The knock on Tim Tebow during Denver’s six-game win streak this season was that his level of performance didn’t match up to his team’s win-loss record. That his stats didn’t befit a guy who seemed to back into wins on a weekly basis. That he was bound to eventually turn back into an extremely marketable pumpkin. We made that argument here, and unless you actually live in Grantland and don’t have a passport, you read the argument elsewhere. Heck, the rumor du jour this week was that the Broncos were about to bench Tebow for Brady Quinn, who couldn’t beat out Derek freaking Anderson for a starting job in Cleveland. If Tebow somehow won against the mighty Steelers in the first round of the playoffs, it was probably going to take a couple of pick-sixes and Ben Roethlisberger’s ankle disintegrating on national television. Right?

Well, on Sunday Tebow delivered one of the finest performances a quarterback has delivered in recent memory. Not in some intangible quality — leadership, heart, grit, you name it, whatever — but an actual quantifiably great game. He’s delivered that before as a pro, but not as a passer, and not against a fantastic defense. In the wake of Sunday night’s remarkable upset, we are here to tell you that Tebow delivered a game as a passer that is worth your respect and then some.

Recognizing that involves looking past his ugly completion percentage. In going 10-for-21, Tebow completed just 47.6 percent of his passes. What mattered, instead, is what Tebow got out of each of his dropbacks. By throwing for 316 yards on those 21 attempts, Tebow averaged a whopping 15.0 yards per attempt. That’s only happened five times in the past five years, and the company isn’t shabby: Drew Brees, Matt Schaub, Jeff Garcia, Kurt Warner, and Philip Rivers matched Tebow’s feat.

If you want to subtract some credit for Tebow’s inaccuracy, use passer rating instead. Passer rating is flawed for a variety of reasons, but the biggest reason is that it favors quarterbacks with excellent completion percentages who never make big plays downfield. The second biggest reason is that it doesn’t consider a quarterback’s rushing ability. If there is any stat that would give an artificially low opinion of your typical Tim Tebow performance, it’s passer rating. And despite all that, Tebow’s performance on Sunday merited a passer rating of 125.6. Since 1990, only 29 of the 485 quarterbacks who threw 15 or more passes in a game put up a passer rating greater than 125.6.

We’re just getting started, though, because there’s one other piece of context we need to consider: the quality of the opposition. The Broncos were not just facing any old defense on Sunday; they were facing the Pittsburgh Steelers. Pittsburgh’s pass defense allowed just 5.6 yards per attempt this season, which was the best in the league by more than half a yard. Houston finished second at 6.2 yards, and they were closer to ninth than they were to first. Nary a single passer threw for more than 300 yards against the Steelers all year. They allowed a pass play of more than 45 yards just once, and that was on a 73-yard touchdown to LaRod Stephens-Howling on a wheel route in which the ball traveled about ten yards in the air. Nobody beat the Steelers deep this year. Nobody.

And then they met Tim Tebow. Tebow, of course, had completions for 51 and 58 yards on back-to-back drives before adding an 80-yarder to win the game on the opening play of overtime. All three of those throws traveled well downfield. Tebow also became the first passer to throw for more than 300 yards against Pittsburgh this season.

That sort of performance just doesn’t happen against dominant pass defenses like Pittsburgh’s. Consider that there have been 44 playoff games since 1990 featuring a defense that ranked first in the league in yards per attempt during the regular season. In those 44 games, the opposing quarterback has only managed to muster an average of 6.3 yards per attempt. Tebow’s 15.0 YPA was more than four yards better than anyone else’s performance against a top-ranked defense, and only one player achieved a higher passer rating in a playoff against such a defense. That player was Brett Favre, who had a 132.9 passer rating in a January 1996 game against the 49ers.

Perhaps out of an incredulous disbelief that Tebow could actually have a huge passing day, we’ve seen two arguments brought up against his performance. One holds merit, but neither are enough to significantly discount what Tebow did.

The first is that the Steelers were riddled with injuries on defense and not quite the unit that their regular-season statistics would indicate. We knew that safety Ryan Clark would be held out of the game because of his sickle cell trait, but the Steelers lost defensive linemen Casey Hampton and Brett Keisel to injuries during the game, forcing them to play three down linemen for the bulk of the contest. Combine that with a clearly limited LaMarr Woodley, who played through a hamstring injury, and Tebow was actually slicing up a pale imitation of the Steel Curtain. Right?

Well, yes and no. It’s obvious to suggest that Clark would have had an impact at safety, especially considering that replacement Ryan Mundy appeared to get lost on the final play. Then again, Mundy also forced the key Willis McGahee fumble in the fourth quarter that allowed the Steelers to tie up the game. Furthermore, it’s not like Mundy was getting lost while he was freelancing; cornerback Ike Taylor was getting beat because Steelers defensive coordinator Dick LeBeau continued to call an aggressive game. The Steelers flooded the line of scrimmage with defenders on many plays in an attempt to flush out the Denver running game, including a big run blitz on the first play of overtime that was based upon pre-snap motion. The game plan was to shut down the running game and challenge Tebow and his receivers to beat Taylor & Co. deep. Even after the Broncos lost starting wideout Eric Decker in the first quarter, the Broncos were able to pull that off, repeatedly, until the very last play of the game.

The other argument is that Tebow’s numbers really belong to wideout Demaryius Thomas, who repeatedly torched Taylor as part of a 204-yard day. This one doesn’t hold up to any scrutiny. There is, admittedly, a case to be made for the idea that yards after the catch should somehow count less for a quarterback. It’s somewhat ridiculous to think that Eli Manning got credit for a 99-yard touchdown pass against the Jets in Week 16 on a play where he dumped the ball off underneath and Victor Cruz made two defenders miss before running for 90 yards. The plays Tebow made on Sunday night were not of that variety. He deserves plenty of the credit. Tebow’s scrambling ability created the time for his first bomb, which went to Thomas for 51 yards (42 in the air), and then he later hit Thomas in perfect stride on completions of 58 yards (28 in the air) and 80 yards (18 in the air). Thomas’ baby Megatron show was fabulous, but he wasn’t doing all the work by himself.

One game doesn’t make a career. For all we know, we might have just seen the best passing performance of Tim Tebow’s life, a fleeting glimpse into what could happen if Tebow got to play backup free safeties with excellent pass protection every week. With that being said, if any other rookie quarterback from the past three years put up numbers similar to what Tebow did against anything resembling the Steelers pass defense in the playoffs, we would be falling all over ourselves to describe it as the first big sign that a new franchise quarterback had arrived on the scene. It’s time to file Brady Quinn’s name away and stop the debate about whether Tebow deserves to keep the Denver job for 2012. After a year in which Tim Tebow occasionally got more credit than his play deserved, on Sunday, Tebowmania lived up to every bit of the hype.

Thank You for Not Coaching

There are two points we make in this space virtually every week. They serve as two simple rules for judging football decisions, and they are not up for debate. They unflinchingly apply to every single scenario, and if you respect them, you will be a smarter football fan, media member, observer, whatever, in the process. If you don’t know them, they are:

1. You judge a coaching decision by its process, not its outcome.

2. Never challenge a low-reward play.

Both these rules were broken this weekend! More than once! Why do you do this to us, NFL?

Of course, rule no. 1 came up more than once during the Falcons-Giants game on Sunday afternoon. The multiple fourth-down decisions made during the game serve as an example of how outcomes in the NFL warp perceptions of decision-making.

Let’s start with the first decision by the Falcons to go for it. As the second quarter began, they faced a fourth-and-inches scenario on the Giants’ 25-yard line amid a scoreless tie. The math here isn’t too complex. A 42-yard field goal attempt will go through 75.5 percent of the time; that figure is probably a little high for Northern New Jersey in January, but let’s stick with that as an aggressive estimate for kicking. When the field goal fails, the Falcons give the Giants ten additional yards of field position, which costs them about 0.28 points of field position versus the option of just leaving the ball for the Giants on the 25. Add up those two figures, and the Falcons will generate 2.21 points each time they kick the football.

Instead, head coach Mike Smith and offensive coordinator Mike Mularkey chose to go for it. Over the past several seasons, teams have picked up fourth-and-1 69.7 percent of the time. While the Falcons might have picked up more than one yard on the run, again, let’s be conservative and just assume that they get the two feet they need. With the ball on the 24-yard line, Atlanta will score an average of 4.09 points. So each time the Falcons go for it, based on history, they’ll score 2.85 points. That’s an improvement of 0.64 points on the decision to kick the field goal. And remember that these are conservative figures; we’re not considering the difficulty of kicking field goals in the new Meadowlands or the possibility of gaining additional yards on the play and giving the Atlanta offense better field position. With some friendlier numbers to the go-for-it decision, we could easily get up to a full point of value on the decision to pass on the field goal. The fourth-down calculator at advancednflstats.com suggests that the Falcons generated 1.21 points for themselves by going for it.

Of course, while the math was on their side, the Falcons also needed to make a sound play call. They did so here. Many teams in this scenario who don’t want to actually go for it would have their quarterback line up and run a hard count and motion some guys around before calling timeout. The Falcons did that, but as the play clock wound down, Matt Ryan actually took a snap and ran a quarterback sneak. There’s some downside to it — your offensive linemen might jump, and it’s hard to get a sustained push on a “surprise” snap — but you also have a shot at getting the defensive linemen to jump before running a play when very few people expect you to. The quarterback sneak is also, historically, about 15 percentage points more likely to gain a first down on fourth-and-inches than a handoff, something we discussed in our analysis of Smith’s first decision. This was a pretty damn great play call. The Giants did a great job of executing up front, though, and the Falcons got a very rough spot. The outcome was bad, but the process that went into the outcome was sound.

Here’s where we got our first fallacious argument against going for it: “Always put the first points on the board.” The idea is that the Falcons needed to attempt the field goal try because it would have given them a 3-0 lead and first blood in what, to that point, had been a scoreless tie. This seems like the antithesis of the also-popular “Wait to go for two until the fourth quarter” argument, even though it also seems like the same group of people would hold on to these same tenets without thinking them through.

What, exactly, is the benefit of taking the early lead? Is a 3-0 lead really likely to hold up? Exactly two regular-season or playoff games since 1990 have finished 3-0, so it’s hard to make that argument. Is it going to change the game? Maybe it would with five minutes left in the fourth quarter, but no offense worth its salt is going to change what it does because it’s down three points with 45 minutes to go. Is it really going to materially affect your chances of winning? Probably not. We could point out that the teams that scored first this weekend went a combined 0-4, but that’s too small of a sample. We went back to Weeks 11-13 (chosen at random) and tracked whether the team who scored first actually won the game. As it turns out, the first scorer went 24-22. Scoring is great, but unless there is a situational reason calling for you to kick a field goal, your goal early in games should be to maximize your expected points. Here, it’s clear that going for it is the right move.

After a holding penalty and an intentional grounding call led to a safety, the Falcons drove into Giants territory and were faced with another fourth-and-1 call, this time from the New York 42-yard line. In lieu of running you through the math again, we’ll go back to the advancednflstats.com calculator and note that the Falcons will pick up an average of 1.52 points by going for it and actually lose 0.04 points by punting.

Instead of realizing that they were in a beneficial situation and going for it, though, the Falcons decided to give up and punt. It was a disappointing move because one outcome doesn’t mean squat in evaluating decisions. Should the Broncos have stopped throwing passes with Tim Tebow in their game because he threw a duck on the opening third down of their first possession? While you can learn something about a decision from what happened in the previous play, the math suggests that the Falcons only should have punted if they thought their odds of succeeding by going for it were below 37 percent. That’s nearly half of what the league average for success on fourth-and-1 is. Were the Giants really that dominant up front that the Falcons thought they could only succeed 37 percent of the time? It’s hard to imagine so.

What made this decision doubly frustrating, though, was that the Falcons didn’t even line up to go for it again. In many cases like this one, where a team is punting after just entering into opposition territory, they will just automatically take a delay of game penalty and move the ball back five yards. With fourth-and-1 in that situation, there is literally no downside to lining up and faking like you’re going to go for it. What’s the worst that happens? An offensive lineman false starts? Well, you were going to take those five yards anyway, so who cares? If the other team jumps, you get a first down, and otherwise, you end up in the same situation that you would have been in to begin with. Even worse, the Falcons had just run a fourth-and-1 play where they had pretended they were trying to draw the Giants offsides before actually running a play! With that in the back of the defensive line’s mind, every little shift and shout would have been more likely to draw a flag! Instead, the Falcons just punted and cost themselves a full point. It was quite the bummer. After the punt, the Giants drove 85 yards and scored the game’s first touchdown.

Then, we come to the third decision. With fourth-and-1 on the Giants’ 21-yard line in an eight-point game with 4:21 left in the third quarter, the Falcons chose to run another sneak with Matt Ryan. Again, we’ll defer to the advancednflstats.com calculator and note that the Falcons added about 1.21 points by choosing to go for it as opposed to kicking, but we’ll raise some qualms about the play call. That a sneak failed once doesn’t automatically mean that it will fail a second time, but the Falcons ran the play without a running back in the backfield. It’s hard to imagine that the Giants were expecting anything besides a sneak there, and even if they hadn’t, they got such a great push up front that the sneak actually lost yardage.

Here, we got fallacious argument no. 2: Momentum, the trick narrative. There’s no doubt that momentum exists, but the concept gets clumsily shoehorned into situations where it doesn’t really apply. Once the game was out of hand, the announcing team beat us over the head with the idea that the Giants had really picked up momentum after stopping the Falcons on their second fourth-and-1 attempt and produced a long scoring drive because of it. Think about that one for a second. Here’s what happened on the three Atlanta drives that ended in a fourth-and-1:

First drive: Atlanta goes for it and gets stuffed. Giants take a safety.

Second drive: Atlanta punts. Giants drive 85 yards for a touchdown.

Third drive: Atlanta goes for it and gets stuffed. Giants drive 79 yards for a touchdown.

How does it follow from those three outcomes that the Giants picked up key momentum by stuffing the Falcons? Perhaps it’s true that teams are more likely to score when they stop an offense on fourth down than if they get the ball in the same spot from a punt or kickoff. Basing that idea on what happened in those three scenarios, though, is imagining an NFL story and fitting what actually happened to what you want your story to be.

It’s also worth noting here, of course, that the Giants went for it on fourth down inside the Atlanta 5-yard line and picked it up with ease on a play that has not been mentioned since it happened. Using the same logic that was employed to criticize Smith, shouldn’t the Giants have kicked the field goal to take a 3-2 lead? To gain momentum? Of course not. Tom Coughlin and Kevin Gilbride made the right decision, and because they got the right outcome out of it, nobody’s thought about it since. It’s consigned to the bins of history with every fourth down conversion the Saints picked up on Saturday night. Both of those teams undoubtedly gained momentum by going for it. They also made decisions that are clearly and quantifiably correct, even if the plays they had called failed.

The other fallacious argument that popped up from the likes of Troy Aikman and Boomer Esiason was the idea that you always take the points on the road. This one seems impenetrable to us. Why do the points matter more on the road? A field goal is worth three points in either scenario. If anything, it’s easier to make a case to go for it more frequently on the road than at home. Here, watch. You should go for it more on the road because a kicker is less likely to know the field and the stadium’s wind conditions on the road than at home, so a field goal is less likely to succeed if you attempt it. And since you’re less likely to drive down the field and score on the road, you have to take advantage of your opportunities to score while you can and get as many points as possible. See! That was easy.

So that takes care of rule no. 1. The Bengals, though, were kind enough to give us two lessons in how to misuse rule no. 2 during the first half of their loss to the Texans.

The idea of what a “high-reward” challenge is can depend on the context of the game situation, but there are some decisions that will never, ever be high-reward. Marvin Lewis started off his day with the red flag by going after one of those very plays. In the middle of the second quarter of a 7-7 game, Lewis actually challenged a spot on a run by Cedric Benson. Was this a long would-be touchdown run down the sideline that was marked out of bounds 30 yards away from the end zone? That would be high-reward. No, Lewis challenged that a second-and-2 run by Benson that was spotted short of the first down actually went fractionally past the first down marker. Spot of the ball challenges are notoriously difficult to get, and while this one was certainly close, consider the tradeoff Lewis was making. The upside of the challenge is getting a few inches that his team is almost sure to get on third down anyway; the downside is the possibility of being down to one challenge with 36 challengeable minutes left. Even if he gets the challenge right, Lewis would have to make sure that his next challenge was a lock or run the risk of also being out of challenges, at that point, for the remainder of the game. The play wasn’t reversed, Lewis lost his challenge, and the Bengals easily picked up the ensuing third down. A total waste of time and resources.

Amazingly, Lewis wasted his second and final challenge on the very next drive. On a third-and-4 play from the Texans 37-yard line, T.J. Yates completed a pass to Owen Daniels for eight yards and a first down. The ball came out of Daniels’ hands well after he hit the ground, but despite that slight slip in logic, cornerback Pac-Man Jones was convinced that Daniels had fumbled the football. Amazingly, faced with perhaps the least reliable source in all of football, Lewis acquiesced to Jones’ insistence and threw his second challenge flag, costing his team its final challenge and second timeout of the first half.

Afterwards, Lewis basically trolled this column. He noted, “The only thing it really would have cost us, which didn’t matter, was the timeouts before halftime.” You know, because timeouts before halftime aren’t important. It’s also worth noting that J.J. Watt’s pick-six came on a two-minute drill that was being hurried up and called at the line of scrimmage because the Bengals had used two of their three timeouts.

He went on to add, infuriatingly, “When you pick it up or challenge it depends on the momentum, and that is why I took the opportunity to go ahead and do it.” As it turns out, attempting to win a momentum battle in the second quarter did not win Marvin Lewis the football game.

It’s also worth mentioning that Lewis has a history of doing this sort of thing. In Cincinnati’s home loss to the Jets in the wild-card round of 2009, Lewis used both of his challenges by the end of the first quarter, including one on a 15-yard completion in the middle of the field. Both challenges did not overturn the ruling on the field.

Listen. Nobody wants head coaches to become numbers-crunching automatons who don’t apply game situations to historically derived pieces of information like expected point values. That’s just as bad as ignoring the numbers altogether. When we base our opinions of how decisions played out solely upon the outcomes and talk about changing the momentum of tie games with 40 minutes to go, though, it’s not about the numbers. It’s about common sense. Don’t go chattering on about how every tree matters. Try to think about the forest.

Bill Barnwell is a staff writer for Grantland.

Previously from Bill Barnwell:

Cashing Out Some Preseason NFL Bets

Gang Green Lacked Leaders

Handicapping the 2011 NFL MVP Race, 2.0

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