The Self-Fulfilling Prophecy of Momentum

A defense of Dan Campbell, and an attempt at self-reflection

In Harry Potter and the Deathly Hallows (Harry Potter and the Deathly Hallows Part II for the movie folks out there), Harry was forcefully wounded after sacrificing himself to Voldemort. He thought doing so would kill him, and so when he woke up in a heavenly-themed Kings Cross Station next to Dumbledore, he asked if this was “real” or just in his head. Dumbledore retorted: “of course it’s in your head Harry but why does that make it any less real?”

I think this quote is very applicable to our perpetual debate about “momentum,” which formed a big part of the discussion following the DET-SF game after Dan Campbell’s two 4th-down attempts in the second half came up short.

I promise that if you think they should have kicked, if you are a fervent believer in momentum, or skeptical of analytics that this is not an article intended to pompously antagonize you. It’s quite the opposite. I will share my opinion on what I think they should have done and why, but I hope this will be a worthwhile discussion to possibly make the debate about these calls a touch more toxic. I only have one rule: if your opinion is that “it didn’t work so it was bad,” this is not the article for you. We’re simply not going to be entertaining purely results-based analysis in any direction, kick or go, in any game.

The first of Campbell’s gambles - a 4th-and-2 stop at the SF 28 in the 3rd quarter - according to the momentum-believers, stunted Detroit up 24-10, and helped to allow San Francisco to gain momentum and turn the tide (in addition of course to allowing them to remain within 14 points and get the ball back).

The second controversial attempt came with the Lions down 27-24 came on a 4th-and-3 at the 49ers 30, and 7:38 remaining in the game. By this time, there is no doubt any existing momentum was firmly with the 49ers, and - in the opinion I’ve gathered from those against Campbell’s decision - made Detroit less likely to convert than a model may dictate. Therefore, Campbell should have opted for the FG to blunt SF’s momentum and tie the game.

As far as whether momentum “exists” in the way that’s functionally measurable, we don’t really know. Several studies have been done, ranging from an individual’s “hot hand” to a team’s performance over a season, or within a game, and results have been mixed depending on the methodology, the sample, or what you’re choosing as your proxy for momentum’s effect. In a study by Paul Roebber, a University of Milwaukee-Wisconsin Professor, a model studying changes in win probability based on momentum in football demonstrated outsized effects of teams able to stack consecutive positive outcomes on drives, independent of those drives’ inherent impact on win-probability. On the contrary, researchers studying the effect of teams making a comeback in basketball, found no negligible increase in teams who had completed a comeback’s ability to close out the win. (These are far from the only two studies available to read on the topic, and there is mixed quantitative research overall)

Whether momentum works differently between basketball and football is also very possible, though hard for me to necessarily put my finger on why. It’s certainly discussed differently. Commentators often refer to basketball as a “game of runs,” in which teams pulling ahead almost expect the other team to make a charge from behind at some point. In hockey, analytical models are sometimes built to diminish the performances of teams in multi-goal games because “score effects” result in trailing teams controlling play at a disproportionate rate.

It’s hard to uncouple the actual performance of teams who may or may not be gaining or losing momentum from the practical effects of trailing or leading within the rules of a game. Teams already behind in football are more likely to pass more frequently which leads to a higher chance to score, but also a higher chance of turnovers and compounding negative plays. Hockey teams are strongly incentivized to play more passively from ahead which will lead to a reduction in the team’s share of play-control, but - if executed well - an accompanying reduction in overall offensive opportunities.

Teams with a lead in any timed sport are incentivized to sacrifice some level of expected results play-to-play, for reducing the variance of the game overall, since a low-event game favours the leading team. But those teams who are ahead are also more likely to stay ahead if all else is equal since they are more likely than not the better team, or at least the better team that day. Teams who were once trailing, and “switch” the momentum, may be benefiting from a game plan adjustment, an injury, or some other tangible in-game change that altered their fortunes. How momentum interacts with those considerations, and several more you could bring up, is a borderline impossible question impossible to answer.

This column is not a scientific study, so I’ll set the following parameters for momentum:

(1) To the extent it exists, it is extremely difficult to measure, and research on the topic typically shows it has negligible or minor effects;

(2) For the same reasons it’s difficult to measure in terms of confirming its existence, it’s impossible to build into a game management model, meaning such that it does exist, it’s a factor that’s not being appropriately considered;

(3) Because momentum is largely “felt” rather than quantified, its effect may plausibly depend on how much you believe in it yourself.

I want to spend most of this article exmaining how we deal with this last point. Not a single person would disagree with the notion that an athlete’s attitude in a given season, day, or moment can affect their performance. We may not be able to measure exactly how or what specific plays are altered, but we know it matters.

I’ve always been a fairly analytically inclined person, but I also played baseball, basketball and golf, competitively. I can easily point to moments in each sport where I’ve either benefited from a high-level of confidence or mental strength, and times I’ve crumbled due to a lack of confidence or increased pressure.

However, it’s occasionally difficult to separate the chicken from the egg. The first golf tournament I had a legitimate chance to win was a 36-hole event over two days. The first day I played a fairly average front 9, but got in a groove on the back and came in 1-under to be three shots off the lead and in the final group for the next day. I was anxious the next day but felt extremely confident about my game, and had a great practice session. I started solid, parring the first 3 holes and avoiding any issue. However, I hit a horrific drive out of bounds on the 4th hole and wound up making a quadruple bogey. I fell completely out of contention over the next few holes and never got back on track for the rest of the day. Was I playing as well as I was for part of the tournament because of positive momentum? Did I crumble because of negative momentum? If I had so much positive momentum, why did I hit such a bad shot in the first place?

What we surely must all acknowledge is that everyone who’s ever played sports has felt “momentum” in some capacity before, can likely cite an example of how it affected them, but can also likely cite examples of momentum shifting rapidly within the same game - sometimes multiple times.

So does the opportunity for momentum to quickly change mean it can’t exist in the first place? Or how does it work?

My personal view is it works like a weight. When momentum is against you, you’re still conceivably able to do everything you could previously, but you now have to do it carrying a slightly heavier weight making it marginally more difficult. But as you build success, that weigh slowly disappears, and eventually gets displaced to your opponent (depending on the game we’re talking about) until it’s shifted back. In essence, you can always shift momentum, but it takes more effort to shift it back in your favour when you find yourself working against it.

But I also think momentum itself is only as real as we make it. Whether it’s confidence, nerves, pressure, or any term you’d like to use, the actual impacting psychological variable is not in my opinion, “momentum,” but rather the way momentum has manifested within you. It stands to reason then that the more you believe momentum exists, the more effected you may be by it. To that end, when assessing what effect momentum should have on the Detroit Lions, it really matters little whether momentum exists in a measurable way, or whether its effect manifests on a majority of the population. But the mental state of Jared Goff, Josh Reynolds and company is quite relevant.

All in all then, I have very little issue with the folks who say momentum or some element of psychological consideration should be part of the decision-making process: especially for decisions that - as was the case in this game - are reasonably close calls based on the models (though both Ben Baldwin and ESPN’s had each as an optimal go spot).

However, I’ve noticed a trend with the momentum argument that seems to permeate the entirety of the 4th-down discourse which I find extremely problematic.

In order to have a good faith discussion about 4th-down decision making I think you need to accept two general truths:

(1) *THE MOST IMPORTANT* The existence of the decision necessitates the making of a decision. Constantly the way people approach these discussions is as if the kick or punt is the “neutral” decision while the team going for it is the one making a decision worthy of criticism or praise. In reality, every single 4th down necessitates a decision to go for it, punt, or kick a field goal. There is no neutral option: just a suite of options, among which you can pick one each time you think gives your team the best chance to win. No decision should be viewed as more aggressive or more controversial inherently. We should be equally willing to criticize any decision which materially lowers your chance to win the game regardless of what decision you make.

(2) You cannot assume the success of the conservative option. When you punt from an opposing team’s 40 you may pin them inside the five, or you may kick a touch-back, or you may get your punt blocked. Field Goals are missed: at a very measurable rate. On the contrary, in 4th-down attempts *not* at the goal-line, you are not assured a touchdown for having converted. There is inherent down-side risk in every option: the best decision depends on being able to choose the option with the best aggregated range of outcomes when considering all the possibilities. My personal soap-box is reminding people that a long FG attempt has more downside risk than a 4th-down stop since you give the ball back eight yards further back than with a 4th-down in-completion. (Though in most cases that risk is less likely to manifest)

However, this last sentence raises the question of the effect of momentum. If momentum is real, and if it manifests in ways that impact the game, perhaps we can’t say with complete confidence that it’s better to be stopped on 4th down than miss a FG. I often discuss my frustration with coaches who are willing to lose games in an “acceptable” way, by kicking or punting in situations where it is the conventional wisdom, but reducing their win equity in the process. But here’s the rub:

Even *IF* we know it’s irrational to think going for it on 4th down has more risk than a FG attempt, if we’ve internalized this to the extent we expose ourselves to a more detrimental ‘momentum’ effect from a 4th-down stop than a missed FG, then maybe going for it is the riskier choice after all.

The above is an example where the actual tangible impact of 8 yards of down-less field position is often negligible enough that I think it’s quite plausible the impact of momentum could make up that difference in ways we can’t incorporate into a model.

If you had proposed this theory to me a few years ago, my response would have been to angrily mutter that people should simply be not be subject to the irrational whims of our perceptions. But as I’ve matured, I’ve left some room open to the notion we are ultimately dealing with people, those people need to make the plays, and to some extent we have to take each other’s mindset as we find them.

I’ve recently been watching The Traitors US: an excellent show by the way! It’s a competition reality show that’s much like the game mafia: most of the house is “faithful,” there are a couple “traitors,” and early in the season if a traitor is eliminated they can recruit a new one to take their place. Each day the traitors murder a faithful, while the whole house banishes someone they hope is a traitor each night. At the end of the game, if any traitor makes it to the end they get the money for themselves, while if all are eliminated the faithfuls split the prize.

I’ve noticed that people seem to play this game extremely irrationally (at least to my perspective).

First of all, the faithfuls constantly try to take out traitors instead of aligning with their suspects and saving them for late game banishment. I’d far rather be a traitor’s best ally and receive implicit immunity from being murdered than out the traitor, and have them replaced with someone new who may or may not protect my place in the game.

Second of all, faithfuls are constantly throwing out names to eliminate, which puts themselves at risk of being banished, and puts their allies at risk by letting the traitors know who is not a suspected traitor and an ideal target to murder. Meanwhile, those who keep silent are proposed as possible traitors despite having the least need to remain tight-lipped.

The thing is, all that ultimately matters in this game is perception. And if you act in a way that’s deemed traitorous or suspicious by the group, even if in a vacuum it should be seen as logical, the meta is so out of whack that playing to the expectations of your cast mates is more important for your survival than playing optimally in isolation. In addition to this, any action can be deemed traitorous either because it is on the surface, or because it’s the *opposite* of something a traitor would do and thus exactly what someone *hiding their traitor status* would do. You can make the case in any direction.

This is ultimately how I’ve grown to see the momentum effect. If I have a team full of players I know are more likely to respond poorly to a missed 4th-down attempt than a missed-FG, maybe that’s something to keep in mind, despite the fact that tangibly you are eight yards better off with a failed 4th down attempt.

On the surface, using momentum as a reason to kick *both* FGs doesn’t make sense. In the first occasion you have to kick or else you might lose momentum. In the second, you have to kick because you don’t have momentum.

How can both of these statements co-exist? If the relevant consideration is how much the ‘possession’ of momentum affects your ability to make the play, then wouldn’t this improve your odds beyond what a model estimates on the first attempt when the Lions led 24-10? If the relevant consideration is that momentum *swings* based on the outcome of a 4th-down play are impactful, then maybe you avoid giving the 49ers a chance to get one at 24-10, but don’t you need a swing of your own at 24-27?

My issue with people blindly invoking momentum or any other intangible effect as a reason to go for 4th downs less frequently than a model would dictate, is there’s no reasonable justification for why it should only affect decisions in one direction - the conservative one - all the time.

I think my intuition aligns with the 4th down models more often than not, but I’m far from perfect. For instance, watching the game live my gut-take was to kick the FG at 24-10, but to go for it on 24-27. My reasoning being stretching the game to three possessions is a massive edge, both tangibly and psychologically, and I think it had even out-sized benefits in this game that may not be picked up on in the model.

Kyle Shanahan is notoriously awful at clock management, is uniquely unlikely to optimize his own 4th-down decisions aggressively enough when trailing by 17, and his offense is most potent when balanced and able to use play-action. I would want to play the man in this case and force him into a position where I see his strengths as most mitigated and his weaknesses most highlighted.

I also generally think you want to invite the least variance possible when your baseline is a 90%+ win probability as it was for the Lions at that time. Ben Baldwin’s 4th down model had the kick (46 yards) as a 75% chance to succeed, and a 4th-down attempt at 59%: that delta was enough for me to err toward the scenario that lowers my already-high win equity less frequently. The models disagreed. ESPN’s had it as a very slight go spot while Baldwin’s had it at as +2.2%.

For the latter decision, I felt it was frankly a clear-cut go spot. It’s not a perfect analogy because there were five more minutes remaining here than in the Bills-Chiefs game last week, but it’s incredible how hysterical we got about this scenario especially after we *JUST* watched the other decision go awry in this playoffs. For anyone who doesn’t recall, Sean McDermott faced a 44-yard FG attempt or a 4th-and-9 with two minutes remaining down 27-24, opted for the kick and missed, losing the game. I argued at the time, including prior to the kick, they should have gone for it, even though the odds of converting were much lower than the odds of making the kick.

Taking into account the general scenarios, but especially the fact they were playing against Patrick Mahomes in a high-scoring game, I saw their odds of stopping Mahomes from getting a field-goal with a full two minutes as quite slim, and if they did it they’d still have to win in overtime. While they were not likely to convert a 4th-and-9, I saw the game as likely lost either way, but at least in that scenario if they DID convert they would all of a sudden be in the driver’s seat with a chance to score the game-winning TD with little to no time left on the clock. For what it’s worth, Baldwin’s model had this decision as +7.5% win probability to kick. I don’t care - I’m going every time.

I had a similar perspective here, though complicated by the additional time remaining. At 27-27, you’re giving the ball back to an offense which has scored on four straight drives, and offering them the chance to milk the remaining clock and deliver the decisive blow. You’re still very live in the game, but you’re clearly playing on the back foot once you decide to attempt the kick, and putting the game in the hands of your weaker unit. I’m putting the faith in my better unit, the offense, to pick up this 4th down, milk several more minutes off the clock and eventually go up 31-27, the only outcome of this drive in which you emerge with a >50% win probability. The models had a similar take on this attempt as the first, with ESPN rating it as a slight go, and Baldwin rating it as +2.0%.

I’ve seen the argument made that you had to play to tie the game because the team was frail at that point and needed a reset. To me, I see that as a reason to go. A field-goal attempt, even if successful, is not going to put you back in the commanding position in this game, and I’d rather take the swing to turn the momentum around in one play - a very manageable one - than hope to swing the game back around with my struggling defense against an opposing elite offense that’s running red hot. The worse position I’m in, the more inclined I am to make decisions that increase variance by putting more of the weight of the game on a single play and less on a series of stops and scores.

Anyhow, I say all this to demonstrate that I don’t generally reach my conclusion on these decisions based purely on what the models say, and if I were a coach, I would have someone feeding my model-based percentages over the headset to makes sure I’m informed as possible, but I’m not sure it would have altered my decision on any of these instances.

In fact, I would argue that models probably undersold the benefit of a 4th-down attempt in this case. Michael Badgley is a career 59% on 40+ yard field goals outdoors, well below the estimated 71% and 75% respectively by Baldwin’s model. Additionally, Detroit had converted 83% of 4th-downs of three yards or fewer this year, and boasts one of the best success rates in the league. It’s reasonable to project their odds of conversion were more likely higher than the estimated 59% and 53% than lower.

So is there any case to be made that Campbell did the wrong thing? Sure. Both were close enough calls that depending on your perspective, you could make a compelling enough case in either direction and make a reasonable decision. This wasn’t a case with a clear cut right and wrong answer that every team in any situation should come to the same conclusion (see: going for two down eight). But by that same token, it’s unreasonable to suggest there is no case for going for it either: every decision is actively made and choosing the more aggressive or less conventional path should not bare an imaginary burden to only be elected in extreme circumstances.

In fact, the only case I could think of which made a coherent argument in favour of kicks as the superior choice in *both* cases is based on the irrationality of our perception of momentum. I write about loss aversion a lot in a dynasty context, typically with disdain. It’s irrational that we as humans percieve a negative outcome as more detrimental than a proportionately positive outcome is beneficial. Nevertheless, if we all suffer from loss aversion then perhaps the momentum effect of these 4th-down calls is not a zero sum game. What if a team’s spirit is crushed more by failing to convert on 4th-down than they are uplifted by gaining it, in addition to percieving that failed 4th-down as more negative than a missed-FG?

Neither of these conclusions are measurable or can be input into a model because they don’t make any tangible sense. And yet, it does seem to explain how people’s natural intution is to so frequently see decisions un-supported by math as the correct one. I struggle with this discussion, because much of my annoyance with the pro-kick crowd is the un-warranted confidence in their ability to out-think an analytical model, and in this case, an NFL head coach. I don’t want to match that over-confidence with over-confidence of my own that models are *always* correct or that I posess some ability to sort out the situations in which they should be deviated from. I want to remain open-minded to the possibility there is some effect out there we can’t measure that explains the gap between intutition and calculation.

If this loss aversion theory has any merit, the theory would stipulate that we should skew toward more conservative decision-making based on the disproportionate momentum effect created by failed high-risk decisions compared to successes.

Ironically, there was a counter-example against this in the early game. On the Ravens second drive, they were down 7-0 facing a 4th-and-1 on their own 34. Momentum was against them, and yet they attempted a high-risk decision and converted. They went on to score a TD that drive and even the game at 7-7. The next 4th-down attempt came with the Chiefs up 14-7 and fresh off a fumble recovery. They could not have possibly had more momentum, and yet they failed to convert. And if you’re more partial to the momentum “swing” half of the 4th-down debate, Baltimore turned that 4th-down stop immediately into a three-and-out and didn’t score again for two quarters. Lastly, in the 4th quarter Baltimore attempted a 4th-and-3 from their own 18 down 10 with 8:47 remaining. This was a daring and commendable decision, but this was also their first drive after Zay Flowers’ goal-line fumble: momentum was NOT on their side. Nevertheless, they converted easily. As for the effect of the momentum they swung back in their favour?? Well they threw an end-zone interception a handful of plays letter.

I’ll just say I’m extremely un-convinced that we should be affording much decision-making impact to an effect that may or may not effect the outcome of a given play, and may or may not effect the plays immediately after. At the very least, if it is worth considering, the impact is on the margins and far from determinative.

Notwithstanding that, even if the loss aversion theory of momentum *is* true to some extent, is it sustainable or desired? Should we really be comfortable making decisions based on contentedness with our own irrationality?

This is why I love Dan Campbell so much. Despite being the most analytically-correct head coach in game management scenarios he never frames it in analytical terms. Whether he’s aware of how analytically-sound his decision making is, and chooses to message it differently, or whether it’s just a happy accident that his natural aggressive intution often alligns with the nerds we can’t know for sure. But I have no doubt his messaging is part of why he’s had so much success this year, not just on 4th-downs but generally with this team.

If I’m playing on your football team and you show me a chart, I’m likely to be pretty responsive. But I understand if that’s not the ideal persuasion method for most NFL players. Campbell’s fusion of analytically-sound decision making with justifying language based in belief and aggressiveness: values more universally appealing to an NFL locker room is a great way to get buy-in, and to mitigate the underlying conservativeness that has potential for teams to derive a more negative momentum effect than is justified by the actual changes in win probability based on 4th down failures.

If any coach could put to rest the (extremely counter-intuitive) association of 4th-down-aggressiveness with spreadsheet soy boys rather than gridiron gladiators it would be Campbell. Much like switches in momentum, there is a chicken and egg effect to the acceptance of 4th-down aggression. If we all became more open-minded to optimal 4th-down attempts in non-traditional situations, maybe we would percieve of 4th-down failures more like we do missed-FGs: an unfortunate, un-avoidable mistake rather than a game-changing decision or coaching error. Maybe this change in mindset could eradicate the invocation of momentum as a reason to always be more conservative… or maybe I’m just too optimistic.