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A single play in the 2014 postseason captivated the baseball world: Alex Gordon’s three-quarters trip around the bases as the Giants’ outfield botched Gordon's line-drive single in the last inning of the World Series. And how could it not? Game Seven, two outs in the bottom of the ninth, down by one, and Gordon—the Royals’ best hitter—facing the suddenly untouchable Madison Bumgarner with a ring on the line. Nate Silver, immediately after the play ended, tweeted the following:

Maybe there’s some recency bias present, but it’s hard to imagine that a play at the plate on an attempted inside-the-park single at that moment wouldn’t go down as one of the great moments in baseball history, right there with the likes of Willie Mays’ catch, Bill Buckner’s error, and Kirk Gibson’s home run. The added wrinkles of the Royals’ storybook run, Bumgarner’s historic playoff performance, and Buster Posey’s involvement in the creation of a new rule that could have been tested on a play with Posey right in the middle just help guarantee it would have been a moment for the ages.

Silver has since written about the play (along with plenty of others), attempting to answer the question of whether or not the Royals should have sent Gordon (yes, says Silver). Others, like Jeff Sullivan at FanGraphs, have focused on how likely Gordon was to score if he had tested Brandon Crawford’s arm (not likely, says Sullivan). There are a lot of opinions on the play, with people dissecting it from every angle and leaving, unfortunately for the deliberate among us, little meat on the bone.

The play seems to have received so much attention because it ultimately didn’t come to fruition, leaving our imaginations to run wild with what it would have looked like (and what it would have felt like) to have Gordon and the ball—an innocent bystander to the chaos—in a race toward home plate to settle a season. That wasn’t to be, of course, and no subsequent histrionics ensued—Gordon didn’t try to steal home, Terrance Gore didn’t pinch-run, and Salvador Perez didn’t channel his inner-Jake Taylor and try to bunt his way on, balky knee and all. The game ended in anti-climactic fashion, with Perez chasing high Bumgarner cheese until finally succumbing to an up-and-in 2-2 fastball that eventually landed in the glove of Pablo Sandoval, reminding us that baseball’s script doesn’t always follow our own, even when it comes desperately close.

Left with a fully satisfying season finale that narrowly missed all-time status, we were left to speculate: What if third-base coach Mike Jirschele sent Gordon? What if Gordon ran faster out of the box, didn’t briefly misstep around second base, and kept full momentum around third? Could he have scored? Would it have even been close? What if Gordon was wearing a pair of 20th-anniversary PF Flyers?

Could Gordon have scored on the play?
Before getting into any hypotheticals, it makes sense that we start with the simplest* question, and the one that everyone has tried to figure out. The short answer: Sure, he could have scored, but the consensus seems to be that it would have taken an errant throw or a dropped ball to give him a legitimate chance. Most back-of-the-envelope estimates have the throw beating Gordon by anywhere from 10-20 feet on the low side to 50 feet on the upper end, which would have given Posey enough time to consult the rule book before deciding how to tag Gordon.

*Yeah, right.

Let’s try to go through the math ourselves, employing video analysis and the power of Google Earth to attempt to find a reasonable answer.

First, let’s figure out how many seconds it would have taken Gordon to reach home if he had been sent by the third-base coach. We have the now-famous freeze frame (borrowed from Jeff Sullivan’s article) below, and we know that Gordon—with the slow start, the subtle stumble, and the deceleration after being held up—reached third base in about 12.3 seconds:

In fact, we can break it down further:

  • Home to first: 4.8 seconds
  • First to second: 3.6 seconds
  • Second to third: 3.9 seconds

Now we need to figure out how fast, approximately, Gordon would have moved from second to third if he hadn't planned on stopping. The simple answer might be 3.6 seconds—the time it took him to go from first to second—but I wanted to double-check by looking at past Gordon triples to see his splits between each set of bases. Unfortunately, the highlight videos from those triples don't provide the right camera angles for that kind of analysis. The good news is that it probably makes more sense to look at inside-the-park home runs, anyway, since that’s what this would have (essentially) been.

So I took a random sampling of inside-the-parkers on MLB.com and recorded each player’s total time, along with their time from base-to-base. Here are the results:

  • Home-to-first: 4.7
  • First-to-second: 3.8
  • Second-to-third: 3.3
  • Third-to-home: 3.4
  • Home-to-home average: 15.2

What’s interesting about inside-the-park home runs is that the baserunners’ speed actually picks up throughout their trip around the bases, with the final two legs ending up almost equal. The fact that it takes the longest to go from home to first isn’t a surprise—the batter has to finish his swing and then, like Gordon in Game Seven, they sometimes break into a singles or (outside-the-park) home run trot. What might be surprising is that they go from second to third and third to home much faster, on average, than they go from first to second. It’s tough to say with any certainly why this is true, but many inside-the-park plays develop after a misplay or a bad hop, so these runners might not fully gear up from a slow start until they're past first base.

Based on this information, I don’t think it’s crazy to give Gordon an estimated 3.3-second second-to-third time had he been sent all along, which also comes close to Sullivan’s estimate. Now we just have the final leg left.

As mentioned above, it appears that players don’t generally tire as they near home. Of the six inside-the-park trots I looked at, only two players—Ken Griffey Jr. and Jordy Mercer—went noticeably slower from third-to-home when compared to second-to-third. The other four—Tony Campana, Jose Altuve, Drew Stubbs, and Craig Gentry (man, that guy’s fast)—ran their final two legs within a decimal point of each other. So extrapolating based on the earlier legs, we end up with something like this for Gordon:

  • Home to first: 4.8
  • First to second: 3.6
  • Second to third: 3.3
  • Third to home: 3.4

That puts Gordon from crack of the bat to home plate in 15.1 seconds, which seems reasonable and just so happens to be right on the average of the sample we looked at.

Now the question: How fast would the Giants, had they been forced to make that final relay, have gotten the ball to home plate?

We know that Brandon Crawford received the relay throw from Juan Perez at approximately 11.8 seconds, which would leave the Giants 3.3 ticks to nail Gordon.

The first issue here is to determine how far Brandon Crawford was from home when he received the throw for Perez. The changing mowing patterns of Kansas City’s grounds crew make it an exercise in guesstimation:

The estimate on the right, with help from Google Earth, puts him 200 feet away from home plate. Other estimates of Crawford’s proximity to home plate seem to underestimate that distance—remember, it’s right around 150 feet just to the edge of the outfield grass where Crawford left the infield, and he wandered quite a way out there. Since the ball rolled all the way to the wall and was eventually bobbled by Perez, it gave Crawford plenty of time to get as far out as he felt comfortable making a relay throw.

Okay—deep breath—now the final question: How long does it take Crawford to deliver a 200-foot relay throw to home plate. Again, like the estimable Mr. Sullivan, I chose to look at a couple of previous Crawford relays to get an idea:

Crawford Relays

Distance from home (ft.)

Time from glove-to-home (seconds)

Est. time from glove-to-home (200 feet)

Relay No. 1

185

2.7

2.9

Relay No. 2

170

2.1

2.5

Relay No. 3

185

2.6

2.8

Relay No. 4

175

2.5

2.9

It’s *really* hard to estimate Crawford’s distance from home on these, so obviously don’t take them as precise measurements. While I’m comfortable saying that Crawford was further out into the outfield in Game Seven than any of the above relay plays, I’m not 100 percent confident whether it was by 10 feet or 30 feet.

If we ignore relay no. 2, which was shorter than the rest and on a different angle, we can assume—while surely breaking a few laws of physics—that Crawford’s throw would have arrived in Posey’s glove in 2.9 seconds. Let’s call it 3.0 seconds because Crawford had to receive the throw on a short hop, where the others were closer to chest high. Admittedly, we’re spitballing a bit here.

So … Alex Gordon arrives at home plate in 15.1 seconds and the Giants’ relay gets there in 14.8 seconds. Assuming Gordon was traveling at 18 mph (Statcast had his peak speed at 18.7 mph), that would give Posey the ball with Gordon just about eight feet from home. While that’s plenty of time to make an easy tag on a strike throw, it also leaves relatively little room for error.

At shortstop, Crawford’s arm strength is more highly regarded than his accuracy. Looking at the Fans Scouting Report, Crawford’s throwing strength is rated behind only Andrelton Simmons and Troy Tulowitzki among shortstops in 2014, though his arm accuracy ranks him a more pedestrian ninth. His career throwing-errors-per-400-assists* of 7.0 rates slightly better than the league average rate (7.7) among shortstops. In other words, who knows how likely Crawford is to make an accurate relay throw from 200 feet with the World Series on the line. In the past, he’s shown that he’s a plus defender with above-average arm strength and closer to middle-of-the-pack throwing accuracy, but to actually pinpoint his probability of success under these conditions, well, we’d have to simulate the play 100 times or so—you know, for science.

*Yeah, I just made that up.

Take a look at this screen grab from a Craig Gentry inside-the-parker in 2011, which puts Gentry in the proximity of where Gordon might have been when the shortstop received the ball:

The above image shows when the cut-off man got the ball. Here’s how that play turned out:

Gentry is a good couple notches faster than Gordon, while Kyle Seager, the Mariners’ shortstop that day, doesn’t have the noted arm strength of Crawford. But it does help to provide some perspective and illustrate one of the possibilities had the play unfolded last week in Kansas City.

Considering that Silver came up with a 30 percent breakeven point for sending Gordon, going for it might’ve made sense. Had Crawford delivered a perfect throw home, Gordon likely would have been out. But if his throw was even a few feet offline, took an in-between hop on Posey, or was simply airmailed or misdirected—or if Crawford hadn't fielded the short-hopped throw from Perez cleanly, which happened after Jirschele threw the stop sign up—the chances of Gordon scoring would have been excellent. Processing all of that information in a few seconds, as both Gordon and Jirschele had to do, while making the correct split-second decision is always a tough task, especially when it’s a borderline call either way.

A few quick hypotheticals:

Would Gordon have scored if he was running hard out of the box?
Ben Lindbergh at Grantland:

“Instead, Gordon coasted to first as one would on the usual presumptive single—understandable, in that a batted ball of that sort almost never leads to a scoring opportunity, but still frustrating, in that one would have hoped the stakes in that moment would have overridden Gordon’s muscle memory.”

Gordon cavalierly made his way to first base after contact, which, as Ben notes, is somewhat defensible given the nature of his hit (and he wasn’t that slow). At the same time, there was a decent chance that Gregor Blanco could’ve muffed that ball, opening up a potential two-base hit for Gordon and putting him in scoring position with two outs. Further, there was a non-zero chance that Blanco lets the ball roll by him to the wall—like what ultimately did happen—opening up triple and inside-the-park aspirations. He probably should have been busting it 100 percent out of the box, even if it’s difficult to be too hard on him for it.

If he had run hard all the way, does he score? It’s tough to get a sense for Gordon’s home-to-first speed because very few highlight videos isolate the runner, but if I had to guess:

  • Home-to-first: 4.5
  • First-to-second: 3.5
  • Second-to-third: 3.3
  • Third-to-home: 3.4

That puts Gordon at home plate in 14.7 seconds, similar both in final time and base-to-base distribution to an inside-the-parker Jordy Mercer hit in 2013. We shaved 4/10ths of a second off Gordon’s actual (estimated) trot time, which seems entirely reasonable. That would put Gordon at home plate right around the time the ball arrived, giving him an excellent chance of scoring.

Would a faster player have scored on the same play?
After the game, Gordon commented on the decision to hold up at third:

“When it got by him, I got a smile on my face running the bases, hopefully thinking to score,” Gordon said. “But they got to it quickly enough, and I don’t have (Jarrod) Dyson’s speed, so I couldn’t make it all the way to home.”

Would a speedier player have scored? Almost certainly. Tater Tracker lists the 12 fastest inside-the-park home run times since 2010 and all of them, from Billy Hamilton’s blazing 13.8 second minor-league tour de force to Curtis Granderson’s 14.66 mark in 2011, would have scored quite easily.

***

There’s a certain element of charm in not knowing what would’ve happened had Gordon scampered home. While we’ve attempted to estimate the results of a would-be all-time great moment, the fact of the matter is that any rehashing of the play on the internet only serves to placate our desire to have seen it unfold in real life.

Game Seven of the World Series, which pitted two endearing, overachieving rosters head-to-head, came down not to physical dominance or mastery of baseball skill (save for Gordon somehow managing solid contact against Bumgarner), but rather a decision. As Gregor Blanco and Juan Perez, a normally reliable outfield tandem, turned a routine single into an exhilarating race around the bases, Mike Jirschele made the conscious decision to avoid becoming a World Series goat—even if it might have slightly decreased his team’s odds of winning. For a 35-year minor-league veteran in his first tour of the big leagues, it’s easy to understand where he’s coming from, especially given the fact that Gordon’s less-than-optimal path around the bases didn’t help matters.

Eventually the familiar free agent chatter of the offseason will drown our memories of Game Seven, leaving us knee-deep in Rule-5-draft scouting reports. But it’ll be hard to forget that fleeting moment of baseball euphoria as Perez booted the ball and Gordon churned for third base, even if it didn’t have a thrilling finish. Sometimes baseball—from the grand stage of the World Series to an independent league doubleheader—works just fine as a manipulator of our emotions.

When does next season start?

Dustin Palmateer once played division III junior college baseball, finishing with a career batting average below the Mendoza Line. He now writes about the game at PadresPublic.com. You can reach him via email.

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Dodger300
11/03
I was not even aware their was any controversy regarding this play until I read about it the next day, as it was obvious that Gordon needed to stop at third base. It would have been utterly foolish to surrender in a World Series by hoping that ones opponent can't throw any better than a little leaguer. The Royals job was to try to win the game, not to excite Nate Silver and others by getting thrown out at the plate by a country mile.
shmage
11/03
The omitted factor is the crippling HBP to Salvador Perez's knee. Harold Reynolds, an excellent commentator, had observed that Perez's legs weren't supporting his swing which was entirely upper-body. The reason why they HAD to send Gordon, matter how slight the odds, was that Perez (who is no K. Gibson!) had absolutely no chance at all against Bumgarner.
Robotey
11/03
Do you mean the same Harold Reynolds who noted that after he'd thrown all of two pitches in Game 2, Hunter Strickland had solved his problems--only to give up a HR and more damage a few pitches later?
BCermak
11/03
Yes, most of us understand Reynolds is a moron. His observation about Perez was quite insightful, however. Reynolds' PA breakdowns are sometimes surprisingly cogent and always more insightful than his ramblings on metrics/the state of the game.
Dodger300
11/03
I guess you're right. But maybe someday someone will invent a concept called a "pinch-hitter."
johnnynyc
11/03
My compliments - well-researched and fun piece. Yes it was a less-than-50% chance he's be safe, but probably a toss-up on those odds versus the odds that Salvy was going to knock him in. Mike Jirschele would never have been forgiven for sending him to an out, but he would have been a gutsy forever-hero for sending him to success. I agree, and it's easy in hindsight - Gordon should have been sent.
oldbopper
11/04
Granted the odds of a bad throw were quite long, but that chance of an errant throw or fumble by Posey was far, far greater than the possibility that the badly hobbled Salvador Perez was going to get a hit. The odds of the Royals scoring here are still very low whichever way the game unfolded but sending Gordon was probably the better chance.
Sacramento
11/03
Once Gordon stopped at third, I thought the Royals ought to substitute a fast runner for Gordon and substitute their best bunter (and fast runner) for the obviously handicapped Perez. The Royals would have forced the Giants to defend against a squeeze bunt or tried for a hit (or misplay) against an anti-squeeze-play infield defense. Allowing the slow, handicapped Perez to bat provided the Giants with their easiest defense scenario. The Giants won one playoff game with a walkoff bunt--the Royals could have played "small ball" for a ninth inning, two-out tie.
rawagman
11/03
I would have put in Josh Willingham, who is a decent hitter against lefties, for Perez, who was not right after getting plunked in the knee earlier on by Hudson.
kmostern
11/03
And then you have a catcher who hasn't played in a month, or much at all all year, take you to extra innings in game 7. One of the main issues in the Royals' miracle was their historic lack of depth and reliance on identical lineups. There is a reason the Royals needed Perez regardless of the injury.
rawagman
11/03
Yes, Kratz is rusty, but Perez was a cracked shell of himself and it is always better to play to get to the extra inning than play a weakened hand now. Besides, who's to say that Perez would have been able to play additional innings anyway. Looks like he could barely play the regulation nine.
Robotey
11/03
You cannot squeeze with 2 outs.
BrewersTT
11/03
You can still bunt.
Robotey
11/03
Yes, but only for a basehit. that's not a squeeze. A squeeze is a sacrifice bunt--the hitter is sacrificing himself, making an out--for the sake of moving the runner. So with 2 outs that's not possible. Now, if Yost had pinch-hit with a hitter who could bunt for a basehit, that would have been some exciting baseball.
kmostern
11/03
I expected this article, in trying to sum things up, to try to assess the likelihood of an imperfect throw/catch/tag. I mean, isn't that what's at stake: to know how often on plays the plate the line of the throw is x number of feet off of perfect, how often the catcher drops the ball, how often the tag is misapplied or the runner makes a superior slide around the tag, etc. There is no way of coming to an assessment of the "should" here without someone taking a look at these variables.
BrewersTT
11/03
Agreed. I think the article handles a number of aspects well. Yet a few more come into play, such as Posey dropping the ball or missing the tag. Each of these may only contribute a percent or two one way or the other, but that could be enough. Neither sending Gordon nor hoping for Perez to win it was a great bet, so a few percent could throw the decision one way or the other. Not that I think Jirschele was making multiple calculations in the moment; I don't think it's fair to him for the article to say that he opted not to risk being a goat.
stevekantor
11/03
No clue whether or not Gordon would have scored. I do know however how one World Series ended on a throw 'em out play. That would be the 1926 World Series when Babe Ruth took off for second in the 9th inning against the CArdinals and was thrown out by Bob O' Farrell.
BrewersTT
11/03
There's one more small factor that cannot be quantified, but would work in Gordon's favor: World-Series-level pressure. If he runs for home, pressure is not really a factor for him, but all of the Giants handling the ball have to focus and execute a part of the play. One of them may succumb and blow it.
BurrRutledge
11/03
In fact, two already had.
Dodger300
11/03
Obviously, "World Series pressure" must be contagious enough to increase the odds past the tipping point so that we could naturally expect three or four professionals in a row would ALL succumb to nerves and blow the same play, right?
BurrRutledge
11/03
What are the chances, right?
Dodger300
11/03
Well, the Giants succumbed to the pressure of the World Series by making 4 errors in 2010. Perhaps being a bit more seasoned, they were credited with only one error in four games in 2012 and two errors in seven games in 2014. How much would you be willing to bet that they would collapse under the pressure and make a throwing error just when KC needed it the most? The Royals would have had to bet everything on it.
BrewersTT
11/04
Well, not quite. A variety of factors add up to the probability of success. All I am suggesting is that the chance of succumbing to pressure (after the point that the article begins from, Crawford receiving the ball) might be slightly tipped in favor of KC on this particular play, because running does not require precise execution in the same way that throwing, catching and tagging do. Runners do not run wide of where they mean to run every once in a while. I am not suggesting that this is the only deciding contributor to their chances.
dutt22
11/03
Hey everyone, thanks for the comments. Great discussion! Just wanted to respond to a few points here without replying to each comment/discussion: Dodger300 -- That's a fair point, but I think the point I was trying to make is that it's not a foregone conclusion that Gordon would've been thrown out by a lot, even with a strong, accurate throw from Crawford. Regarding the discussion on what the Royals should have done once Gordon held at third: I agree, I think they should have made a move there. Dyson to pinch-hit and Gore to pinch-run would have been really interesting from a bunt/speed standpoint, though Dyson's terrible against lefties. Willingham would have been an option too. You have to wonder what Perez's true talent level is at that moment -- 165th game of the year, mostly at catcher, with the bad knee and all. I'm guessing, as long as he could swing a bat, Yost wasn't going to pull him with the WS on the line having ridden him all year. kmostern/BrewersTT: great points. I thought about trying to handle that aspect by looking at highlights of past relay throws, but quickly realized that they're highlights -- they likely had a good, accurate throws and clean catches, or a really slow runner, or whatever. You'd really need a bunch of randomly sampled relay throws, I'd think, maybe something that BIS might have some info on. Good points, though, I wish I could have done more with that aspect of the play, as it's an important one.
jnossal
11/03
I thought it was a terrible mistake not to send Gordon as soon as I saw the play. The Royals best chance to tie that game was for Gordon to score right then. Down 1 run with 1 out left in Game 7 of the World Series is not the time to play it safe. Yes, Crawford had the ball and probably has a decent arm, but even if Gordon has only a 25% chance of scoring, that's almost certainly better odds than any other strategy with two outs and MVP Bumgarner dealing from the mound. KC left a bullet in the chamber and their fans will go to their graves wondering "what if?"
rweiler
11/03
Holding him up was the right play. Perez had a BA of 0.226 against LHP for the season, Bumgarner was obviously not as sharp as he had been starting, and Perez already had the only true XBH that Bumgarner had allowed in the series. You figure that Perez has at least a 25% chance of driving in the run. If Gordon had been running at top speed right out of the box anticipating that the Giants would make 3 errors on a routine line drive, then sure, send him. Gordon didn't anticipate that, and there was not reason that he should have, and wasn't running at full speed, and Crawford is plenty accurate enough to make that throw.
buddha
11/04
Given that Gordon was held at 3rd, I think there's another avenue to tread...the wild pitch/passed ball scenario. Are either Bumgarner or Posey (either together or separately) more likely to commit one of those than average? Might be a little more/less to add to the calculation.
dsilvers
11/04
One more scenario to consider: what if Ned green lights Gordon to steal home? Crazy? Maybe. But given a) MadBum is NOT pitching from the stretch, and appears to be paying little attention to Gordon, and 2) given where it was most likely that MadBum was going to pitch Perez (either as he did, up, or outside and low), Gordon's chance of success would have been higher. With Posey staying fairly upright to get MadBum's pitches, he would have had to drop down to attempt a tag. With Perez's size blocking Posey's view (he was peeking down AFTER pitches, when Perez was not in the box normally), Gordon has a better chance to make a sudden break for home with at least partial cover. And as loud as the stadium was, would MadBum have heard someone yelling or would he have paid any attention to Belt at first who would have been the closest person in his line of sight with his back to third? It's as risky a play as there is. But given that KC had pretty much abandoned the running game, it would have had the element of surprise as well. Ah, well. My boys came up short, but it sure was a heck of a ride. #BeRoyal.
mattgold
11/04
I keep waiting for someone to take up Nate Silver's comment that had Gordon gone it would have been one of the 5 greatest plays in baseball history. Granted, it could have been a great play (depending a bit on how close it actually was), but there have been a lot of great plays in baseball history! It seems like a great topic for a separate article (or book), especially now that the season is over.
lyricalkiller
11/04
Okay, give me a few days, probably
thegeneral13
11/04
There are a few interesting elements of this that haven't been mentioned (here, anyway). First, I think the elimination of home plate collisions significantly reduced the odds of Gordon scoring if he was sent, both because of the lost opportunity to jar the ball loose AND the increased probability of Posey mishandling the throw under the threat of a collision. Second, the odds of an error increase with the difficulty of the play, and I think that Crawford had the ball with so much time that the odds of a throwing error were quite low. These guys hit each other in the chest every time from 250 feet playing long toss, so if the throw is routine there's just a very low probability of an error. Thirdly, if the argument to send Gordon is that the Giants might make an error (because with a competent throw he is out with certainty), then we have to incorporate the probability of an error on a ball put in play by Perez if Gordon is not sent, not just his likelihood of getting a hit. And for that matter the odds of a wild pitch, or even a BB or HBP that allowed Moustakas to come to the plate with a better chance of success than Perez (though obviously the joint probability of that is very low). Given the routine nature of the throw that Crawford would have had to make, I don't know that the odds of him making an error would be that much higher than the odds of an error on any given ball in play, or at least not sufficiently higher to offset whatever admittedly small odds Perez had of getting a hit (plus the odds of a wild pitch, etc.). Forgive me if this is addressed elsewhere on the internet, but some of the commenters seem to be ignoring it. It's an interesting discussion, but I think it was very, very clearly the right call to hold him up.
dutt22
11/05
It's tough to say with any certainty, but I still don't think that throw from Crawford could be considered routine. If my estimation is correct/in the ballpark, it's a 200 foot throw that has to be put on Posey on a line, where a short/in-between hop or a few feet in the wrong direction could mean Gordon's safe, with the pressure of a World Series victory in the balance. And it came to Crawford on a short-hop at a deeper-than-normal cutoff position, too, both of which I think take it out of the routine throw bucket. I wouldn't expect Crawford to make a poor thrown there, but it hardly seems like a given that it would have arrived chest high to Posey. As others have mentioned, it's definitely an aspect of the play where more attention is probably due. And regarding factoring in an error/passed ball/etc. on the next at bat to Perez, that stuff should all be factored in with the empirical data that was used by Silver and others to come up with the 25-30 percent breakeven point for sending Gordon, even though it's essentially the "average" data and isn't necessarily tailored to the specific situation. Thanks for the comment -- everyone else, too.