Sunday was a weird day of football, ending with a bizarrely fascinating game between the Chiefs and Broncos in Denver. The AFC West rivals put on a defensive clinic for most of Kansas City's 30-27 overtime win, led by two mostly unstoppable outside linebackers in Justin Houston and Von Miller. When these two teams went to halftime at 9-3 (which included a safety and a free kick return for a touchdown), who could have expected they would somehow squeeze out 45 points after halftime?

To get there, the pass rush had to tire a bit, and it would also require overtime and a series of questionable decisions along the way. Gary Kubiak and his Denver players faced a run of thorny propositions en route to nearly winning this game. None of those questions had easy answers, especially in real time. Some coaching decisions are obvious and should be easy to handle if a coach has drilled in decision-making during the offseason, but others -- especially in games with particularly extraordinary contexts like this one -- are harder than they seem.

Let's run through those decisions and try to figure out whether the people in charge made the right calls. Of course, hindsight is 20-20, so we're trying to figure out what the right decision would have been in the moment given the knowledge the players and coaches had at that time. And let's begin, actually, with a call Kubiak watched his opposite number dial up ...

Should Andy Reid have gone for two?

It's lost in the shuffle because of what happened, but there's a reasonable case to be made that Andy Reid made a mistake before Kubiak even had any options available. The Chiefs scored on a sweep from Tyreek Hill past a diving Miller to make it 15-10 with 37 seconds left in the third quarter. It came at the end of a drive in which Reid (correctly) took points off the board after a formation penalty on a successful field goal gave the Chiefs a new set of downs. It wasn't just Kansas City's first offensive score of the night; the Chiefs drove for 75 yards with five first downs after accruing a total of 38 offensive yards and four first downs on their first seven possessions combined.

Justin Houston accounted for three of the Chiefs' five sacks of Trevor Siemian. Isaiah J. Downing-USA TODAY Sports

When the Chiefs broke through for a touchdown, they kicked the extra point to go up six, which has its advantages: In a game in which points are at a premium, as they say, there's some value in knowing the other team needs to score a touchdown to win as opposed to being able to win with two field goals, which would be the case with a missed two-pointer. Was that the right move? I consulted the two-point calculator built by ESPN's Brian Burke, which is built off a win expectancy model similar to the one currently used in ESPN's win probability data.

Burke's model suggests that the Chiefs' odds of winning, given a 95 percent chance of converting the extra point and a 47 percent chance of converting the two-pointer, would have been slightly better if they went for the two-point try. But the difference is only about half of 1 percent, at 72.8 percent to 72.4 percent. The break-even rate at which point it's better to go for two is 43 percent, which is where I start to wonder.

The league-average rate is 47 percent, but this was not a league-average game. The Broncos had basically terrorized the Chiefs up front for most of the game up to this point. Kansas City had two rushing first downs all game before the Hill touchdown. Both the Broncos' defense and Chiefs' offense have been relatively middling in power-running situations this season, but every 2 yards in this game also felt like more of a fight than it would be in a typical contest. It's not difficult at all for me to believe that the numbers actually leaned toward the Chiefs' kicking an extra point here, even if they would suggest that going for it was the right call in a vacuum.

In either case, it's difficult for me to believe that Reid's call was definitively wrong, even if it wasn't clearly right.

Should Bennie Fowler have fallen down?

It feels like the ultimate sitting-on-the-couch move to suggest, but we know that players are at least occasionally situationally aware that it can be better to just go down with a clear path to the end zone as opposed to running the ball in for a score. You remember Ahmad Bradshaw trying not to score at the end of Super Bowl XLVI and failing. The Giants won, of course, but the Patriots did get a minute-long drive from their own 20-yard line to try to win the game; had Bradshaw kneeled at the 1-foot line, the Giants could have bled the clock before kicking a chip shot to win.

Bradshaw had time to think about his plunge before deciding to score. That could not have been the case with Bennie Fowler, who couldn't possibly anticipate this situation. The Chiefs sent a huge blitz at Trevor Siemian on third-and-2, and Siemian floated a deep out to his little-used backup receiver. With no safety help, cornerback Phillip Gaines appeared to lose track of the ball, and Fowler easily won a footrace to the end zone for a 76-yard touchdown.

I don't think it's fair to criticize Fowler for running in for the touchdown, and I'm not going to, but what would the correct decision have been? As Fowler was sprinting toward the end zone, the Broncos were up 17-16 with the clock approaching three minutes, and the Chiefs were out of timeouts.

Trevor Siemian finished with 368 yards (a career high) and three touchdowns through the air. AP Photo/Jack Dempsey

Let's give Fowler two realistic options. Option 1 is to score as he did, giving the Broncos a 24-16 lead (after the extra point) with 3:02 to go. According to Burke's win probability model, the Chiefs were left with just a 4.7 percent chance of winning the game. If that seems low, keep in mind the Chiefs had to drive the length of the field for a touchdown, convert a two-pointer to tie the game, and then win the game as slight underdogs (they were 3.5-point underdogs before the game) in overtime.

In Option 2, Fowler gets a message from the scoreboard telling him to go down, and he kneels at the 2-yard line. The Broncos can then kneel before attempting a field goal from the 2. In this scenario, the Broncos would plan on handing the ball back to the Chiefs with a four-point lead and, assuming Denver runs off 39 seconds of clock pre-snap and three seconds post-snap per play, 33 seconds left.

Burke's model is even more dismissive of the Chiefs' chances if Fowler kneels. Kansas City's chances of winning after Fowler gives himself up with 3:02 to go are a lowly 0.7 percent. After three Siemian kneel-downs, the Chiefs' odds climb to 1.3 percent, basically relying upon a botched snap, a blocked field goal or a kickoff return for a touchdown, and 11 of the 12 kickoffs in this game resulted in a touchback, thanks to the thin air in Denver.

Down four points with 33 seconds left and no timeouts, the Chiefs' chances of driving 75 yards for a touchdown were basically nil: Burke gives them a 0.1 percent chance of succeeding. I can't fault Fowler for scoring, but the Broncos would have been better off if he had fallen down.

Should the Broncos have gone for two after Fowler scored to try to put the game away?

I discussed this topic a few years ago, but it has come up in recent weeks after Seahawks coach Pete Carroll went for two in a similar situation against the Patriots. Here, the Broncos were up 23-16 after the Fowler touchdown pending the extra point, again with about 3:02 to go.

There are two tantalizing benefits to going for two and trying to make it a nine-point game late. If you do it while there isn't much time left on the clock, you've basically ended the game -- the other team needs to find two possessions in an impossible length of time. The Chiefs could have scored twice in three minutes, but it would have required an expected onside kick recovery, which is somewhere in the 10 percent range.

The other benefit is that there's little punishment given how opposing coaches are likely to react. If you go for two and succeed to go up nine, the game is basically over. If you go for two and fail, the downside isn't all that bad. You're still up seven, and if the other team comes down the field and scores, it virtually never goes for two to end the game in regulation, which is about a once-per-decade moment of coaching gutsiness.

Chase Stuart wrote about some of the problems in that logic back in 2012, though, and he correctly distilled it down to a simple choice. It's true that if you go for two and succeed, you win the game. It's also true, though, that if you kick the extra point, and the opposition responds with a touchdown, and then you stop the two-point conversion, you win the game. The question you should ask yourself in the situation, then, is simple: Do you think your offense has a better shot of succeeding on a two-point conversion than your defense does of stopping a two-point try?

Yes, I understand that the Chiefs would later go for two and get it to tie the game up at 24. We didn't know that with three minutes to go. In this case, Kubiak was right. Burke's model suggests the Broncos would have needed a 57 percent chance of converting the two-pointer to justify the move, and the outdated (pre-extra-point changes) model from Football Commentary is similarly dismissive, at 64 percent.

Should Kubiak have asked Brandon McManus to attempt a 62-yard field goal in overtime?

This is one of the more difficult decisions I've seen a coach forced to figure out on the fly. It's like Kubiak got to the final question on an exam and had five minutes to answer a question that was supposed to take a half hour. He basically had 40 seconds to answer a multilevel problem. This was not an easy call.

But to be fair, the thing we can all agree on is Kubiak and the Broncos shouldn't have put themselves in this situation to begin with. When they picked up a first down just before the two-minute warning, the Broncos could have basically removed losing from the equation. The Chiefs were down to one timeout, and the Broncos had the ball on the Kansas City 44-yard line. They could have kneeled three times and attempted the same 62-yard field goal with no time remaining if so inclined.

Gary Kubiak was forced to untangle an extremely complicated situation in real time. Justin Edmonds/Getty Images

I don't think that's a good idea -- 62 yards isn't classic "field goal range," even at altitude -- so I support the idea of the Broncos trying to advance the ball. I even think throwing the ball, at least once, is a good idea. There's significant value in advancing the ball 10 yards. The plays Kubiak dialed up, though, weren't great. On second down, the Broncos freed up a throwing lane for a backside slant to Emmanuel Sanders, but Siemian's pass was knocked away by lineman Chris Jones. And on third down, the Chiefs showed and then sent pressure and Siemian threw a desperate fade to Fowler, with the ball bouncing off the receiver's fingertips. (It looked like Siemian's hot route against the blitz was the fade to Fowler, which in itself is a bad idea for this specific situation.)

I don't enjoy the "like the decision/hate the playcall" arguments, since they're usually arguments masquerading against the decision anyway, but these were relatively low-percentage passes. It would have made all the sense in the world to throw a bubble screen or some sort of high-percentage pass to get the ball outside while keeping the clock moving.

After Denver failed to advance the ball on three downs, Kubiak was left with the best of a few bad decisions:

He could punt the ball away, pushing the Chiefs inside their 20-yard line with a minute to go and one timeout, which would have likely forced a tie.

He could have gone for it on fourth-and-10 and hoped for a completion from Siemian, which would have set up an easier field goal attempt from McManus.

He could line up McManus for a 62-yard field goal.

He chose Option 3, which went wide and gave the Chiefs the ball on Denver's 48-yard line. Alex Smith drove 32 yards in a minute, setting up Cairo Santos for a 34-yarder, which he banked in off the right upright.

Let's start on the level of the best decision in terms of game probability. I've seen comparisons of the chances between converting a fourth-and-10 and hitting a 62-yard field goal, which aren't a good way to think about the problem. Even if Siemian had picked up 10 yards on that play, McManus would still be in line to kick a 52-yard field goal, which is no gimme. Likewise, if the Broncos missed the field goal, it was hardly a fait accompli they would lose the game; the Chiefs could have stalled out on offense or Santos could have missed his field goal attempt, which is what nearly happened.

Burke tweeted out the results of the findings from his model, which argued in favor of punting. With ties counting as half-wins, he suggests the Broncos had a 52 percent chance of "winning" with a punt, a 47 percent chance of winning by going for it and a 41 percent chance of winning with the field goal try. You can argue that a tie might not be worth a half-win to the Broncos; it might be worth more or less depending on their playoff situation, and we'll get to that idea in a moment.

What's crucially missing here, as Burke also noted in his tweet, is the altitude in Denver. Kicking in Denver is fundamentally different than it is anywhere else in the NFL (outside Mexico City). Just as the altitude carries fly balls over the fence in the hitters' paradise of Coors Field, the thin air of Denver is a blessing for kickers. Their attempts travel further and stay truer than they do in other cities, which adds range. Burke estimates that there's an additional 5 yards of range in Denver, which jibes with what I've heard from NFL coaches.

To put the difference in context, here's a chart comparing field goals in Denver from 2006 to 2016 (as of last week) to field goals in all other NFL locations over the same time frame. To avoid capturing the particular skills of the Denver home kickers, these samples only include kicks attempted by the visiting team, which should give us a random group of kickers with varying skills.

Field goal success in Denver vs. elsewhere Yards In Denver Elsewhere 50-59 70.0% 60.1% 40-49 79.6% 77.1% 30-39 92.5% 87.8% 19-29 100.0% 96.2%

Kickers are better across the board in Denver, and that is specifically true on extremely long kicks. It's a small sample, but on attempts of 55 yards or more, road kickers are 8-for-10 in Denver since 2006. On those same kicks elsewhere, they are 46-for-109, a success rate of 42 percent.

I'm not suggesting that the "true" success rate for such a kick in Denver is 80 percent, nor should you believe that a 55-yard kick is the same as a 62-yarder. (Denver's home kickers are 8-for-13 on these same kicks.) It's very clear, though, that a 62-yard field goal in Denver isn't the same thing as one in New Jersey. The cold may have affected the kick slightly, and there had been some wind at kickoff, but McManus also gets the benefit of trying his attempt at home, where kickers are nearly 1 percent better (83.8 percent to 83.1 percent) than they typically are on the road. You can't use a typical model to gauge McManus' shot at hitting that kick, which I suspect were double the odds of a typical kicker in a league-average kicking environment.

The other problem with analyzing Kubiak's decision in a vacuum is that the possibility of a tie throws a lot of things off. In a vacuum, the value of winning and losing is pretty clear. If we treat a tie as being worth half a win, it's relatively easy to just split its value two ways. What if a tie is worth more or less than half a win, though? In the context of a divisional race, it's almost impossible to tell how valuable it is to tie because its impact might not be felt until much later in the season.

Unfortunately, most playoff probability models don't handle ties very well, because (until this year) they've been so infrequent that it's easier to leave ties off the table as a possibility. We have to estimate Denver's chances, so let's do that with the playoff model generated by The Upshot.

Before the game on Sunday night, after inputting every other contest's results, The Upshot's model gave the Broncos a 22 percent chance of winning the division and a 66 percent chance of making the playoffs. We can't ask the model how things might have gone with a tie, but we know what Denver's odds were in the case of an affirmative outcome. With a win, Denver would have had a 30 percent chance of winning the West and an 80 percent chance of making the playoffs. After their loss, though, the Broncos' chances of winning the West fell to 8 percent, with their playoff odds dipping to 49 percent. ESPN's playoff model is slightly more sanguine, with an 8.8 percent chance of winning the West and a 53 percent chance of hitting the postseason.

The Broncos are rightly motivated to win their division because it would create a far friendlier path for their playoff run. Indeed, The Upshot's model gave the Broncos a 29 percent chance of picking up a first-round bye with a win.

Just a doink will do. Cairo Santos nearly missed the game winner on Sunday night. AP Photo/Jack Dempsey

With a win, even if they hadn't won the division, the Broncos also would have been the favorites to grab at least the fifth seed. The Broncos would have had a 33 percent chance of finishing fifth and a 64 percent chance of finishing with a spot among Seeds 1-5 with a win. Instead, with the loss, they now have a 28 percent shot of finishing sixth and a 21 percent shot of finishing within Slots 1-5. The sixth seed probably faces the AFC North champ in the wild-card round before matching up with the Patriots in the divisional round.

If the Broncos don't win the division, though, they were going to start running into tiebreaker issues if they didn't win this game. A tie simply wasn't going to help them very much. They were already 1-2 in the division (the Raiders were 2-1 and the Chiefs were 2-0), so they're in rough shape against the teams that will both be their divisional rivals and their primary competitors in the wild-card race. The Broncos were 4-2 in the conference, which would have helped a bit if they split with the Chiefs and Raiders, but it's hardly clear that a tie would have done much for them.

I suspect Kubiak wasn't thinking about all of these permutations in the 25 seconds or so he had available before making his decision. He does have a director of football analytics over the headset in Mitch Tanney, which assuredly helps on fourth-down calls, but this sort of season-long expectancy is too complex to figure out unless you purpose-build a model and are willing to accept very difficult assumptions as facts.

My best guess is Kubiak felt it was better to try to win the game than play to settle for a tie, and given the altitude in Denver, his shot of hitting a 62-yarder was better than picking up a first down with one of the league's lesser quarterbacks, and then kicking a 50-yarder. (He said as much after the game.) The math is likely within the margin of error one way or another, and I don't think there's obviously a wrong decision to be made. Anecdotally, though, given the altitude in Denver and the value of a win here versus a tie, I think he made the right decision.

Where we are now

While Denver isn't in horrible shape, its margin for error is disappearing. The Broncos are 1-3 in the West and on the wrong end of those head-to-head tiebreakers vs. the Raiders and Chiefs. The surging Dolphins, who have won six straight against mostly middling competition, are ahead of the Broncos because of a 5-3 record against AFC teams. The conference is still a convoluted mess; the Patriots have a 68.9 percent chance (per ESPN's Football Power Index) of coming away with the No. 1 seed, but everything else is still up for grabs. The Steelers, currently out of the playoffs at 6-5, still have a 69.3 percent chance of winning the North. The Texans laid an egg at home and still have a 57.3 percent chance of winning the South. The Chiefs have a 39 percent chance to win the division crown, thanks to the fact that the Raiders still have to play each team in the AFC West on the road over the next five weeks. There are plenty of more coaching decisions, overtimes and goalposts to come into play before the AFC shakes itself out.