundskeeping pattern. I've rotated the image counter-clockwise by 2 degrees to line the field up horizontally and vertically, then added the relevant portion of the pattern as green outlines (click to enlarge):

Now that we have the grid laid out, we dispense with the satellite view, go through the video, and place the various events on our overlay (click to enlarge):

These events include positions of Blanco (B1 and B2), Pérez (P1, P2, and P3), and Crawford (C1 and C2) throughout the play, as well as the path of the hit ball through the outfield (H1, H2, H3, and H4). We now remove the grid as well, and connect the main events (click to enlarge):

The throw that Crawford would have had to make is the dotted orange arrow to home. By measuring against the 100-foot scale, we see that the throw is about 212 feet. I estimate this method to have an error of maybe ±10 feet, so it's somewhere between 202 feet and 222 feet, but the rest of my analysis will assume a distance of 212 feet.

That's well outside most casual estimates. ESPN's article gauged it at 180 feet, which is 15 percent low. My first off-the-cuff estimate was 140 feet, which is on the skinned infield and ridiculously low, though it was echoed by multiple commentators; then, I guessed 180 feet, in line with ESPN's estimate. Crawford himself thought he was 30 to 40 feet out onto the outfield grass, which would put him 180 to 190 feet from home plate. The longer throw makes the potential play closer than otherwise—but is it close enough to send Gordon?

So Much Crawford

The critical factor is how long Crawford reasonably needs to turn that throw around to home plate. Fortunately, we have plays to compare this one to. The closest play I could find is from September 9, 2016, with the Arizona Diamondbacks hosting the Giants. In the bottom of the seventh inning, with the Giants leading 5–4, Chris Owings hits a fly ball to deep center that bounces off the glove of Denard Span. Socrates Brito scores easily from second base to tie the game, and Owings tries to come all the way around to score also, but he's nipped at the plate by a strong throw from Crawford. (The game went into extra innings tied at 5, and the Giants eventually won 7–6 in 12 innings, so the play turned out to be critical.) Again, we can create a timeline:

• 0.00 s: crack of bat
• 11.47 s: Crawford fields ball (about 235 feet from home plate)
• 12.20 s: Crawford throws ball
• 14.33 s: Posey fields ball
• 14.80 s: Posey applies tag
• 14.93 s: Owings reaches home plate (already out)

This play is almost directly behind second base and there is a convenient sequence of 25 light and dark diamonds, again created by groundskeeping. Crawford is in the middle of the ninth diamond, counting from the edge of the skinned infield, at 155 feet—the skinned infield is a partial circle with a 95-foot radius centered on the pitching rubber—to the edge of the 16-foot warning track in deep center, at 391 feet. That gives us our final figure of 235 feet (again, ±10 feet).

On this play, Crawford took 0.73 seconds to throw the relay, which traveled 235 feet in 2.13 seconds, for an average speed of about 110 feet per second, almost exactly 75 mph. Posey then needed an additional 0.47 seconds to tag Owings. When Posey fielded the ball, Owings was about 13 feet from home plate (that's the radius of the circle surrounding home plate), and he applied the tag when Owings was about 3 feet from home plate.

It's worth noting that a thrown baseball loses a lot of velocity in the air, about 15 percent per second at typical speeds. Crawford probably threw the ball at around 90 mph, and it slowed down to around 60 mph by the time it reached Posey.

There is also a play from September 7, 2013, in the top of the eighth inning of a game in San Francisco between the Giants and Diamondbacks, where Crawford relays a throw from center fielder Ángel Pagán. It's difficult to determine Crawford's distance from home plate; I estimate that he's 195 feet away. The throw covers 1.77 seconds in the air, which is consistent with an average speed of 75 mph, but because of the uncertainty in the distance, it's not my primary comparison.

Additionally, in the second inning of this Game 7, Crawford threw a relay to home plate from right fielder Hunter Pence. Again, it's hard to tell just where Crawford is, but I estimate he's 50 feet past the skinned infield, or 205 feet from home plate, and the throw took 1.90 seconds to get there, an average speed of about 74 mph. The throw was not in time to catch Billy Butler scoring the Royals' first run, but Butler was already halfway from third base to home plate when Crawford made his throw.

Later, in the fourth inning, Crawford made a snap throw to first to complete a sparkling double play started by second baseman Joe Panik, who made a catch diving to his right and glove flipped the ball directly to Crawford. That throw was made under different circumstances, but Crawford's performance was similar: As this MLB Statcast video indicates, he needed 0.77 seconds to throw the relay, which he did at 72 mph, though he was forced to throw it flat-footed.

Reconstructing the Sequence

With all this in mind, let's run through the play again, annotated this time with the sequence and commentary (click to enlarge):

1. At 0.00 seconds, Gordon hits the ball to left center (blue dashed line). The ball is hit near the end of the bat, which causes it to tail away toward left field; see the path above. Blanco initially thinks he can catch the ball on the fly, and he charges forward. Pérez also thinks Blanco will catch the ball and starts jogging toward the infield; Posey similarly jogs to the mound, anticipating a celebration involving the notorious Posey Hug.
   
2. By the time the ball hits the ground at 2.97 seconds, Blanco has realized that he can't catch up to the ball, but it's too late for him to pull up to play it on the bounce. It squirts right by him toward the fence. This counters the notion that by running hard out of the gate, Gordon would risk being caught between first and second; he would never get to first base within 2.97 seconds. Pérez has to turn around and sprint toward the ball, and Blanco pulls up as he realizes he can't get there any quicker than Pérez.
   
3. At 4.00 seconds, the ball bounces a second time. Had Blanco played the ball safely, he would have caught it at about 3.90 seconds. He would have been about 210 feet from second base and would have gotten the ball back well in time to keep Gordon from advancing past first base. In reality, the ball continues bouncing toward the wall, Pérez in hot pursuit.
4. Meanwhile, Gordon has run toward first base, but not at top speed. At 4.73 seconds, he reaches first base, having seen the ball bounce once and then twice. At this point, Gordon knows he'll get to at least second and has a good chance at third. Posey returns to the plate for a potential play, and Bumgarner retreats toward the backstop to back him up. Crawford began the play at the edge of the skinned infield, but now runs out to short left field to act as the primary relay. Panik sets up about 40 feet behind him as the secondary cutoff.
   
5. At 6.63 seconds, the ball reaches the fence. Pérez gets there shortly thereafter, but at 7.80 seconds, he boots the ball about 10 feet leftward along the fence. However, even if he fields it cleanly, he is over 300 feet from third base. It would take a phenomenal throw to nail Gordon there, even with Crawford relaying. Blanco's misplay is almost solely responsible for Gordon advancing, and indeed the official scorer assigned an error only to Blanco, not Pérez.
   
6. At 8.43 seconds, Gordon reaches second base. He stumbles slightly as he rounds the bag, but regains his balance. He turns his head to the outfield to try to gauge the play, but it turns out he can't see it clearly because of glare from the outfield display.
   
7. At 10.17 seconds, Pérez has finally secured the ball and throws it (orange dashed line) to the cutoff man Crawford, who stands 212 feet from home plate. Panik is behind him, keeping an eye on the play in left field as well as Gordon's progress on the basepath. Meanwhile, Jirschele starts raising his hands, and at 11.17 seconds (give or take), the stop sign is up.
   
8. At 11.77 seconds, Crawford fields the throw, having had to "pick" it on the short hop. Normally, the cutoff man is supposed to avoid trying to catch a throw on the short hop; he should let it go to the secondary cutoff man to avoid the ball bouncing away and letting the run score uncontested. Crawford later said, "Nothing against Panik, who was the second cutoff man on the play, but I was going to catch the ball unless I couldn't catch it [that is, literally couldn't reach it]." Panik puts his hands up to forestall an immediate throw home.
   
9. At 12.17 seconds, Gordon pulls in at third base. Crawford has turned around, poised to throw home, but after seeing Panik's signal and checking that Gordon isn't going, he tosses a more routine 140-foot throw at 13.53 seconds to Belt, who catches it at 14.93 seconds. The umpires call time.
   

So much for what actually happened. It's time to speculate! Suppose that Crawford again takes 0.73 seconds to turn around his relay throw, which we'll suppose averages 75 mph. (At 212 feet, this throw is somewhat shorter than our comparison, but it's close enough that the difference is probably minor. If anything, however, this approximation overestimates the time elapsed by the throw.) He would then make that throw to the plate at 12.50 seconds, and it would be fielded by Posey 1.92 seconds later, at 14.42 seconds.

Would that be in time to catch Gordon? He actually got into third base at 12.17 seconds. Let's suppose he could have gotten home in another 3.50 seconds, landing him there at 15.67 seconds. He would be more than 30 feet from home plate as the ball reaches Posey's glove. That gives Posey more than a second to apply the tag; in the play on Owings, Posey needed less than half a second to apply the tag.

The What-If Scenario

But suppose that Jirschele hadn't put on the stop sign, and encouraged Gordon to run all the way home. It remains to be seen whether that would be a good idea, but suppose he did that. Let's also assume that Gordon ran flat out all the way and didn't stumble going around second. Gordon would then have reached third earlier, but how much earlier?

On a triple the previous season, on April 5, 2013, in which Gordon seems to have run hard the whole way, he slid into third base 11.90 seconds after the crack of the bat. (AZ Central ran an article on this play, and somehow measured the run at 11.03 seconds. Again, I'll stick with 11.90 seconds to keep the methodology consistent.) If he ran the same way in Game 7, his time to home plate would be longer, by about the time on one of his intermediate legs (first to second, or second to third). As far as I can tell, Gordon is rarely better than 3.60 seconds on any of these—his intermediate first-to-second leg in Game 7 was 3.70 seconds—but again, let's say it adds 3.50 seconds. That gets him to home plate at 15.40 seconds, and still gives Posey nearly a full second to apply the tag. Gordon would be about 25 feet from home plate when Posey fielded Crawford's throw.

All in all, it seems as though Posey would tag Gordon comfortably out in almost any circumstance—barring an error. So how often does Crawford uncork a wild throw? In 2014, Crawford committed 21 errors, on 634 opportunities, which included 185 putouts and 428 assists (throws that lead to a putout). It's unlikely that all 21 errors were throwing errors, and also unlikely that he only threw 428 times, but let's assume both of those are true to put an upper bound on his error rate. In that case, he would have 21 errors on 449 throws, for an error rate of 0.047, a bit under 5 percent. You'd never send a runner if you thought his chances of making it were under 5 percent.

Of course, most of those throws were from shortstop to first base, a throw that averages about 120 feet. The throw in this case was 80 percent further, certainly well within Crawford's range, but probably it increases his error rate. Let's say it doubles it, to 10 percent. Is that high enough to send Gordon?

Probably not. Statistically, for the 2010–2015 era, with a runner on third base and two outs, that runner scores about 26 percent of the time. That itself should be enough to settle the matter, but there's more. In that situation, the team scores an additional run (or more) about 7 percent of the time; otherwise, in this case, the game goes to extra innings and it's a coin flip as to who wins. Maybe the home team has an edge, but it's small. Rob Mains's study in Baseball Prospectus suggested it was about 52–48 to the home team (less than it is in regulation, interestingly).

That means that with Gordon stopping at third, the Royals have about a 17 percent chance of eventually winning the game (a win in nine innings with 7 percent probability, and a win in extras with 0.52 times 0.19, or 10 percent). If he goes home and makes it, the Royals have about a 55 percent chance of eventually winning the game (a win in nine innings with 7 percent probability, and a win in extras with 0.52 times 0.93, or 48 percent). If he goes home and is tagged out, of course, the Royals simply lose.

So in order for it to be worth it to send Gordon, he has to have a success rate of at least 17/55 or 31 percent. Incidentally, Nate Silver did only this part of the analysis, arriving at a figure of 30 percent using slightly older scoring statistics. (He then simply assumed that Gordon would score more often than that and therefore advocated sending him. Very lazy, Nate!) David Freed, writing for the Harvard Sports Analytics Collective, determined a threshold of 29.6 percent based on more specific statistics (though they use the dramatic underestimate that Crawford stands 140 feet from home plate for the rest of their analysis). So there's general agreement on that roughly 30 percent figure.

I don't see Gordon scoring with anything like that probability. Maybe the long throw increases Crawford's error rate a bit more than double, maybe that 30 percent can be edged a little downward because Salvy was hit by a pitch earlier in the game, but I just don't think those two lines cross. Crawford was no playoff newbie in 2014, and sending Gordon just to force him to make a play isn't the percentage call. I'm sympathetic to those who wanted Gordon to be sent home for the excitement value, but it should be recognized for what it is: a gut reaction call that goes against both traditional baseball judgment and post-mortem analysis.

Thursday Morning Third-Base Coaching

Afterwards, there were a lot of fans who insisted that not only should Gordon have been sent home, but that people who agreed with holding Gordon were flat out wrong. Frankly, I think that's a little crazy. It comes from thinking that because Salvy did in fact pop out, he was destined to pop out. Even having been hit by a pitch back in the second inning, Salvy had a chance of walking it off against Bumgarner. He had hit a homer back in Game 1, accounting for the Royals' only run against Bumgarner. And there's the history of Kirk Gibson hitting a home run off the great Dennis Eckersley in Game 1 of the 1988 World Series. Does anyone watching that video think that either of Gibson's legs was in better shape than Salvy's? Salvy would go on to earn the 2015 World Series MVP when the Royals came right back to win the title.

Other fans thought that Bumgarner's admittedly dominant performance argued for a more aggressive stance on sending Gordon home. But again, this smacks of after-the-fact destiny. Bumgarner had already thrown 62 pitches (before facing Salvy), after throwing 117 pitches in Game 5 just three nights earlier. It was by no means a foregone conclusion that he was unhittable. Certainly Yost thought they would get to Bumgarner.

Tim Kurkjian wrote the ESPN article that analyzed the video for timings. That same article also collected quotes and observations from many of the principals involved. To a man, they all agreed that the right call was made. Most of those interviewed thought it wasn't close. (Yost thought Gordon would have been out by 40 feet, which I think is a bit of an overestimate.) The only player who was even halfway wondering what would have happened was Gordon himself, and by his own admission, he couldn't clearly see what was going on in the play at the time, because the bright display on the left field wall cast a glare that obscured Blanco's and Perez's hijinks.

Some other observations out of that article: Jirschele claimed that he was waiting for Crawford to field the throw from Pérez cleanly before holding Gordon up. But Jirschele began holding his hands up over a second before the ball had gotten to Crawford. I suspect he felt Crawford's chances of fielding the throw cleanly were too high not to put the stop sign up before it was too late; if so, his intuition was vindicated.

Gordon recalls running hard out of the box. It didn't seem that way to most observers, including Jirschele, and in fact some fans thought he was just jogging to first until the ball dropped. The 4.73 second time to first base suggests that he was moving faster than that, but not running all out. The explanation is pretty straightforward—Gordon clearly thought that he could expect no more than a single and ran accordingly—but the charge that under the circumstances he should have been running harder than he did is a reasonable one. As we've seen, though, even his fastest run would have had a hard time beating a halfway accurate throw home.

During the following offseason, a local college baseball team reenacted the play and nailed the runner five times out of six, failing only the first attempt on an overthrow. Some fans pointed to that one failure as an additional point in favor of sending Gordon, but that first reenactment got the timing wrong; the shortstop didn't throw until the runner was nearly a full second past third base. (This video is encoded at 24 frames per second.) Seeing the runner that far ahead may have caused the shortstop to rush the throw; also, with that extra time, the catcher could plausibly have retreated to catch the ball properly and race back to tag the runner. This experiment differed too much from the original game conditions to be of much probative value, though.

Finally, five years after the game, Jirschele revisited the call, affirming that he made the right call, and capping it all with an amusing anecdote. But the plain fact of the matter is that if he had sent Gordon home, there would very likely be no debate, and instead Jirschele would be held up as the Royals' third base coach who made the call that ended his team's season.

 [This post is adapted lightly from a Facebook post I just made.]

• –1
• 0
• 1/2
• 1
• 10
• infinity

• A player or any other person who is out-of-bounds.
• The floor or any object above, on or outside the boundary line.
• The backboard supports, the back of the backboards or any object above the playing court.

Joe Borgia, NBA Senior Vice President of Replay & Referee Operations, joined @NBATV to discuss three plays from Sunday's NBA Playoff action:
- Butler charge in Q1 of #TORatPHI
- Gasol offensive foul in Q4 of #TORatPHI
- Murray shot over backboard in Q1 of #DENatPOR pic.twitter.com/5Lto9JNxOr — NBA Official (@NBAOfficial) May 6, 2019

After that, I took a bit of a break.  I had intended to continue on to 紅樓夢 A Dream of Red Mansions by 曹雪芹 Cáo Xuěqín, and had even read a couple of pages, but my father warned me against that one, suggesting instead 三體 The Three-Body Problem by 劉慈欣 Liú Cíxīn.  Well, I read a couple of pages of that too, but put it aside, probably because I read the Wikipedia plot summary and I decided I didn't like the conspiracy-theory angle.

Then sometime in the spring of 2018, I restarted Red Mansions once again, this time in (relative) earnest.  I had bought David Hawkes's English translation around the time of my first abortive attempt, and I now followed along in both languages, more or less as I had with my previous projects. It took a year and change, but I did finally finish it. And far from a chore, I enjoyed most every step of the way. (Though I did occasionally lose patience with some of the characters...)

Red Mansions (more commonly translated as The Dream of the Red Chamber, but Hawkes suggests this is misleading, and I tend to agree) is unusual—perhaps even unique—in Chinese literature for persistently and insistently asserting its own fictionality.  Other Chinese novels exhibit an array of the magical and the mystical, more so than Red Mansions, but even with that wink and nod to the reader, the novels themselves typically present the events as though they really happened, usually tying the events to a specific epoch in Chinese history (for example, such-and-such a year in so-and-so's reign).  Historicity is a big deal in Chinese fiction, ironically enough.

Not so Red Mansions.  After Cao motivates his novel with the desire to commemorate the young girls he knew as a well-to-do boy, the rest of the novel is said to be a story engraved on a consciousness-endowed, polymorphic jade stone, whose own story frames the central story, and who is brought down to earth to experience life by a Daoist priest and a Buddhist monk.  Echoes of all three (or perhaps it is they themselves) reverberate throughout the book, pushing the plot—engraved on the stone, remember!—this way and that.  Such adumbrations seem familiar to those of us looking back at the evolution of 20th-century Western literature; see James Joyce's Finnegans Wake for a notable, if rather denser, English analogue.  But for a novel written in 18th-century China (manuscripts were circulating at the time of Cao's death in 1763 or 1764, and the first printed edition arrived in 1791), it was positively revolutionary.

Perhaps because of that, perhaps because of the iconic love triangle in the central story, or perhaps it is supposed to be revered in the annals of Chinese literature, Red Mansions occupies a central position in the Chinese collective literary consciousness.  (My mother started reading it when she was younger, and never finished it.  She found it fairly ordinary, but in addition, she has a tendency to mistrust any hyperbolic criticism, positive or negative, and the mountains of praise heaped on the story, amounting almost to hysteria, turned her off to reading it.)  When I went to Taiwan earlier this year, I stopped in a bookstore, and there were no fewer than a dozen different editions of Red Mansions, along with at least as many critical studies and examinations. 

And Red Mansions is enormous.  I read a version I had found online, cobbling it together and having to fix occasional typos, and in one case, replacing three pages that had strangely gone missing.  At a normal font size, it occupied nearly 1400 pages; this is typical of printed editions too.  The English translation by Hawkes and John Minford (Hawkes's student) runs about 2500 pages, in five volumes.  (This kind of expansion is typical of translations from Chinese to English, and there's plenty of speculation as to why that is.)  This is something you have to commit to.

On the other side of the ledger are troubling inconsistencies of the same sort, which already appear in the first 80 chapters that are universally acknowledged to be Cao's.  The root of the problem is that Cao was an inveterate reviser, who by his own admission (in the body of the novel itself, naturally) had already rewritten various parts of the entire story several times.  Over time, he must have changed the fates of many characters across the entire breadth of the book.  He was not, however, the most careful reviser, however, and scattered in the thousand-plus pages are numerous continuity errors.  Chief among these were the various poems.  They could not be rewritten nearly as easily or as transparently as prose, so in many cases, Cao merely left them the way they were (possibly intending to return to rewrite them, should the opportunity arise), preserving the older versions of characters (in Hawkes's words) "like flies in amber."

Such observations have led Hawkes, Minford, and Anthony Yu (who authored the tremendously literate translation of Journey to the West, remember) to conclude that despite the questions raised by some of the unfulfilled prophecies, the last 40 chapters in Gao's edition appear to complete Cao's general intent, if not his exact wording, and that Gao likely did just edit some collected fragments, rather than creating the completion out of whole cloth, as used to be the prevailing opinion. Of course, that editing could have been quite substantial, especially if the parts that Cheng and Gao collected were substantially incomplete in patches. But the debate continues.

Its Place in Chinese Literature

All of these needlesome questions notwithstanding, Red Mansions engrosses more of the Chinese reading public than ever.  What accounts for its endless fascination?

Some of it is surely what my mother complained about: a kind of worship cult that has grown up around it.  Because it is continually written about, readers conclude, there must be something for people to be writing about.  We always want to know what all the fuss is about.

But it seems to me that there is more to it than mere reputation.  There is an air of mystery pervading it, both in the story itself and in the story of its creation.  And despite its occasionally glacial pace and fascination with 18th-century Chinese high-class culture, it confronts questions about the meaning of life and reality more directly than any other prominent piece of Chinese literature.  To read Red Mansions is to expose oneself to contradictions of experience and truth. One can decide that they are merely a matter of perspective, but I think it is hard to argue that they are immaterial—fictional or otherwise.

Remember that Red Mansions itself states baldly that it is fiction. There are parts of it that clearly belong to the realm of magical realism: monks disappear into the mist almost in front of one's eyes, characters somehow discover truths that they should not be able to know, and even some lives are lost by some kind of sympathetic magic. Yet this mysticism runs headlong into the crushingly realistic depiction of the juxtaposition between rich and poor, and the cataclysmic fall of the Jia family.

Cao even alludes to this duality in the names of two families in the novel: the aforementioned 賈 Jiǎ family, central to the story, and another, more peripheral family named 甄 Zhēn. There is even a Baoyu in the Zhen family, who closely resembles Jia Baoyu. Nor are these two names chosen by accident, for they are exactly homophonous with the characters 假 jiǎ "false, not real" and 真 zhēn "real." But aside from this obvious piece of symbolism, what exactly does Cao tell us?

As it happens, Cao was born into the lap of luxury, but when he was about 13—the same age as Jia Baoyu at the start of the novel—the old emperor (who had grown up with Cao's grandfather and always supported the Cao family) died and the new emperor, intending to make a political example and distance himself from his predecessor, had the Cao family's holdings stripped. By all accounts, Cao's own family's decline mirrored the Jia family more closely than the Zhen family, who never make much of a deep impression on the story. Does the Jia family in the story merely represent an exaggerated version of Cao's own family?

There is a suggestion that Cao knew, or was told, that it would be impolitic for him to make the Jia family's decline too obviously an unmitigated disaster, that his family (already poor) might have more miseries visited upon it by the powers that be if he were not to soften the blow. Seen in that light, the use of the Jia name might be a way to deflect additional persecution over what could be seen as overly frank criticism of the emperor.

Even then, however, the mere presence of that kind of symbolism (for there is more of it, usually less obvious, scattered throughout the names in the novel) makes it almost irresistible to treat the novel as a roman a clef, which we could interpret as a kind of biography of Cao, if we could only discover the key. Contributing to that sensation is the fact that the earliest versions of the novel include annotations by some commenters who are clearly closely connected with Cao, and which indicate that many of the characters were closely modeled on real people. I think that certainly accounts for a large part of the novel's appeal to readers, year after year after year.

To be sure, there are plenty of episodes that Cao has clearly put in as comic relief or dramatic color. And yet even the characters that Cao puts forth here, these one-offs, are memorable in their short appearances because Cao endows them with recognizable human weaknesses and biases. They do not serve solely to further the plot—in fact, they frequently don't advance the plot at all—but in addition (or instead) remind us of people we all know, until it almost seems as though Cao knows our friends better than we do.

The bulk of the rest of it, of course, is the love triangle between the three main characters. It is not, plotwise, a very complex story, and flatly described, it would not be very compelling. But though it is occasionally sentimental and overwrought, it is nonetheless told with such richness and verisimilitude that generations of readers have found it memorable. And in this novel, it is tied together with notions of predestination and of former lives, which I think Western and even modern Chinese readers associate with some distant ineffable Eastern mysticism.

But in fact, for all its romantic filigree, that part of the story is remarkable at its heart for its utter ordinariness. The emotions, though they may be expressed in a foreign and unfamiliar way (especially for Western readers), are still clearly recognizable. Seeing themselves in the novel, readers have for centuries envisioned themselves as Lin Daiyu or Jia Baoyu, much as people in the West have envisioned themselves as Romeo or Juliet, or Puck. It is the ease with which the novel transports readers into its milieu—its seductive immersiveness—that truly makes this novel a cornerstone of Chinese culture.

I got the tl;dr out of the way in the title.

I've written previously about the value of multiple points of view (literal points of view in this case, but I think it's valuable for figurative points of view, too).  Last night, in Game 4 between the Boston Red Sox and the Houston Astros, was another example.

Here's the situation as it was in Houston (the location is kind of interesting, though not really important to the ruling).  It's the bottom of the first, and the Astros are already down 2–0, but they have George Springer on first after a one-out single, and Jose Altuve up to bat.  Altuve hits a deep fly to right, and Red Sox right fielder Mookie Betts reaches up and seems about to make the play, when his glove is closed shut by a fan's hand.  The ball bounces back into right field, where Betts retrieves it and fires it back into the infield.  Altuve ends up on second, and Springer (who presumably had to wait to see if Betts made the catch) stands on third.

Umpire Joe West initially calls a home run, and then appears to indicate interference (as shown here at the 8:48 mark).  The umpires collectively go to the replay, and after a delay of a few minutes, they call Altuve out, and order Springer to return to first.  After Marwin González is hit by a pitch, Yuli Gurriel flies out more conventionally to right and the Red Sox escape without further damage.

In the aftermath of the Red Sox' 8–6 victory, however, there was considerable controversy over whether the interference call was the right one.  The ruling was that because Betts's glove did not exit the field of play—that is, it did not cross the imaginary plane of the outfield fence—he was interfered with.  Had the glove been beyond the fence, then any contact with the fans would not have been considered interference.

The problem is that it's far from obvious where Betts's glove was at the moment of contact.  The Red Sox observed (as did some others) that Betts's body had yet to reach the fence, but the Astros pointed out that Betts was reaching backward for the ball.  Both sides agreed that the ball would have gone into the stands were it not for Betts, and both sides agreed that Betts had a good chance of catching the ball.  (I've seen a few fans claiming that Betts simply closed his glove early, but neither I nor any professional commentator seems to find that credible. See here at the 0:45 mark for a pretty clear video of Betts's glove being closed by a fan's hand.)

Incidentally, whether Betts would have caught the ball doesn't have any bearing on the correct call. West's call was predicated only on whether the fans interfered with Betts's fielding in the field of play. The approved ruling associated with Rule 6.01(e) reads:

If spectator interference clearly prevents a fielder from catching a fly ball, the umpire shall call the batter out.

The comment on that rule goes on to clarify:

No interference shall be allowed when a fielder reaches over a fence, railing, rope or into a stand to catch a ball. He does so at his own risk. However, should a spectator reach out on the playing field side of such fence, railing or rope, and plainly prevent the fielder from catching the ball, then the batsman should be called out for the spectator’s interference.

That's what made the correct interpretation of the replays so vital.

Nevertheless, both sides also thought the replays confirmed their conclusion, each perhaps pretending to a greater certainty than they really felt.  They're really not that conclusive either way, at first glance, and it was important, probably, that the call on the field was interference.  Here's a shot from one angle, for instance (the left-field camera, I think):

limx→af(x)=L⇔∀ε>0,∃δ>0,∀x,0<|x−a|<δ⇒|f(x)−L|<ε

The limit of f(x) as x approaches a equals L, if and only if for every positive ε, there exists a positive δ such that whenever x is within δ of a (except possibly exactly at a), f(x) is within ε of L.

Falsifier.  I don't think it's true; I think the limit is not 13.

Verifier.  Well, if that's so, then you must think there's some neighborhood of 13 that I can't force f(x) to lie in.

Falsifier.  Right.  OK, I challenge you to get within 0.1 of 13.

Verifier.  Sure.  If x is within 0.05 of 5, then f(x) will be within 0.1 of 13: f(4.95) = 2×4.95+3 = 12.9, which is within 0.1 of 13, and f(5.05) = 2×5.05+3 = 13.1, which is also within 0.1 of 13.  [There is more to it than that, such as that f(x) is monotonically increasing, but we'll leave these details out for now.]

Falsifier.  All right, but can you get within 0.01 of 13?

Verifier.  Yes.  All I have to do is force x to be within 0.005 of 5: f(4.995) = 12.99 and f(5.005) = 13.01.  In fact, I can answer any neighborhood of 13 you challenge me with, simply by halving it to obtain my vicinity of x = 5.  If you want me to be within ε of 13, then all I have to do is be within δ = ε/2 of 5.  Then f(5–ε/2) = 2×(5–ε/2)+3 = 13–ε, and f(5+ε/2) = 2×(5+ε/2)+3 = 13+ε.  It's foolproof.

Falsifier.  Hmm, I guess you're right.  I'll have to concede that the limit is 13.

Le mariage est une forteresse assiégée, ceux qui sont dehors veulent y entrer, ceux qui sont dedans veulent en sortir.

1. People were embarrassed to admit voting for Trump (i.e., he was viewed as the less respectable candidate), but that shame didn't translate to the actual ballot. That doesn't mean that people voted for Trump on a whim; it just means that they weren't keen on admitting that to someone else, even a pollster they'd never see again.
    
2. Exit polling was not done at all locations, for obvious reasons. So projections were based on a regression analysis that fits estimates to the sampled locations. That regression assumes, among other things, a certain degree of polarization between demographics. It looks like that polarization was even more extreme than expected (which was already significant).
    
3. Trump was simply a higher-variance candidate than the traditional Republican. This strategy makes sense in any contest where you're the underdog (as Trump was for most of the time)—if he were to play a low-risk strategy, he was almost guaranteed to lose. Employing a high-risk strategy increases the probability of a blowout loss, but it also increases the probability of a close win, which is what happened. We're seeing this all the time in sports, where endgame strategies by the trailing team are becoming more aggressive. That increase in variance translated to the polls. Five thirty-eight was very open about this—they pointed out that their model, though predicting a Clinton win, had about three times more variation (by some metric) in it than in past years.

• It can be used on any dumb text terminal you can think of, as long as it can log into my machine.  I occasionally have to check my mail on some remarkably incapable devices, and mutt will work on all of them.
• It is blindingly fast, meaning that I can access and search my entire mail archive from years back and expect results back effectively the moment I hit the enter key.
• It is remarkably configurable.  That's not a bonus for some people, but I like tinkering with my e-mail interface, and this suits me.
• A somewhat backhanded compliment of mutt is that it prevents me from being exposed to e-mail attacks that depend on code being automatically loaded and executed within the e-mail message.  Well, OK, I do like that, but it's really a way of admitting that mutt can't possibly support the same kind of message display interface that a graphical mailreader can.

• The letter is repetitive. Homework creates a burden for parents. It also takes away time. It also causes conflict for families. All placed in separate bullets that can't help but overwhelm the reader into thinking the conclusion is right along so many different directions.

• He also believes that a single anecdotal piece of evidence (the educational background of his daughter) is compelling.  I'm sure it is to him, because she's his daughter, but that's an advantage that her teachers don't have.  They are beholden to many more people than that.

• The letter places any objection in a belittling light.  This is a "(hopefully minor) conflict."  The implication is that it's minor, unless the teacher makes it major.  (That won't happen, so long as the teacher simply acquiesces, perhaps.)

In any system, at equilibrium, the average number of things in that system equals the average rate at which things enter the system, multiplied by the average time they spend there.

"All truth passes through three stages. First, it is ridiculed. Second, it is violently opposed. Third, it is accepted as being self-evident."

(Incidentally, you would think that we're fighting thousands of years of racism, but racism in the way that we think of it today—based principally on skin color—is a comparatively new phenomenon.  Several hundred years ago, Europeans considered Africans unusual-looking, but not inherently inferior.  It was only when they found they could manipulate them with marginally more advanced technology that they then had to justify the manipulation.  We don't even know for sure whether the Egyptians of the dynastic era were "Nubians."  As I understand it, we think they were, but we don't know, because people of the time didn't think it noteworthy enough to comment on consistently.  That's not to say that they weren't prejudiced, but their prejudices apparently had more to do with place of origin than with skin color.)