Final Project
Cam Schmidt
Get help with sizing for final, make separately and link/embed shinys and tbx?
Intro
The rise of analytics in the sports world has caused a schism - should we, as players, coaches, or observers, place an emphasis on what the numbers say or what our senses tell us? It isn’t possible to quantify when a player is (or is going to get) hot. Statistics cannot explain why Stephen Curry plays so extraordinarily well at Madison Square Garden (Champion). And year after year we see ESPN’s predictive measures proven wrong (Bauer). But statistics let us locate trends - and one such trend that falls in the middle of the analytics versus the eye test debate is score effects.
I have only ever heard the term score effects be used in reference to hockey. So, I’ll use the sport to paint a picture of what it means. Team A is playing Team B and, after a scoreless first period, Team A finally takes a lead in the middle of the second period. The rest of the second is played evenly, but then the third period starts and Team B shells Team A. They seem to get all of the chances, win every battle, and even out-shoot Team A 15-3 in the frame; and yet they lose 1-0. Why? Score effects. Team B may have looked better, but Team A changed the way they were playing because they were winning. This is not unique to hockey. Basketball coaches often beseech their players to hold onto the ball down the stretch when they are winning games, football teams run the ball more when they are up, and baseball teams even have a special pitcher meant for scenarios when they need to preserve a lead late. But these are anecdotal pieces of evidence. Different philosophies of coaches and scenarios do not make score effects statistically meaningful. In fact, many would argue that they are not real at all. Why would you wait until the 4th quarter of a game to start taking smart shots or until the third period to push for offense when you can do both of these all game? It is possible that us viewers are simply falling victim to an observational bias and seeing these effects that we believe are there. So in this piece, I am going to investigate whether or not score effects are actually real. Are teams playing differently purely based on whether they are winning or losing? I have spent my entire life watching hockey and basketball, and know them the best, so I will keep my research focused on those two sports
Before we begin, some things to keep in mind. First, the NBA data is taken from just the 2024-25 season. The data set is comprised of four different game states, not all of which are independent. The all situations data accounts for every second of every game played in the 2024-25 regular season. The rest of the data is all from clutch situations, which is a subset of that. The NBA defines clutch as the last five minutes of the 4th quarter or any point in overtime when the difference in scores is 5 points or less (Martin). So, for example, there is a potential for issues that arise when teams are trading baskets and the difference in scores bounces back and forth from 5 to 7. However, the NBA does not offer data based on score outside of the clutch. Additionally, teams tend to play non-rotational players during blowouts, so any differences in style or efficiency that arise during those games could be attributed to the players, not the score. So, the clutch game state will be the most suitable to dive into. Lastly, both the trailing and leading clutch game states include ties, so there is some overlap between the two states. Since the game is not tied more often than it is, we can consider this negligible for our purposes; but it would need to be considered if further statistical testing was to be performed.
The NHL data is a collection of 5 on 5 data from the 2022-23 season to the 2024-25 season. Note that this is not all even strength data, as the NHL qualifies 4v4, 3v3, and 6v5 situations as even strength as well. The data set is again comprised of four game states - all situations (analogous to the NBA case described above), leading, trailing, and tied. This data accounts for any point the game is played at 5v5, regardless of time remaining. There is only one hiccup in the data. Prior to the 2024-25 season, the Arizona Coyotes relocated to become the Utah Hockey Club (now the Mammoth). While the players and organizations remained the same, the NHL recognizes them as different franchises. So, rather than having 32 teams for three seasons, this data has 31 teams for three seasons, one team for two seasons, and one team for one season. An 82 game season is a large-enough sample size where this should not be too much of an issue. The last thing to keep in mind is the subjectivity of some NHL data. Each arena has its own scorekeepers, so when it comes time to determine what is a shot attempt or what counts as a save (the puck must be headed into the net to be considered one), there can be some discrepancy across venue. It is very unlikely that this discrepancy is going to pose any issues, but it is just something to keep in mind.
I will be defining and explaining relevant statistics as we dive into them, but the full glossaries of terms are linked here.
Big Picture
First, let’s take a look at some of the most general advanced statistics both sports offer.
In basketball, we are using net rating; net rating is the difference between a team’s offensive and defensive rating, which are how many points a team scores or allows per 100 possessions, respectively. Positive net rating is good. For example, the extreme, positive outlier in the leading game state is this season’s champions, the Oklahoma City Thunder. In their games, the lead seemed to have a positive effect, as they played with out-out-of-this-world efficiency when they were up late in games. On the flip side, the negative outlier in the trailing state was also the Thunder - they showed their greatest weakness when playing from behind. While we are able to clearly see the evidence of score effects on the Thunder, the league as a whole does not seem to be following this pattern closely. The density plots for the clutch game states (which may be affected by a one-season sample size) are erratic in terms of modality and relatively symmetrical. The medians reflect this. While not all pictured, the medians for all situations, all clutch situations, and clutch trailing situations hover around 0, which is what would be expected. Despite being the furthest away from 0, the clutch leading game state’s median does not wander far either. The lack of difference between the medians suggests a lack of difference between the groups. Overall, there is a lack of evidence for score effects in the NBA shown here.
In the NHL, the plot shows the densities of expected goals for percentage (xGF%). This is a measurement of what share of the expected goals (xGs) during a team’s games that they held. In other words, it is xG for divided by xG total. xGs is a statistic used to measure a team’s performance outside of goaltending. Goalies are often erratic, so we isolate the skaters when we look at underlying performances. Additionally, different sources use different models to develop xG numbers. The source used here, NaturalStatTrick, is one of the most well-regarded public models. The density curves for the NHL data are a lot more normal-looking than the NBA data. There are few to no outliers, and the curves are pretty symmetrical. Not pictured here, the medians of the all situations and tied game states fall around 50%, which indicates equal play across the league and is what we expected. However, when we look at the medians for teams that are winning or losing, we see them head off in opposite directions. Teams that are leading tend to lose the xG battle, while teams that are playing catch-up tend to win it. This supports the existence of score effects, as this idea is the very philosophy behind them.
So, does this mean score effects exist in hockey and not basketball? Not exactly. The reason that we can clearly see evidence of them here in the NHL data is that xG reflects play style. Teams that are pushing for offence dominate possession, win puck battles, and are in general taking more shots; all of which equate to more xGs. Net rating, however, almost exclusively measures efficiency. While being one of the best overarching statistics to judge teams, it is not able to catch stylistic differences in the same way as xGF% because of the nature of basketball. Both teams are guaranteed almost the same number of possessions, and net rating only measures how effective you are with them. In order to find evidence of score effects, we may need to look at some more play-style-related statistics.
One way we can look at play style in basketball is by investigating where points are coming from. The following plots show what percentage of every team’s points come from 2-pointers, 3-pointers, or free throws.
The first observation is that the clutch data is more spread out than the all situations data, which is likely due to the amount of time that is spent in clutch situations when compared to all situations. Additionally, we can see some clusters. There is a clear red cluster that is at the left of all of the points, and there appears to be a green cluster at the far right end. This indicates that teams score fewer of their points from free throws in all situations when compared to clutch situations in which they are winning. And this aligns with the idea of score effects - down the stretch, losing teams may foul intentionally to stop the clock, giving the leading team free throws (thus also preventing them from scoring in a traditional manner). The medians, however, tell a story that is a bit counterintuitive. Logic would dictate that teams that are losing would shoot more 3s so they can catch up, while teams that are winning would try to take safer 2-pointers to avoid letting their lead dwindle. Instead, the score effects are telling a story through defense here. Losing teams are selling out to defend easier 2-point shots in order to prevent the lead from growing, while winning teams are trying to prevent 3-pointers that can get a team back on top. While the tendency of shots may be the same, the actual rate at which points are scored from each reflect this increased defensive attention.
This provides pretty solid evidence that score effects exist in basketball as well. But just to confirm, let’s take a look at one more stylistic aspect of basketball - risk. We can anticipate that teams that are losing will make more high-risk, high-reward decisions. Additionally, we may expect them to play faster, which can lead to a loss of control. On the other hand, teams that are winning will play slower and take care of the ball on offense. The speed at which teams play is tracked through their pace, which is their possessions per 48 minutes (the length of a non-overtime game). We can quantify risk and lack of control through a team’s turnovers, which is the most common consequence of this style of play. To do this, we use turnover percentage (TOV%), which is the percentage of a team’s possessions ending in a turnover.
By transitioning from all situations to all clutch situations, we can see that teams avoid playing slow, risky styles when games get close, even if they played that way during the rest of the game. It is also evident that many teams speed up down the stretch, as is evident by most of the points in the plot moving to the right along the pace axis. This means that when games get close, teams are trying to maximize the number of possessions they get and hopefully get the last possession, a clear indication that their play style is altered based on the score. This is also potentially caused by the strategy of fouling to stop the clock late in the game. Fouling leads to free throws, which in turn leads to a change of possession (more often than not), which increases the pace of the game.
If we compare the leading and trailing game states, we can see an interesting pattern as well. TOV% was selected to be a measure of risk-taking by these teams; it was expected that when they are winning, these teams would take fewer risks and have a lower TOV%. However, only one team, the Los Angeles Lakers, sported a TOV% of less than 10% when winning in clutch situations. When losing, eight different teams met this threshold, with the Sacramento Kings even dropping to below 8%. But this does not mean that TOV% is not telling a story of risk; while the anticipation was that it would tell us about offensive risk-taking, it is actually telling us about defensive risk-taking. When teams are winning, they are more conservative on defense, as extra possessions are not of utmost importance - no need to jump for a steal and get easily beat to the rim if you miss. On the flip side, teams that are losing need the ball back to score as soon as possible. They pressure more and take gambles hoping to come away with steals, which thus leads to more turnovers by the winning team, giving us this shift in TOV%. Regardless if the risky or conservative play occurs on offense or defense, it is a direct result of the score. Therefore, it is even more certain that score effects exist in basketball.
Unfortunately, there is not an exact parallel in hockey that allows us to look at risk, especially in the way of turnovers. Giveaways and takeaways are the most subjective data in the sport and usually disregarded when comparing players or teams. But it would still be apt to find more evidence that score effects do exist in hockey. One statistic in which they are evident is scoring chances, specifically high danger scoring chances. The way scoring chances, and its offshoots of the high, medium, and low danger variety, are defined is a little complicated, but a full definition is provided in the glossary. What it boils down to is when a shot is taken and where it comes from. Just as we did with xGs, we can track scoring chances for and against, which allows us to also calculate a percentage share. In the following plot, we are going to be looking at the high danger scoring chances for percentage (HDCF%).
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Over the course of the last three years, a singular team - the Seattle Kraken - had a larger share of high danger scoring chances when they were leading compared to when they were trailing. And the difference between their HDCF% in these game states was less than 1%. That means that 32 of the 33 franchises that were in the NHL over this time frame generated more (many a lot more) dangerous looks at the net when they were losing, often in games they were being outplayed. In fact, the Kraken are also the only team that has a higher HDCF% in all situations than in trailing situations, and one of only seven who have stronger numbers when tied versus trailing. Similar patterns emerge when looking at other game states as well - only the Edmonton Oilers have better numbers when leading than in all situations, and that count only rises to seven when we look at leading compared to tied. These patterns among game state make it abundantly clear that score effects exist in hockey, and the explanation behind this phenomenon is similar to the one in basketball. When teams are winning, they are more conservative on the defensive end, less willing to apply pressure and win the puck back. Because of this, the losing team is easily able to rack up shots, some of which will be from high-danger areas, off the rush, or rebound attempts, all of which result in high danger chances. What these chances do not tell you, however, is that the defense is often able to block these shots or otherwise disturb them, making them high danger only in name. Furthermore, because the losing team must be more aggressive, they are more likely to force turnovers when on defense, which would prevent high danger attempts from stacking up in the other direction.
Before we move on and take a look at how certain teams are performing across game state, I want to point out something that has really stood out to me about all of these plots. If you have been around these sports, or any really, you get the feeling that the most damage to or control you can have to the flow of the game comes when you are on offense. You can make the decision to slow down or speed up, or even regulate what quality of shot you want to take. Because of this, I expected the score effects to be most prevalent from an offensive standpoint. Having looked at several visualizations so far, it is clear that score effects manifest mostly on the defensive side of these sports. In hindsight this makes sense - you cannot magically change how well you are shooting based on the score, but you can definitely control your effort and the tactics to which you employ yourself, both of which make up most of what defense is.
Team Performance
Now that we can confirm score effects exist, let’s look at how certain teams played within during score states. We will begin with some NHL data. Below is a radar plot providing information on xGs, scoring chances, and Corsi. All of these are provided on a per 60 minute basis (a full game) and are given as either for or against (eg. xGA or XGF). I have already defined xGs. I have discussed scoring chances as well, but there is a little more nuance here. While low, medium, and high danger chances exist, it is only labeled as scoring chance if it is of medium or high danger, so scoring chances for and against (SCF and SCA) ignore low danger chances, which is a bit of a misnomer. Corsi is a measure of all shot attempts, whether they be blocked, saved, wide, or scored. Corsi for and against (CF and CA) are useful measures of offensive zone possession and more importantly how that possession is being used, especially when used with other measures that quantify the threat of the shot attempts, such as SCs and xGs. In order to put the data into a radar plot, the data was standardized into z-scores. For all of the “for” statistics, more is better, so positive z-scores are good. For the “against” statistics, fewer is better - so to avoid issues, the z-scores were reflected for this data in order to make positive z-scores good. When looking at the unstandardized data, just keep in mind that lower CA, xGA, and SCA are better. As far as the radar plot goes, the further the area stretches in the direction of a statistic, the higher the z-score for that statistic. So, the larger the area of the plot, the better the team’s performance.
With 33 teams in the data set and the ability to compare any two of them at once, there are 528 possible comparisons we can make using this plot. Since that would be time consuming, we will focus on just a few of the more noteworthy comparisons across the league.
First, over the course of the three seasons from which the data is gathered, the Florida Panthers made all three Stanley Cup Finals and won two of them. They defeated the Edmonton Oilers in both of those years, so let’s start by comparing them. At all situations, the Oilers were better at generating high quality looks, as evidenced by their very strong xGF and SCF numbers. The Panthers, on the other hand, threw a ton of pucks at net, leading to their high CF numbers. Their quantity of shots is also evidence of their strong possession numbers, which, when paired with their stellar defense, led to their xGA and SCA numbers being better than those of the Oilers. Curiously enough, the Oilers were much better than the Panthers when holding a lead, being able to create both chances and xG at an extremely high level to close out games, all while limiting their opponents as well. When trailing, the trends match those of all situations. And while the Oilers may have been better than the Panthers in these clutch situations, the Panthers were still very good. This, and their ability to up their game even further in the playoffs, allowed them to defeat Connor McDavid and Co. two years in a row to win the Stanley Cup.
From the start of the 2022-23 season to the close of the 2024-25 season, the team with the most points (highest in the standings) was the Dallas Stars. All six of these metrics are above average in all situations for them, but none particularly stand out as excellent. What contributed greatly to their success over this time was score effects. Compared to when they were leading or any situation, the Dallas Stars saw an improvement in all but their SCF when they were losing. When they were down, the Stars were able to take advantage of how the game changed and maximize their performance, leading to a high comeback potential in every game they were a part of.
The last comparison that we will look at is the Utah Hockey Club (UHC) and the Arizona Coyotes. As mentioned earlier, the Coyotes relocated to become the UHC during the last year of this window, so this is really the same team. By comparing them, we can see the year-over-year improvement of the team, going from below average the previous two years in all six metrics to above average in all six during the next. But comparing the unstandardized numbers of the two franchises really allows us to see score effects in action. Since the UHC was better than the Coyotes, there was a shift of all of their metrics that reflected the improvement. But when looking at the differences between the leading and trailing game states for both franchises individually, the differences between the metrics is almost identical. The difference in xGF was 0.25 for the Coyotes and 0.26 for the UHC and SCF saw differences of 1.91 and 2.16, respectively. This demonstrates the strength of score effects - it does not matter how good or bad a team is, score effects still affect them just the same as everyone else.
Some other noteworthy teams that could be looked at: - Impeccable numbers: Carolina Hurricanes - Bad numbers: Chicago Blackhawks, San Jose Sharks, or Anahiem Ducks - Extreme score effects: Boston Bruins or Los Angeles Kings
https://www.nba.com/warriors/news/among-the-greats-stephen-curry-has-made-madison-square-garden-his-playground-20250305 https://bauertology.com/2024/01/19/its-time-to-abolish-the-bpi/ https://www.nba.com/news/stats-breakdown-coming-through-in-the-clutch
HAVE ABOVE, NEED CITATION: NHL: https://www.naturalstattrick.com/glossary.php?players