Momentum vs. Confidence

Momentum is an inherently intangible concept. The idea exists because for the most part we view sports as an entertainment. So we watch and enjoy the game, then we create a narrative to explain what happened. When a game turns on a certain play, and one team has more success after that point then goes on to win. We all talk about how they got the momentum at that point. When the rally fails we simply forget and create another narrative. Maybe we decide the other team got the momentum back at that point?

Several comments:

1. If the call for a precise definition and method of statistical analysis stems from the assumption that meeting these two conditions are necessary for the phenomenon to be real or meaningful, then I strongly disagree with that. Just because an aspect of sports can't be precisely defined (for statistical purposes) or analyzed statistically, that doesn't mean the aspect isn't real or isn't important; nor does this mean we can't talk about these aspects. Our discussion and analysis of sports would be incomplete and less meaningful if we eliminated everything but stats.

2. I think momentum can involve two factors--morale/confidence and rhythm/flow. I do believe that events can occur that can be highly discouraging to a team--Schaub's penchant for pick-6s this year; Percy Harvin's TD return in the Super Bowl. Professional athletes aren't immune to discouragement. When these things happen, momentum can shift.

But momentum also involves rhythm--which usually involves the offensive side of the ball. An individual or even a team can find a groove. Even an offensive play caller can find a good rhythm as well. Can you define what being in a rhythm is? No, I don't think so. It's not something you can just see through statistics.

Finding a good rhythm isn't easily controllable, either. It's not something you can just turn on or off. Individuals and teams work to find this rhythm. Sometimes they get find it and sometimes they don't. Momentum can often involve this moving in and out of rhythm.

By the way, musicians and music fans can really understand this concept--especially if fans of jazz or funk/R&B music. These musicians and fans enjoy when the music "grooves" or "swings." When it happens you can hear and even feel it, but, again, it resists a precise definition. Musicians also can't easily control this aspect, either, although, like athletes (on offense) they're constantly trying to find "it." Now, you can't measure or statistically analyze this. Does that mean it's not real or unmeaningful? I don't think so. Same with momentum and rhythm in sports.

Sometimes there are no adjustments that work. One team is successful until the other figures it out and the first team has no answer.

The most important thing to realize is that there is no single talent level on offense vs a talent level on defense which even exists. It's not that we can't estimate it. It's that it does not exist. Those who think in those terms don't understand the game.

If you could "somehow" extract or estimate the true talent of an offense and defense on a given play context, then I think you could define momentum as the autocorrelation function of success between subsequent plays.

If you had 2 perfect 0.0 True talent DVOA teams (in all situations), then you would expect no autocorrelation between 1 play to the next. But if momentum was real, then you would observe an autocorrelation or "snowball effect"

The difficulty in real analysis is that the actual talent difference will also have an autocorrelation. So I don't know how a priori you can tell the difference between a better team (well, unit considering offense and defense independently) and one with momentum.

There seems to be quite of bit of confusion about how players actually play the game. Players are NOT automatic robot-types who function at the same level all the time with differences in production being nothing more than random rolls of the dice.

Of course there is such a thing as momentum. Anyone who has seen a game where Peyton Manning eventually figures out the defense has seen momentum shift.

Momentum absolutely has an emotional element, but I would argue that the emotion usually comes initially as feedback. Players or teams often get on a roll because of strategy or tactics or individual fundamentals. And the roll can stop because the opponent figures out how to stop what was working.

A pitcher may be struggling with his arm angle, his plant foot, a blister, or a sore elbow. If he figures out what is wrong, or comes up with a way to compensate, momentum will change as he starts getting guys out. The basketball player that misses 3 FTs in a row and then realizes he is rocking to his heels rather than finishing on his toes. When he gets his fundamentals back, his shooting improves.

Players figure out how to deal with something their opponent is doing and outcomes change. The chess matches can produce runs. These runs are momentum. Emotion can take a run and make it bigger.

Failure to start Joe Webb leads to lack of momentum, obviously.

- Momentum, if it exists (which I am sure is the case), is deeply linked to human emotions, which are not only complex, but very different from person to person. -> Trying to measure "momentum"/trying to model what would be a "normal" reaction to a bad or good play is very difficult (warning, cliche alert): Player A will feel down from throwing a pick, player B will be even more "driven", and "focused", because he wants to make up for it.
- Football being a team sport, players interaction, coaching, team culture, leadership, etc. makes measuring the team's reaction to such a play/drive/quarter/game even more impossible to model/predict than the individual's one.

I think that because of those 2 things above, trying to prove the existence of momentum at a team level, is impossible. Therefore, trying to conclude anything out of studies done about football are bound not to prove not that momentum does not exist, but bound not to prove anything.

It raises the question: Is there any reliable study about momentum done for non-team sports (tennis, golf comes to mind as good ones)?

Personally, I think the real problem is the confusion between the impact of psychological and emotional factors on the players, and the attempt to reduce the story of the game to a narrative. I think Danny captures the point well, in noting that the effect gets diluted across the team as a whole.

I'm not surprised that individual players would talk about momentum, because they'd all have experience feeling the very real psychological effects as individuals. Confirmation bias would then lead them to remember those feelings when they were answered by results on the field, and forget that they had them when the results went another way (not unlike how a mother might say "I just knew when you left the house that something bad would happen!" when her teenage son gets into an auto accident, ignoring the fact that she had the exact same anxiety the dozens of times he drove without incident).

There may be some momentum effect, that if enough data is assembled, enough tests run, and enough numbers crunched, that some discernible (though likely nominal) result is found. But football commentators go far beyond that, using "momentum" as shorthand for "two or more good things in a row just happened to Team X." In doing so, they've managed to convince themselves that they can then apply this alleged intangible predictively: "A good thing just happened to Team X, therefore good things will continue to happen."? And therein lies the problem: assigning meaning to unmeasurable factors and by doing so ignoring the impact of measurable factors--or coming to believe that random events were the product of some repeatable skill or emotional state.

I really like Noah of Arkadia's linking of momentum to "initiative", and think that is a good way to think about it. But I think the problem may be that momentum is also caught up in the very real randomness that is a huge part of every game.

A team can have momentum as defined (more likely to succeed on next play), but the effect of randomness on that play is bigger than the momentum effect. So if the momentum effect is plus-5%, there is still a huge impact of luck/randomness that could make the play fail, and thus shift initiative to the other team... a bad bounce, the D-coord lucking into the perfect play call against the DEF (leading to a pick), etc. and initiative shifts to the other team.... and then you get a run the otherway. Or on the very next play luck/randomness (or even something boring as player quality advantage) shifts the balance again and there is no run eitherway.

So it doesn't surprise me that we can't find statistically significant evidence of momentum/intiative... my guess is it actually is insignificant compared to the magnitude of luck/randomness on play outcomes, so searching for it is likely a futile endevour. It undoubtedly is over-used and hyped. But that doesn't mean it doesn't exist.

We can't measure player's psychological states, nor do we know what inputs will affect them or how.

Without these things, it doesn't matter how real momentum is. You can't predict when momentum will shift. What magnitude it will have. How long it will last. So it's useless as an analytical tool.

Still fun to talk about in comments or bars though.

These concepts might have a better connection to "flow," which appears to be a relatively well-studied phenomenon in athletics. I am not familiar enough with the literature to design a statistical analysis, but the definitions are absolutely there to do so.

Aaron above: "I would suggest it takes a lot more to shake the confidence of a professional athlete than it would to shake the confidence of a high school athlete or something. (By professional, I would also include the top college athletes.) And thus, players' lack of confidence is unlikely to heavily affect their performance. . . ."

Aaron in the Vick/Sanchez post last night: "Michael Vick signed a one-year deal with the New York Jets today for an undisclosed amount. This will of course do wonders for Geno Smith's confidence, I'm sure."

One deeply related thing which I suspect makes momentum harder to figure out is injuries.

I have seen teams fall apart when specific injuries occur. That can give the appearance of momentum, even with there isn't anything actually happening, because the preferred competitor was replaced by one who is presumed inferior for the specific task.

I don't even think injuries would always make a team perform worse, rather causing them to perform differently. Sometimes that could cause improvements, or schematic changes. With so many variables, I think it would be hard to create a general rule. But I do think that it opposes every argument for momentum, and creates even more noise.

First of all, in order to define momentum, let's move to another, competitive endeavor: chess. It might seem rather counterintuitive to look for momentum in chess, but there's actually something eerily similar there, called "initiative". Initiative means one player is dictating the action: one player acts and the other reacts. This is a great advantage and it is also temporary. You try to keep it alive as long as you can, but at a certain point, it's over. It's gone.

This is real and beyond the realm of emotion. Yet, it cannot be measured! Not even in chess! Yet to say initiative in chess doesn't exist because it cannot be measured would be beyond ridiculous. Strong players will often sacrifice material in order to gain the initiative. Its existence cannot be doubted. So I'm going to call momentum initiative since it's the only thing that makes sense.

Moving on to more physical endeavors, in war initiative exists. Of course, now there is an emotional element in it because war happens in real-time and is physical, whereas chess is turn-based and mental. Initiative in real time is related to the fact that the party that is reacting is facing new situations it can barely handle before new ones arise. He who hits first hits twice, they say.

Looking at sports, in soccer the same element of initiative is present. In fact, it's called by that same name. There will be stretches of the game when a team holds all the initiative and the opponent can only defend. This is also related to effort. Players cannot go 100% all the time. Cramps are evidence of that, if you need any. When they do, they can easily gain the initiative. In war you'll hear about "low morale", which is very similar. When a team or faction feels it has the initiative, it feels optimistic and hopeful and gives a little extra. This is sometimes called the "killer instinct".

So, does initiative exist in football? There is a lot of evidence that suggests it does. Players also cannot go 100% all the time (substitutions are evidence of this). The element of morale is reflected in home-crowds getting louder when momentum or initiative is perceived. Tactically, the no-huddle offense is further evidence. Aggressive and creative play-calling might also confuse the opponent, in both offense or defense. Same as in soccer, where the reacting team will try to cool down the game by controlling the ball, in football offenses will go back to basics, usually try to run the ball.

The measurement problem is nothing but that: a problem. It cannot be considered as evidence of initiative or momentum not existing. It's one thing to get fed up with how announcers abuse the term, but to say it doesn't exist? C'mon, son.

------
The man with no sig

For many of the reasons discussed in the article, it seems likely that the existence of momentum would be much more plausible in an individual sport, such as tennis. And indeed, if you watch a match between two great players, such as Roger Federer and Rafael Nadal, you will indeed hear the commentators constantly attributing much of the results to swings in momentum, as each player takes turns reeling off several points, or even several games, in a row.

But therein lies the problem. Why all the sudden shifts in momentum? If, as many have suggested, momentum is a manifestation of confidence, then you would expect just the opposite. It would be a vicious cycle, as each consecutive point Federer won would cause his confidence to rise and Nadal's confidence to fall, thus increasing the likelihood of Federer winning the next point, thus further increasing his confidence and reducing Nadal's confidence even further, thus increasing Federer's chances of winning the next point even more, ad infinitum. Thus, at some point, you would expect Federer to feel (and in fact be) almost invincible, while Nadal would be a broken man. At this point, Federer could be expected to cruise to an easy victory.

However, it virtually never works out like this. I have seen these two play many times, and there is virtually always at least one stretch where it seems as if one or the other of them is completely dominating the match, often winning 4 or 5 games in a row. But that person very rarely proceeds to cruise to an easy victory. Rather, their opponent almost always rebounds, often going on their own extended tear, or at the very least, returning to a competitive balance. Furthermore, these shifts are rarely gradual, but instead usually happen very quickly, just at the time "momentum" would least predict them.

So, even in a situation so apparently conducive to the influence of momentum, there appears to be very little evidence to support it.

As Danny mentioned, Brian Burke took a look at momentum. Here's a link to his last piece, which includes links to the first four:

http://www.advancednflstats.com/2014/01/momentum-part-5-series-level-analysis.html

His conclusion:

"This series of articles examined momentum in a number of ways--using different definitions of momentum and different methods of analysis. It looked at momentum at the game level, the drive level, the series level, and the play level. Although it can't be ruled out that there is some grain of truth to the role of momentum, the effect sizes we observed are probably too small to be noticed by a fan or even by a player or coach."

I think the most like explanation is that professional are so disciplined and well-trained that they aren't going to be effected to any significant degree by emotional ups and downs. Note that after almost any incredible rally or the like, the members of the team that pulled off the feat will talk about how confident they still were even in the darkest moment, how they retained belief in themselves, etc. In other words they seem to ALWAYS be confident. The attitude of athletes is generally somewhere between stoical acceptance and irrational confidence. Whatever their attitude is, they always think they can still do it… or if some part of them finds that doubtful, they're going to try as hard as they can anyway.

I'm sure motivation and something that could be called 'momentum' is important on a month to month, season to season basis. Some teams seem to have more momentum than others (Patriots), and that is probably a matter of success building on success. A great coach will be able to motivate his players to work harder and ultimately perform better over an entire season, I'm sure. We can all come up with examples of players who performed far better for certain teams than others. Think of Randy Moss' switch to the Patriots from Oakland.

But momentum actually existing in an individual game? I think it would've been found by now. Most arguments for momentum on the level of an individual game still boil down to "well, it just feels that way." Players aren't actually machines, of course, but I think they are so disciplined that they essentially function as something like a biological machine on the field. Robots competing against each other would probably operate as much by the rules of 'momentum'.

What would be interesting is to examine amateur athletic performance and see if any evidence of momentum showed up there.

ok, so how about this? look at a quarterback's completion percentage after completing a pass. then, his completion percentage after an incomplete pass. that's easy enough to test real quick, right? at least if it's way different, gives a reason to investigate further.

if you want to be fancy, and remove possible play-call biases (maybe coaches call more short passes after an incompletion, whatever), then break it down by length of pass and adjust for dvoa.

i suspect it'll be no real difference, but i like the general idea of breaking it down by player instead of team... instantly increases your data points by orders of magnitude.

I have alluded to this very vaguely in comments from time to time. The basic idea is that you could model a football team X playing a team Y with a matrix M_X,Y such that M_X,Y(ij) represented the expected yards for offensive play against defense j. This kind of model would presume that the outcome expectations were essentially constant throughout the game.

If you wanted to allow for momentum to play a role, you could postulate a second matrix M'_X,Y that was in effect when team X had momentum, which presumably had entries that expressed higher performance for X. And then what you would do is have a transition variable theta, such that on any play you had a probability of _gaining_ momentum or _losing_ momentum. So if on play k you were using M, then with a probability determined by theta, instead of using M on play k+1, you would transition to using M'.

From a standpoint of estimating parameters, this approach entails more than twice as many parameters than a simpler model. There are ways that this doubling could be reduced, say, by having all of the entries expressible as a fixed function of theta. Another thing you could do is allow for a range of matrices M_t, with t a continuous parameter.

I am just throwing ideas out here. I know there are statistical tests that are used to decide whether or not it makes sense to refine a statistical model by adding more parameters. That's what you'd be doing by incorporating "momentum" into your modeling. I'm not an actual statistician, though.

I would also say that, should you flesh all of this out and do a test for "momentum", the most you could conclude is that there's no support for such a theory, based on the data you have. You cannot really conclude "momentum doesn't exist". Our reality could always be generated by a more complicated model than the reality we actually experience.

Aaron - you do realise that just because someone on the internet can't find a rigorous definition of something (such as momentum, or trap games) using available data, that doesn't imply it doesn't exist right?

Mainstream commentators say some oderous, arrogant things; but certainly nothing as bad as suggesting that.

Ian

My quick off-the-top-of-my-head definition of "momentum" would be "an increased likelihood that the value of the next play will be similar to that of the previous play". This can be easily tested -- Is a good play more likely to occur (compared to random chance, adjusting for the ability of the players/teams) when the previous play was a good play? What about if there was a string of good plays in a row?

The tricky part would be adjusting for the quality of players on the field. My suspicion is that "momentum" (as defined above) is more likely after a defensive injury -- as in the defense has to play a backup cornerback that the QB can then "pick on".