Momentum and hockey

Momentum does not exist!

Yes it does!

No it doesn’t!

Yes it does!

Actually, it both exists and doesn’t exist simultaneously!

Perhaps Rocco Mediate sums it up this debate best, saying 

“As any athlete knows, momentum is the most unstoppable force in sports. The only way to stop it is if you get in your own way, start making stupid mistakes, or stop believing in yourself.”

Okay then.

What to make of all of this? What is the best research that has been done?

Quantifying momentum is a difficult and arduous task for any researcher, the naive of whom (such as coaches and media members) use anecdotal evidence to drive discourse. Alternatively, there can also be a tendency to use arbitrary cutpoints (i.e., the last five games, or the last 10 plays) when describing momentum, which is also less than ideal.

Before I try to quantify momentum, I want to point to a few recent studies that have done an excellent job of accounting for game-specific factors which, for the most part, have made studies of momentum in sports difficult.

First, Cornell’s Kevin Kniffin contrasted Division 1 ice-hockey games played on consecutive nights, and found that neither game 1’s outcome nor its margin of victory was associated with the game 2’s outcome, after accounting for team strength. This suggests that carry over momentum, from one game to the next, is negligible, even when using game’s played by the same teams in the same venue.

Second, there is now momentum behind the idea that momentum exists on an individual level (get that?). For example, slight evidence of a hot-hand has been shown in basketball (excellent summary here), and in baseball, where players exhibit more streakiness than we would expect by chance. If individuals can get hot at shooting (a basketball) or hitting (a baseball), it’s not a stretch to argue that their teams could get hot, too, at least within a single game.

Lastly, Ken Pomeroy ($), looked at runs in college basketball, and showed that the trailing team (i.e., the team without momentum) was more likely to go on runs of 10-0 or greater, and that it was the trailing team which was more efficient offensively. Pomeroy surmised that much of these results may be psychological, and that teams take their foot off the gas, so to speak, when leading.

In-game momentum in hockey

To add a small piece to the momentum puzzle, I focused on goal outcomes during tied-game action in hockey.

The idea of studying momentum in hockey is appealing for a few reasons. First, unlike baseball, basketball, and hockey, where formal changes in possession impact scoring opportunities, both teams have equal opportunities at scoring after a goal in hockey. Second, by looking at tie games, I don’t have to worry about score effects (like Pomeroy’s study) that might be driving team motivation. Moreover, tie games are much more common in hockey, which is great as far as sample size

The question I want to know is: Are teams more likely to score given that they have momentum? 

Of course, there’s no real way of knowing which team believes it has momentum.

So perhaps this question is more appropriate: Are teams more likely to score if they were the more recent team to score?

To answer this question, I extracted NHL goal-scoring plays using the R package nhlscrapr, which gives me play-by-play data for every NHL game since 2002 (see my code at the bottom, if interested).  There have been 75,219 goals scored since 2002.

Specifically, I looked at all games tied either 1-1, 2-2, or 3-3, and calculated the likelihood of the home team scoring the next goal, conditional on the previous sequences of goals. Of course, because home teams score more goals than away teams (52.6%, to be exact), comparing the proportion of home goals to 0.50 doesn’t make sense.

Instead, I contrast home goal likelihood across the different sequences of prior goals. If momentum was a strong determinant of hockey outcomes, one would expect the home team (abbreviated, H) to score more often than the away team (A), after a scoring sequence of AAHH, relative to a scoring sequence of HHAA. In the series AAHH, the home team would **appear** to have momentum, while the away side would have momentum after the HHAA sequence.

Here’s a table with the fraction of future goals scored by the home team, given previous scoring sequences, for each of the three tied scores. The shades of green behind each percentage indicate the deviation above or below the average home goal percentage of 52.6% (darker indicates a higher home goal likelihood).

If momentum was playing a large role in future goal scoring, we’d expect the shades of green to get darker for the lower rows in each tied game scenario.

For example, the home team scores more often after sequence AH than sequence HA (54.3%, versus 52.1%), suggesting a slight increase in goal likelihood for the team that tied the game at 1-1.

However, home teams appear to score more often in 2-2 and 3-3 games when they don’t have any supposed momentum, as opposed to when they do (that’s comparing sequence HHAA versus AAHH, and sequence HHHAAA versus AAAHHH).

The home goal rate after sequence HHAA is 54.4%, for example, while the rate after sequence AAHH is 52.7%. If home teams have momentum after scoring two goals to tie the game at 2-2, they certainly don’t play like it.

Note: The table omits the large number of sequences in 3-3 games where the previous two goals were not scored by the same team; these proportions paint a similar picture to the ones above.

Final Notes

On the whole, there is little to no evidence that momentum exists within hockey, as judged by whether or not previous goal sequences imply future outcomes.

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Here are two more studies for those interested:

Dennis Lock used log-linear modeling to look at momentum in four-seasons of NHL games, using a per-period analysis. His conclusions were mixed, and he cautions against making any concrete conclusions from his analysis.

Jason Abrevaya inspired my table above in his analysis of penalty outcomes in hockey. Abrevaya found that previous penalty sequences are highly correlated with future penalty calls (i.e, AAA implies a future penalty on the home team, while HHH implies the next infraction on the away team). This paper requires a subscription.

Lastly, here’s my code.

####First, read in the data (it's a large data set!)
memory.limit(4000) 
library(nhlscrapr)
library(plyr)
load ("posts/nhlscrapr-probs.RData")
####Next, isolate goals and which team score the goal
set.goal <- grand.data[grand.data$etype == "GOAL",]
set.goal$GameSeason<-paste(set.goal$gcode,set.goal$season,sep="")
set.goal$TeamScored<-"H"
set.goal[set.goal$ev.team==set.goal$awayteam,]$TeamScored<-"A"
set.goal$Prev.Seq<-""
head(set.goal[set.goal$home.score==0&set.goal$away.score==0,])

#####Let's use an easier file name
sg<-set.goal 

#####Here, I assign previous scoring sequences within each game
for(i in 1:nrow(sg)){
 if (sg[i,]$home.score+sg[i,]$away.score>0)
 sg[i,]$Prev.Seq<-paste(sg[(i-1),]$Prev.Seq, sg[(i-1),]$TeamScored,sep="")
 }

####And our results
sg2<-sg[sg$home.score==1&sg$away.score==1,] #Game tied at 1 goal apiece
prop.table(table(sg2$Prev.Seq,sg2$TeamScored),1)
sg4<-sg[sg$home.score==2&sg$away.score==2,] #Game tied at 2 goals apiece
prop.table(table(sg4$Prev.Seq,sg4$TeamScored),1)
sg6<-sg[sg$home.score==3&sg$away.score==3,] #Game tied at 3 goals apiece
prop.table(table(sg6$Prev.Seq,sg6$TeamScored),1)