Revisiting Kansas St.-Xavier thriller through a fascinating new prism

SI sent two writers -- me and Kelli Anderson -- to Salt Lake City, and we split up the bracket. Butler knocked off top-seeded Syracuse in the early contest, and

SI sent two writers -- me and Kelli Anderson -- to Salt Lake City, and we split up the bracket. Butler knocked off top-seeded Syracuse in the early contest, and I was more than happy to jump on that. Stories like the Bulldogs' are so rare and inspiring that it's unwise to pass on them, for fear of going years before falling into another one. (And I also figured there were slim odds that Kansas State-Xavier would be more entertaining.)

You know what happened: the drama of two overtimes, 13 ties, 17 lead changes, 197 points scored and a 101-96 win by the Wildcats. I watched the early parts from the press room on TV (while trying to write), and then saw all the defining sequences courtside. Elements of it reminded me of being at the Syracuse-UConn six-OT thriller the previous March -- the absurd shot-making, the audible gasping from the crowd, and especially, the suspension of jadedness in press row. That does not often occur.

I used a ticket stub from that Sweet 16 doubleheader as a bookmark for the next few months. It kept the game on my mind to the extent that when, in late May, efficiency stats guru Ken Pomeroy released Win Probability graphs for nearly every game of the 2009-10 season, charting how teams' odds of victory changed on each possession, Kansas State-Xavier was the first thing I examined. Some of you might consider it blasphemous to re-live such a game through a chart, but this is a previously unavailable prism through which to view it ... and as charts go, this one is pretty amazing.

Some important explainer-info, before we proceed: Kenpom's Win Probability figures are based on time-and-score data from thousands of college hoops games in his database. Games don't begin with even odds; because Kansas State was the more efficient team, it theoretically opened with a 56.9 percent chance of beating Xavier. All possessions aren't created equal, either: The charts are color-coded to show the varying stakes of each possession; the highest-leverage possessions, shown in yellow, have potential to create at least a 10 percent swing in Win Probability. As Pomeroy wrote of his leverage ratings, "You can think of [them] as a proxy for the watchability of a game at that point."

Kansas State-Xavier was eminently watchable. Of its 50 minutes of game-time, 15:04 was high-leverage -- a figure that blows away any other NCAA tournament game. BYU and Florida's double-OT duel in the first round featured only 9:29 of high-leverage possessions, because its second extra period wasn't competitive. The Wake Forest-Texas single-OT game in the first round had 8:27 of high-leverage possessions. Northern Iowa's second-round upset of Kansas had 4:52. The Michigan State-Maryland second-round thriller had 1:32. And the Duke-Butler national championship game, despite its tense finish, had just 1:16. Because of Duke's sizable efficiency advantage, on only one possession -- after Kyle Singler missed a shot with 37 seconds left and a 60-59 lead -- did its Win Probability drop under 65 percent.

The Kansas State-Xavier chart is far more volatile than that of the title game, almost giving off the appearance of a tachycardic ECG reading. Because the Wildcats opened with a slight advantage (56.9 percent WP), when they fell behind on the scoreboard on a few early occasions -- at 0-2, 2-4, 31-32 and 33-34 -- Win Probability remained on their side.

The game got interesting once it passed the nine-minute mark of the second half. Curtis Kelly scored off of an offensive rebound to put K-State up 56-49, and lift its Win Probability to 83 percent. Xavier calls a timeout, for which Gus Johnson's outro-to-commercial line is, "Here come the Dobermen!" Things were looking bleak for the Musketeers, who followed the timeout with a turnover and a missed shot on their next two possessions. With 8:06 left in the game and a seven-point lead, the Wildcats' Win Probability was 86.5 percent. It wasn't over, but mathematically, it was heading in that direction.

Over the course of the next 12 possessions, Xavier brought the Win Probability back down to even (at 50 percent), tying the game at 67-67 with under a minute to play and setting up a stunning sequence of events.Earlier this summer, when I talked to Kansas State coach Frank Martin about the game, he said he'd yet to review the tape in its entirety. "But," he added, "I've replayed the end of it in my head hundreds of times."

Martin has to enjoy the first part, which went right: The Wildcats got the ball back with 47 seconds left, and instead of gunning for a two-for-one opportunity on the 35-second shot clock, they patiently ran a pick-and-roll at the top of the key with their two best shooters, guards Jacob Pullen and Denis Clemente. Pullen kept his dribble into an iso situation on the left wing, and his three (complete with a "BURIES IT!" exclamation from Johnson) with 23.6 seconds left was a true dagger. It put K-State up 70-67, and elevated its Win Probability from 57 percent to 79.

The ensuing possession is palatable for Martin, too: He frantically ordered his team not to foul, because there was too much time left on the clock. Although Xavier hit a quick two-pointer (on a Jason Love putback with 12.1 seconds left) to cut it to 70-69, it only reduced the Wildcats' Win Probability from 79 percent to 77.5. (It's interesting how little affect that late two had on the game odds; given how hot Jordan Crawford and Terrell Holloway were from long-range in the second half, it seems they would have been better off taking a three.)

Xavier was forced to foul, Pullen hit both free throws to make it 72-69 with 9.7 seconds left. K-State's Win Probability was 85 percent. And this is where disaster struck for the Wildcats, after Martin gave instructions to foul. "Every time, everywhere I've been, we've always fouled in that situation," he said. "It's just what I believe in."

Clemente dutifully tried to foul Holloway shortly after he dribbled past halfcourt. But ... Clemente didn't foul hard enough to guarantee a whistle, and the refs remained silent. That caused Wildcats guard Chris Merriewether -- heretofore considered a heady defensive sub -- to reach in a second later, allowing Holloway to sell the act of shooting a three, and draw an improbable three-shot foul. During the slow-motion replays, CBS color analyst Len Elmore said, "Now you see why coaches are loath to foul in that situation."

Holloway, an 84.6 percent free-throw shooter, nailed all three attempts, tying the game and reducing K-State's Win Probability from 85 percent to 56. The Wildcats, who watched Pullen's buzzer-beater go off the rim, were temporarily shell-shocked heading into overtime, but Martin is still adamant that he made the best tactical decision. "If I'm in that [situation] next time," he said, "I'm fouling again."

And you know what? He's right. The odds are overwhelmingly on his side.

Let's say that a smart team up three in that situation -- and Martin said his team had rehearsed this scores of times -- commits the shooting-foul blunder on 1 in 8 occasions. Even if that happens, a jittery 18-22-year-old will still be forced to hit three consecutive free throws to tie the game. The odds of even an 85 percent free-throw shooter making three in a row are 61 percent. So we're talking about 1/8 odds of putting the guy on the line, and then only 6/10 odds, at best, that he ties the game -- which means there's only a 7.5 percent chance of that doomsday scenario. Would you rather take that risk, or let a 35-40 percent three-point shooter attempt a long-range shot while you're being careful not to foul?

Here's the statistical picture of what happens when a team up three correctly executes a non-shooting foul in the waning seconds of a bonus situation:

A 70-85 percent free-throw shooter needs to make his first attempt in a high-pressure situation. Then the odds turn against him. To create a long rebound on shot two, he needs to miss artfully -- a skill that's rarely practiced because it's rarely required in games. How often can a player throw up that perfect brick? One in five times? One in 10?

His teammates then need to get an offensive rebound, and this is when they're at an even bigger disadvantage. Teams, on average, only grabbed 32.7 percent of available offensive boards in 2009-10 -- under normal circumstances. But Martin makes the point that free-throw rebounding is an abnormal situation: "Ever since the NCAA changed the free-throw lane rules, where [the defensive team] gets four guys, and [the shooting team] gets three, one of whom is the shooter," he says, "the chances of getting an offensive board went way down."

Let's generously assign the odds of getting that offensive board at 30 percent. After that, the team would still need to make a two (a 47 percent shot, on average) to tie, or a three (a 34 percent shot) to win.

The odds of that tie sequence playing out are around 2 percent, and odds of a different tie sequence (with an unintentionally missed first free throw, an offensive rebound, and a three) are also around 2 percent. That's a rough total of 4 percent, which, combined with the odds of the aforementioned K-State three-shot-foul doomsday scenario (7.5 percent), only totals 11.5 percent.

So, in summation: If you chose to foul in this situation -- and you do it the right way or the wrong way -- my estimate is that there's only an 11.5 percent chance you'll allow a tie, and a 1.5 percent chance you'll allow a win. On the other hand, if you let a decent-shooting opposing player take a three, you're at least three times more likely to be forced into overtime. The foul is the smart play.

The Butler-Michigan State Win Probability chart from the Final Four is an example of how the up-three foul can seal a victory: The Bulldogs held a 52-49 lead in the final 10 seconds, with a Win Probability of 82 percent. Their late foul, after which Michigan State succeeded in making the first free-throw, and missing the second, actually increased Butler's Win Probability, and Gordon Hayward sealed the game by pulling down the final rebound.

The end of the first overtime of K-State-Xavier was as thrilling as the end of regulation -- mostly because the Wildcats had another three-point lead (at 87-84) and didn't foul. This wasn't an egregious mistake, though: Xavier's final possession began with 18.1 seconds left, which was too early to commit a foul, and the Musketeers were in shooting range by the time a foul would've been appropriate. That last possession didn't come off of a stoppage, either, and Martin didn't want to risk yelling in fouling instructions from the opposite bench, for fear of them being processed too late. Crawford, a 39.1 percent three-point shooter, was allowed to launch an NBA-length trey. It went through the net, sent Gus Johnson into an enhanced state of mania, and sent the game to another overtime.

All but the last three possessions of the second overtime were considered high-leverage, but Xavier's gunners failed to make anther three. Thus there were no more heroics and no more dilemmas. With five seconds left, Clemente iced the game with two free throws that sent K-State's Win Probability into the 90th percentile. The score was 101-96, the same way it would end, going into the annals as the 2010 NCAA tournament's high-leverage masterpiece. "There were two teams that day," Martin said, "that just refused to end their seasons." Crawford logged on to his Twitter that night and told Xavier fans to be proud. "Stand up!!" he wrote, before describing the Musketeers' exit in a way no Win Probability graph could. We "went out," he said, "like Gs."