Every year, the MLB showcases its best players in the All-Star game. The game is never without controversy, as certain players who seem to deserve the honor are left off the league rosters (“snubs”), whereas others having not-so-stellar seasons find a way into the game. This is in part due to how the teams are selected: fans vote for players they think deserve the honor, and the player with the most votes at each position earns a starting spot on that league’s team. The players then vote for their peers to fill out the reserve rosters.
As one may expect, fans often “stuff the ballot box” for home-team players, such as in the notorious 2015 All-Star game, when the American League starting roster featured four players from the Kansas City Royals (at one point in balloting, eight of nine players were Royals).
The overall impact may seem marginal, especially given that a player who misses out on the starting lineup still has a shot at the reserve lineup, which is decided by peers. Nonetheless, it’s worth investigating the structure of the All-Star game starting rosters. In particular:
To conduct this analysis, I used pybaseball, an open-source python library for baseball statistics, to pull statistics on the first half of each season for every position player in the MLB, starting from 2008 (the farthest back pybaseball’s database goes). Players who played fewer than 45 games or recorded fewer 135 at-bats are removed. I then marked all players as All-Star starters or not based on Baseball Reference data. An example entry looks like this:
While 2008 is an arbitrary cutoff enforced by the pybaseball package, it doesn’t necessarily compromise our analysis, as (1) online voting has dramatically changed fan voting, so 2008 seems like a reasonable starting point, (2) the criteria for what fans look for in players has also changed; some fans nowadays care about WAR, which wasn’t the case in the 1950s, for example. Nonetheless, we should be mindful of the limitations of our data.
To start, let’s look at how All-Star starters and the rest of the league differ across various statistics (all stats are converted to rates to control for All Stars having more plate appearances, so HR is actually HR/Plate Appearance):
Figure 1: Percentage Difference (where 1.0 represents 100% difference) between All-Star Starters and Rest of League across various statistics. Note that All-Star starters were intentionally walked at a far greater rate than others.
We see a large difference in intentional walks — All-Star starters are intentionally walked nearly 150% more than average — which makes sense, as pitchers intentionally walk batters when they believe they have better chances against the next batter (indicating the current batter is stronger). Interestingly, All-Star starters had fewer sacrifice hits than the rest of the league, perhaps because they got their RBIs while also getting on base (as opposed to sacrifice hits). All-Star starters also struck out at a lower rate, as expected.
We can formalize these ideas in a table using a two-sample t-test. The t-test tests the plausibility of the assumption that two datasets are from the same model. The p-value essentially indicates how often we can expect the two datasets to be as different as the ones we have assuming a certain model for both.
For example, if we get a p-value of 0.01 for the difference in home runs between All-Star starters and everyone else, then if All-Star starters and other players both had the same probabilities to hit home runs, we’d expect to observe the differences we see between the two groups about 1% of the time.
Here are some p-values from our two-sample t-test (we convert all stats like home runs to rates like home runs per plate appearance to control for All Stars having more plate appearances):
Age | 0.26 |
Games | 2.09*10-31 |
At Bats | 8.66*10-57 |
Runs/PA | 3.25*10-57 |
HR/PA | 5.26*10-31 |
RBI/PA | 1.14*10-36 |
Avg | 3.11*10-53 |
SB/PA | 0.39 |
These are some ridiculously low p-values, but this is exactly what we would expect: All Star starters are supposed to be the best of the best, so we would expect them to hit home runs, drive in runs, and get on base at a significantly higher rate. It’s worth noting, though, that voters don’t seem to care as much about speed (stolen bases had a p-value of 0.39) or age (perhaps countering the notion that the All Star game features well-past-their-prime players who find a way in because of generous fans).
Figure 2: Age Distribution of All-Star starters (red) vs rest of MLB (blue)
To find the snubs and fairies, we need a method to predict All-Star starters. Since being an “All-Star” is a subjective notion, any metric we use, such as WAR, VORP, or HRs, is subject to our own biases. Our goal is instead to see who the fans left out by their own metrics. To do so, we train three machine learning models — Logistic Regression, k-Nearest Neighbors (kNN), and Random Forest — to predict whether a player is an All-Star starter or not. In each case, we train the model on 80% of the data, make predictions on the remaining 20%, and repeat this five times to ensure every point in the dataset also gets a prediction (except in Logistic Regression, in which case the model is trained on all the data).
Note that this means our “snubs” and “fairies” list relies on the imprecision of the model: if our model were perfect and classified each player as a starter or not correctly, then there would be no snubs or fairies! If we visualize each player as a 0 or 1 in this space defined by various statistics (each axis is a different statistic, like HRs, RBIs, ABs, etc.), then what we’re looking for is essentially 0s surrounded by a lot of 1s (snubs) and 1s surrounded by a lot of 0s (fairies).
Figure 3: We want to find a model to distinguish the All-Star starters (orange) from the rest (grey). Here we plot an example with two statistics: HR/PA and Batting Average. As we add more and more statistics, our model will try to distinguish between the two clusters of data (this plot will become multi-dimensional in our model).
Let’s start by looking at the players that all three models agree were snubs (there’s a lot: 20+!):
No Love: Players Classified as Snubs by KNN, RF, and Logistic Regression
Player (Team) | Year | HR | RBI | AVG |
Paul Goldschmidth (Arizona Diamondbacks) | 2018 | 18 | 48 | 0.274 |
Melky Cabrera (San Francisco Giants) | 2012 | 7 | 39 | 0.354 |
Martin Prado (Atlanta Braves) | 2010 | 7 | 36 | 0.355 |
Carl Crawford (Tampa Bay Rays) | 2010 | 7 | 40 | 0.316 |
Jose Altuve (Houston Astros) | 2015 | 7 | 35 | 0.302 |
We can also look at this from another perspective; whereas kNN and Random Forest are pure classification algorithms, logistic regression outputs a probability that a player is an All-Star starter. If this probability is greater than 0.5, we say he’s an All-Star starter.
No Love: Snubs with Highest Logistic Regression Probability to Be an All-Star Starter
Player (Team) | Year | HR | RBI | AVG | All-Star Starter Probability | Lost Out To(which player was the starter?) |
Victor Martinez (Detroit Tigers) | 2014 | 21 | 55 | .328 | 89.3% | Nelson Cruz (Baltimore Orioles) |
Justin Morneau (MinnesotaTwins) | 2009 | 20 | 67 | .320 | 85.9% | Mark Teixeira (New York Yankees) |
Miguel Cabrera (Detroit Tigers) | 2011 | 17 | 67 | .324 | 85.8% | Adrian Gonzalez (Boston Red Sox) |
Miguel Cabrera (Detroit Tigers) | 2012 | 18 | 56 | .323 | 85.1% | Prince Fielder (Tigers) |
Joey Votto (Cincinnati Reds) | 2017 | 24 | 61 | .312 | 83.4% | Ryan Zimmerman (Washington Nationals) |
Some of these snubs are truly head scratching. Rafael Devers’ exclusion from the All-Star roster, both starting and reserve, for example, was hotly contested in MLB circles this year. Others, however, just took a backseat to other outstanding players at their position. First basemen are generally renowned for the batting abilities and don’t have many defensive responsibilities, so it’s no surprise that four of the five logistic regression snubs were first basemen, who all took a backseat to other first basemen having excellent seasons.
Moreover, all three of our models agreed that the Tigers, Diamondbacks, and Blue Jays had the most snubs, so get on it Detroit, Arizona and Toronto! Support your players!
And who were the biggest fairies? Well, our models agree on a lot of them — 71 to be precise! Here’s a list of 5:
Free Pass: Players Classified as ‘Fairies’ by KNN, RF, and Logistic Regression
Player (Team) | Year | HR | RBI | AVG |
Jackie Bradley Jr. (Boston Red Sox) | 2016 | 13 | 53 | .294 |
Chase Utley (Philadelphia Phillies) | 2014 | 6 | 40 | .286 |
Rafael Furcal (St. Louis Cardinals) | 2012 | 5 | 32 | .274 |
Alcides Escobar (Kansas City Royals) | 2015 | 2 | 28 | .277 |
Joe Mauer (Minnesota Twins) | 2010 | 3 | 34 | .310 |
Free Pass: Fairies with Lowest Logistic Regression Probability to Be an All-Star Starters
Player (Team) | Year | HR | RBI | AVG | Prob |
Scott Rolen (Cincinnati Reds) | 2016 | 4 | 32 | .256 | 0.8% |
Derek Jeter (New York Yankees) | 2014 | 2 | 21 | .268 | 1.1% |
Dan Uggla (Atlanta Braves) | 2012 | 11 | 43 | .229 | 1.1% |
Yadier Molina (St. Louis Cardinals) | 2015 | 5 | 25 | .278 | 1.3% |
Salvador Perez (Minnesota Twins) | 2010 | 13 | 34 | .263 | 1.8% |
And which teams had the most fairies? The St. Louis Cardinals, with a “whopping” 6 over the past 11 years, so congrats Cardinals fans? And sorry Royals fans, even your brave efforts in 2015 weren’t quite enough…
Nevertheless, there are a couple limitations to our model worth discussing.
There are various methods to possibly correct for these limitations. For example, we could try to adjust for the quality of the season; if home runs were up across the MLB in 2015, for example, we would want to make each home run count less. We could try standardizing each statistic by year, but this also runs into problems: do we standardize with respect to the entire league for that year? Do we standardize only with respect to players who meet a certain baseline (i.e. do we want to standardize home runs and include a bunch of pinch hitters with lots of at-bats)? The general fear here is overfitting; if we adjust for year, position, park, etc., we may begin to model the noise in our dataset, although admittedly adding one of these may help our model.
It’s my belief, however, that having two exceptionally strong shortstops (or multiple exceptionally strong players in a year) still warrants labeling one as a snub — good hitters shouldn’t be penalized just because they happen to play the same position and same year as a slightly stronger player.
Nonetheless, our model showed that All-Star starters, for the most part, are indeed very good players and while a few players get snubbed every year, fans on the whole select players with strong seasons.
If you have any questions for Shuvom about this article, please feel free to reach out to him at ssadhuka@college.harvard.edu
]]>The off-season is a time in hockey when teams can make large improvements in order to win more games in the following year. One way to do this, and probably the most notable, is through the player movement that occurs during the off-season. However, a second way is to analyze and improve the tactics a team will deploy for the next season. I focused on one area of the game that I think has room for improvement: special teams’ strategies.
There is a hypothesis in the NHL that during a short-handed situation, the team with fewer players on the ice should primarily focus on defense, preventing the other team from scoring a goal. In case you are unfamiliar with the rules, a power play occurs in hockey when one team receives a penalty for violating the rules of the game. When this happens, the team that is penalized has one less player on the ice, so they are considered “shorthanded.” With fewer players on the ice, a common strategy is to ice the puck immediately at every possession, rather than attempt to score a goal (“icing” is to send the puck from one’s own defensive zone to the other end of the ice). Normally, icing the puck results in a penalty and the offending team cannot change players while having a faceoff in their own defensive end. However, killing a penalty when a team has fewer players on the ice allows them to ice the puck.
When talking with the Harvard Hockey coaching staff and former assistant coach Rob Rassey, we had the idea that it might be beneficial to focus on offense, rather than defense, in a shorthanded situation because of the emotional boost that scoring a shorthanded goal would give a team in the middle of a game. Additionally, this might also create a negative sentiment within the team enjoying the power play. While scoring a goal at any strength is technically worth an equal amount on the scoreboard, we might be able to say that shorthanded goals are more “valuable” than power-play or even-strength goals if this emotional effect indeed impacts a team’s chances of winning. Therefore, I set out to determine if there was a significant improvement in a team’s probability of winning if they had scored a short-handed goal, relative to that from a power play or even-strength goal. If we find a significant result, then not only would this signal that teams should be more aggressive on shorthanded (or penalty-kill) situations, but also that teams on a power-play might want to be less aggressive.
In order to answer the question of whether shorthanded goals lead to wins more often than even strength or power play goals do, I retrieved data from hockey-reference.com and hockeyeloratings.com. This gave me a full dataset of each goal scored from the 2005-2006 through the 2017-2018 seasons with the following variables: the score of the game at the time each goal was scored, the final score of the game, and the Elo ratings of each team playing. Elo ratings are simply used to account for the strength of the two teams playing. I also added a column for the current goal differential in the game by subtracting the current away score from the current home score. If a game went to a shootout there were not extra observations in the dataset, but the final score is indicative of which team won. For example: if the Stars beat the Bruins in a shootout 2-1, this dataset would only include two observations for each goal that was scored in regulation.
I decided to use Logistic Regression for this analysis since my response variable had a binary response. The first thing I did to check if there was any validity to this theory was run a simple regression using only the strength of the goal scored (power-play, shorthanded, or even-strength) to predict the winner of the game. This model had shorthanded goals as the reference level, and the coefficients for even strength and power play goals were significant and negative. Thus, I knew that more investigation was needed, but at least there was some evidence to demonstrate that there might be a significant difference in a team’s winning percentage based upon the strength of the goal being scored.
Next, I created both a win probability model and a model that calculated the probability that a team would win a game given that they had just scored a goal. The response variable for my first model was whether or not the scoring team won the game. The predictors for this logistic regression included a factor for the strength of the goal with even-strength being the reference level, the current score of each team, the time and period of the goal, and the Elo ratings of the two teams. Additionally, an interaction term between the Elo ratings of the two teams was included. For the second logistic model predicting the home team’s winning probability, the predictors included the current difference in score, the time of the goal, the home and away team’s Elo ratings, an interaction between the time of the goal and the current goal differential, and an interaction between the two team’s Elo ratings.
For the model that predicted the home team’s win probability, results matched our expectations. For example, the probability of a home team winning a game when they were tied halfway through a game with both teams having an average Elo rating, resulted in a win probability of 50%. For the model that predicted whether the team that scored would win the game, the model predicted a team that tied a game between two average opponents at 1-1 halfway through the game won 69% of the time if the goal was a shorthanded one. If the goal were even-strength, the model predicted that the same type of team would only win 67% of the time, and only 64% of the time if the goal were scored on a power play.
Looking at the summary produced by the second model for whether or not the scoring team would win the game, we note that the factor for the goal being scored as a shorthanded goal is positive with a p-value of .0479 < .05. We also see that the factor for the goal being a power play goal is negative.
The most important takeaway from the above model is that there is a positive and significant linear relationship between shorthanded goals and an increased winning percentage when we hold these other variables constant. This demonstrates that scoring a shorthanded goal leads to a higher chance of winning the game as opposed to an even strength goal. Since the coefficient for the goal being scored on a power-play is negative, we conclude that it is also statistically significant that short-handed goals lead to a higher win probability than power-play goals do when holding other factors constant. The plot below illustrates this relationship:
Looking at this plot, we are able to observe that the red line, which is the win probability when a team scores a short-handed goal, is consistently above the other two lines for other types of goals. This might be caused by the emotional benefit of scoring a shorthanded goal and the deflating emotional consequence of giving up a shorthanded goal. This model was fit using a smoother.
There are still some confounding variables that could have skewed the results. One of these is the fact that when a team scores a shorthanded goal, they are inherently still killing a penalty. In theory, the fact that they are still one player short should decrease their winning percentage given that the other team has a higher chance of scoring while they have a power play. This situation can be juxtaposed to scoring an even strength or power play goal when the game would then be at even strength or in some circumstances, the team that scored would still be on the power play. Another factor that could be affecting the model is that the model cannot take into account how aggressive a penalty kill or power play will be. Finally, there could be a confounding variable that teams that are giving up shorthanded goals against might be having a bad night as this is something that should not happen. This could be indicative of a team that is not focused on a given night, turning the puck over more often or giving the other team too much time and space. Additionally, of course, teams that give up more shorthanded goals might be weaker defensively than their Elo rating would suggest. Though, I’m skeptical; a team’s defensive strength is naturally baked into its Elo rating, and some of the best teams in the league gave up the most shorthanded goals. More investigation may be necessary, but assuming that these confounding variables even out, then the results of the model may still be valid. In order to account for these variables, we would need a more comprehensive dataset.
The question that must be answered next using more granular data, would be whether the benefit of scoring more goals, given that those goals are less likely to lead to wins if they are on a power play, still outweighs the risk of giving up a goal. To answer this question, a dataset that has the formation of each power play unit and the times that they were on the ice should be collected. With player tracking data available in the NHL next year, an answer to this question will be possible.
If you have any questions about this post, feel free to contact Paul at pmarino@college.harvard.edu
]]>One of America’s greatest borderline sporting events is almost upon us. On Independence Day, about twenty brave souls will compete in the Nathan’s Hot Dog Eating Contest. The event has been held annually since 1978, although one-off events have allegedly taken place since 1916 (including one in 1967 where a man ate 127 hot dogs in an hour). Even though robust data on participants who finished outside the top slots only date back to 2004, Nathan’s has kept record of each winner and their amount of hot dogs and buns eaten (often abbreviated as HDB). The data not only tells a story that is both uniquely American but also owes a great deal to a wave of Japanese competitors. Below are 9 charts that explain the Nathan’s Hot Dog Eating Contest.
The official Nathan’s website keeps results of their contest dating back to 1972, which, for our purposes, began the “modern era” of hot dog eating. To study the world of hot dog eating, I started with a dataset of Nathan’s eaters from 2002-2015 from former HSACer Daniel Alpert ‘18 and expanded it using the official results to include all eaters in the modern era. As I found out, the early years were unstable and marred by organizational changes. Jason Schechter’s 1972 feat of 14 HDB in 3.5 minutes stood as the record for seven years, even as the time grew to 6.5 minutes and then 10 minutes. The best example of how loose things were run in the contest’s rise to relevance is the 1981 edition. After a dismal 1980 contest that saw a tie for first place with 9 HDB in 10 minutes, The New York Times recounted how Thomas DeBarry “downed 11 hot dogs in five minutes and then rushed off with his family to attend a barbecue.” That the years 1972-1998 had written records of only the winners goes to show that Nathan’s didn’t take itself too seriously at that point.
The contest continued to find its footing before deciding on sticking to 12 minutes in 1988. From there, the record increased at a fairly linear pace. The relative parity of the 1970s and early 1980s began to fade away, though, signaling the potential for eating powerhouses. Between 1988 and 1998, there were 5 repeat winners. International eaters began to enter the contest. After the first female victory in 1984 (by Birgit Felden, a West German judo practitioner who claimed to have never eaten a hot dog before the contest), there was a 13 year wait before another international winner. Hirofumi Nakajima’s victories in 1997 and 1998 as well as Kazutoyo Arai’s 2000 victory signaled that more was to come. But for now, the record stood at 25.125 HDB, set by Arai in 2000. Unbeknownst to the Coney Island crowds, the competition was about to have a watershed moment.
In the span of 12 minutes, Japanese eater Takeru Kobayashi more than doubled the competition record by eating 50 hot dogs and buns, ushering in a new era of the Nathan’s Hot Dog Eating Contest. Arai ate at a rate of 2.09 HDB/min. Kobayashi ate twice as fast at a rate of 4.17 HDB/min. He claims his secret was largely psychological, but he brought new techniques (such as the Solomon Method) to the competition that outlasted him. After 6 straight titles, Kobayashi won a share of the crown in 2008 but never won again. He was infamously arrested after attempting to go on stage in 2010 and had a contract dispute with Major League Eating that continues to this day.
The man who carried on his legacy is fascinating in his own right, but it is also worth questioning whether Kobayashi’s success trickled down to average competitors. Luckily, Nathan’s has increasing amounts of data available for the Kobayashi years and beyond, allowing me to compare middle-of-the-pack eaters with previous champions. I decided to average the results of each year and weigh each point in the graph below on number of eaters in my dataset. There is a clear jump due to Kobayashi breaking out in 2001, and while there seems to be a drop afterwards, this can be attributed to an increase in contest data from Nathan’s.
The graph makes two things clear: Nathan’s data has improved substantially in the last ten years, and the average HDB has followed the trend started in the 1990s. But since the number of recorded competitors has grown, this trend means that even the average eater today would still beat out the champions of the pre-Kobayashi era. Since there is only data on winners until 1999, this difference in ability across eras is even more pronounced. Similar to how medal-winning swimmers in the early Olympics had times that would not even allow them to qualify today, the champions of the 1970s are similarly flat-footed compared to today’s eaters. Some of this is due to training. Competitors take the contest much more seriously today, as the mere existence of Major League Eating demonstrates. Some of this may also be due to the increased prestige of the event, now drawing eaters from all over the world.
That said, I wanted to confirm this trend was evident even under different rule changes. Although the time was actually reduced to 10 minutes in 2008, I made the same plot as above but using HDB/min on the y-axis. The first two contests have abnormally high HDB/min since the contest was 3.5 minutes, but that number began to dip as the contest time increased. That could point to the event being more a spring in its early incarnations before transforming into the endurance test it is today. After timing stabilized in 1988, it appears that the average eaters of today beat out the champions of yesterday.
That slower pre-Kobayashi growth trend is still evident in two areas of today’s competition. Nathan’s introduced a separate women’s competition in 2011. After Sonya Thomas took home the first three titles, Miki Sudo has reigned supreme over the field since 2014, as she gears up to claim her sixth consecutive victory. While Birgit Felden was the first female victor in the modern era in 1984, the women’s competition tends to see a lower HDB count than the men’s. But this count is still high relative to the pre-Kobayashi eaters. Indeed, the women’s champions today seems to be where we would expect the overall competition to have ended up by now had Kobayashi not revolutionized the event in 2001. I chose to analyze champions only since they provide the only reliable data pre-1999, but I would expect the trend to be similar when judging the entire field.
Next, I took the pre-Kobayashi champions and graphed their HDB with the eaters who finished in places 3-5 since 2001. The trend curves upward only a bit sharper than with the average eater, which means that outliers in either direction — good or terrible — skew the results. That the fifth-best eater today is eating around the average in a field of 20 is evidence that the ridiculous surge in eating ability may be concentrated at the very top, while the average eaters are still improving.
Today, nobody is pushing the record more than Joey Chestnut. After beating the record by more than 12 HDB in 2007, he has gone on to win 11 of the last 12 editions of Nathan’s Hot Dog Eating Contest. He has broken his own record 5 times and is the heavy favorite heading into the 2019 contest.
The easiest way to visualize his dominance is to plot the 20 all-time best performances at the Nathan’s Hot Dog Eating Contest. Kobayashi has 3 entries on the list. Carmen Cincotti and Matt Stonie (who broke Chestnut’s streak in 2015) each have 2, and Pat Bertoletti has 1. The other 12 belong to Chestnut.
His dominance still stands when measured in HDB/min. In fact, the only difference is that Kobayashi’s 2007 second-place finish (63 HDB) falls off since the competition was still 12 minutes at the time. Tim “Eater X” Janus’ fourth-place finish in 2009 (53 HDB) enters, which points to a spectacular feat.
The top four finishers in 2009 were among the 20 greatest performances of all time at Nathan’s Hot Dog Eating Contest. Even then, the gap from the top was still enormously high. Janus finished 15 HDB away from Chestnut’s record-breaking 68. It was Kobayashi’s last year at the contest, after which he would begin his contract dispute with Major League Eating. It was the highest HDB for Kobayashi, Bertoletti, and Janus. Chestnut, on the other hand, has beaten 68 HDB 4 times since then. 2009 was, for all intents and purposes, the greatest Nathan’s Hot Dog Eating Contest of all time.
That is not to take anything away from this year’s upcoming contest. As the number of hot dogs eaten continues to increase, perhaps Chestnut will find new challengers awaiting him on the Coney Island boardwalk. Or maybe the world will get to witness a true master of the craft on display with another dominant performance. Regardless, Nathan’s Hot Dog Eating Contest is a semi-sporting event with a mostly-storied history that started to tell a great story once someone had the thought to start writing it down. And that story will continue this Independence Day on the Coney Island boardwalk, as a handful of men and women attempt to push their stomachs to the limit in front of cheering crowds.
If you have any questions for Jack about this article, please feel free to reach out to him at jackschroeder@college.harvard.edu
]]>For the past few years, the NBA has seen a fair number of teams tanking; that is, teams lowering their level of play and purposely losing games in the hopes of receiving a higher draft pick through the lottery (the worst teams lottery to determine the exact draft order). The NBA draft is traditionally viewed as more top heavy than other leagues; LeBron James, Kevin Durant, Tim Duncan, Anthony Davis, Kobe Bryant, and Allen Iverson all were selected through the lottery, with all but Kobe being selected with one of the top two picks. As such, teams like the Philadelphia 76ers accumulated poor records to receive higher draft picks, drafting stars like Joel Embiid and Ben Simmons in the process.
In an effort to reduce tanking in the NBA, the league rolled out a new lottery system in which the very worst teams in the standings were given lower overall odds to receive a top-4 pick. The first lottery under the new system rewarded the 9th seeded New Orleans Pelicans with the first pick, hailing as a win for the league and a loss for tanking.
Figure 1: Odds Under New Draft Lottery vs. Old (from ESPN)
Compared to the old system, each of the fourteen lottery teams now has a chance at drawing a top-4 pick, lowering the probability that the very worst teams get one. So, given this new system, what is the expected value added to a team by tanking? How good of a player can the worst team expect to receive, compared to the old draft lottery system?
HSAC has previously analyzed the expected career win shares by pick and seed; I will conduct a similar analysis, analyzing all drafts from 1985 (the first year of the lottery system) to 2011. 2011 was selected for the end date because it allows enough time for an “average” NBA player to reach his peak (i.e. players who were drafted more recently have not recorded enough data for us to know how good they will be). A few additional tweaks have been made from the previous HSAC article:
Figure 2: Histogram of Career Win Shares for Players Drafted 11th Overall, 1985-2011
Win shares tend to be right skewed for each draft pick, including the 11th pick shown above. Below is a table summarizing the results when we simulate each draftee’s value from a gamma distribution:Figure 3: Table of Draft Value Simulation Results
And here is just the expected win shares for each draft pick under the new and old systems, shown as a line plot:
Figure 4: Trends in Expected Career Win Shares by Draft Seed, New vs Old
We see that expected career win shares from the first four seeds has decreased under the new system. Simultaneously, the value of seeds six through nine have noticeably increased. After the 9th seed, the draft pick values under the two systems begin to converge.
The uptick in win shares at the nine seed is due to some exceptionally strong players being selected at ninth overall (and the ninth seed has the best shot at ninth overall): Tracy McGrady, Dirk Nowitzki, Shawn Marion, Amar’e Stoudemire, Gordon Hayward, Kemba Walker, and DeMar Derozan were all drafted 9th overall. Compare this to the best players selected at eighth overall — Jamal Crawford, Andre Miller, and Rudy Gay — and it’s clear that the ninth draft pick is an anomaly.
From the table, we also see large standard deviations in the career win shares. This is reflective of uncertainty generated from two places: first, the lottery, as being the worst team doesn’t guarantee receiving the top pick. Second, once the team receives a position in the lottery, there is variance in the actual pick’s career win shares. For example, even if we know a team got the fifth overall pick, there is still a lot of uncertainty in how good their drafted player might be.
Moreover, even when we simulate other value-added metrics, such as BPM or VORP, we get similar results — the new lottery system hurts the top four seeds, helps the middle seeds, and has roughly no effect on the bottom seeds.
Figure 5: Expected VORP by Draft Seed Under the New and Old Systems
Overall, however, the differences are marginal. The second seed dropped from 63.07 expected career win shares to 53.87, about the difference between Richard Hamilton, a three-time All-Star, and Caron Butler, a two-time All-Star, respectively. Moreover, the standard deviation and skewness for each seed’s career win shares, in part, overpowers any major change in expected win shares. Considering that the largest difference in expected career win shares is only 10 win shares, it seems that teams that want to tank still have strong incentives to tank, even if the restructured NBA draft lottery makes it less likely for them to receive the best picks.
If you have questions for Shuvom about this article, please feel free to reach out to him at ssadhuka@college.harvard.edu.
]]>With the Boston Bruins set to take on the St. Louis Blues for the Stanley Cup Finals tonight, Boston is on the verge of being the first city since Detroit in 1935 to hold at least three of the four major North American professional sports titles (sorry, MLS). Earlier this postseason, I wrote an article detailing Boston’s chances of achieving the “Boston Slam” and holding all four titles at the same time, and then detailed Boston’s chances on the HSAC Twitter page throughout the two conference semifinal series. Unfortunately, the chances never got much higher than 1% as the Celtics flamed out in the Eastern Conference semifinals to the Milwaukee Bucks in 5 games.
However, the Bruins have just kept on winning, winning their last seven games and completing an impressive sweep over the Carolina Hurricanes in the Eastern Conference Finals to claim the Prince of Wales Trophy. During this excruciatingly long time period between the Conference Finals and the Stanley Cup (11 days for the Bruins, 6 for the St. Louis Blues), I was asked on Twitter about what the chances of one city winning three out of the four major titles in the same year.
I immediately realized that this was an interesting combinatorics problem that did not require super sophisticated math, and decided to set out on finding an answer.
There were some interesting things to think about with this problem. The first is that there are effectively five ways for a city to hold three out of four championships. They can win all four in the same year, or they can win exactly three out of four, leaving one sport out (four combinations). The second is that some cities have teams in exactly three out of the four major sports (like Atlanta, Pittsburgh or Houston) and thus can only have at least three out of four if all of their teams win. Meanwhile, some cities have exactly one team in all four sports (like Boston, Philadelphia or Detroit) and others have more than one team in at least one sport (like New York, Los Angeles or Chicago). Finally, some cities (like Seattle, St. Louis or Baltimore) do not have teams in at least three sports and thus are ineligible from achieving this feat. Thus, each city does not have an equal chance of attaining this feat. Finally, it is impossible for more than one city to achieve this in the same year (as that would mean at least six championships!), so it is sufficient to independently sum each individual city’s probability of winning at least three out of four.
In order to compute each city’s chances of winning at least three out of four titles, I made a simplifying assumption that in a given league, each team’s probability of winning a championship is uniform. Thus, it is assumed that the Patriots have a 1/32 chance of winning the Super Bowl, while the New York Yankees have a 1/30 chance of winning the World Series. This is not a totally reasonable assumption, as it ignores the effect of teams in “big markets” having the ability to spend more money and thus will have a higher probability of winning a championship than a team in a smaller market. However, in absence of any formal modeling of this effect,, a uniform distribution will have to do.
I wrote the following function in R to determine the chances of a city winning at least three out of four, given the number of teams that city has in each individual league, based on the five potential combinations described above.
For example, to compute the probability of New York doing this, you would feed in (3,2,2,2) to the function because New York has 3 NHL teams (yes, the Devils count), 2 NBA teams (yes, the Knicks also count even though New Yorkers would prefer if they didn’t exist), 2 NFL teams (technically, although they both play in New Jersey too) and 2 MLB teams. For Boston, you would feed in (1,1,1,1) and for Atlanta you would feed in (0,1,1,1) since Atlanta does not have an NHL team (#RIPThrashers).
In this analysis, we used 20 cities that had a team in at least three of the four major professional sports leagues. Some subjective judgements were made in terms of determining what counted and what didn’t. For example, I decided that the Green Bay Packers were a Milwaukee team despite being a two hour drive away and I also decided that all teams in the San Francisco Bay Area were considered to be from the same city, thus grouping together San Francisco, Oakland and San Jose. On the flip side, I decided that teams from Nashville/Memphis and Charlotte/Raleigh should not be combined, so none of the teams from those four cities were considered in this analysis.
After computing the above function for each city, I found each individual city’s probabilities of winning at least three out of four.
When we sum up the individual probabilities, we get 0.43%. Thus, ignoring the “big market” effect and assuming all franchises in a given league have a uniform probability of winning the championship, we would expect one city to win at least three out of four titles about once every 227 years.
As a note, these calculations will be slightly altered when the new Seattle NHL team enters the league in 2021/22, giving Seattle 3 teams and adding to the denominator for the NHL calculations.
It is also interesting to calculate the probability of Detroit achieving the same feat in 1935. Back then, there was no NBA, the MLB had 16 teams, the NHL had 8 (as the NY Americans and Montreal Maroons had yet to fold to give the traditional Original Six), and the NFL (in the pre Super Bowl era) had 9. Four cities (New York, Boston, Chicago and Detroit) had at least one team in all three leagues. New York was boosted by 3 MLB teams (New York Giants and Brooklyn Dodgers), 2 NFL teams (New York Giants and Brooklyn Dodgers) and 2 NHL teams (Rangers and Americans), while Chicago was boosted by having two teams in both the NFL (Bears and Cardinals) and MLB (Cubs and White Sox) and Boston had 2 MLB teams (Red Sox and Braves). Thus, Detroit’s probability of winning all three was 0.08%, Boston’s was 0.17%, Chicago’s was 0.35% and New York’s was 1.04%. If you sum all four of those up, the probability of a city winning three championships in 1935 was 1.65%, and we would expect it to happen once every 60 years given the league compositions in 1935.
Another interesting thing to study with this is when did the probability of a city winning at least three out of four peak, and how high was this probability? This was likely in 1947/48, during the 2nd year of the NBA.The NBA had 8 teams, the NHL 6, the MLB 16 and the NFL 10. There were six cities that had the chance to win three titles, and Chicago (boosted by having two teams in both the MLB and NFL) had the highest probability with 1.25%. The overall probability of one city winning at least three out of four was 3.37%, meaning we would expect this to happen about once every 29 years.
It would be interesting to control for the big market effect to redo these calculations. If you have any ideas for how to go about this, or have any questions/comments about the article, please feel free to reach out to me on Twitter @andrew_puopolo.
In June 2008, Boston stood atop the sports world; the Celtics had just won their first championship since 1986 with their new “Big 3”, the Red Sox were reigning World Series champs with David Ortiz and Manny Ramirez, one of the best 3-4 punches in MLB history, and the Patriots were one drive away from becoming the first team to ever go 19-0. The Bruins, on the other hand, were not quite at the same heights as the other Boston teams, leading to jokes around the country thanking the Bruins for giving other cities a chance.
Despite all this dominance, Boston only held 2 out of the 4 major professional sports league championships that year. Only once has a city controlled three out of the four major championships at the same time. This was in 1935, when the city of Detroit had the NFL Champion Lions, the World Series winning Tigers and the Stanley Cup Champion Red Wings. No team has ever held all four titles at the same time. The closest a city has come to true dominance was in 2002, when the city of Los Angeles had the winners of the NBA (Lakers) and MLB (Angels), as well as the smaller leagues MLS (Galaxy) and WNBA (Sparks).
Fast forward to April 2019, and Boston once again controls two out of the four major championships. In October, the Red Sox saw off the Los Angeles Dodgers in five games to win their fourth World Series title since breaking the curse in 2004. In February, the Patriots defeated the Los Angeles Rams 13-3 to win their sixth Super Bowl since 2002 and continue their awe inspiring dynasty.
Currently, Boston’s other two major professional sports teams are in the midst of playoff runs. The Bruins defeated the Toronto Maple Leafs in Game 7 of a very tense opening round series, and fortunately do not have to face the record setting Tampa Bay Lightning in the second round, as the Lightning were swept by the Columbus Blue Jackets. The Celtics are coming off a sweep of the Indiana Pacers, and face the Greek Freak and the Milwaukee Bucks in Round 2. It is very plausible that Boston could become the first city since 1935 to control three out of the four major championships.
In 2015, on the back of the famous Seahawks-Patriots Super Bowl, former HSAC Co-President Harrison Chase dubbed Boston “The Most Successful Sports City Of the 21st Century”. However, if Boston were to win one (or both) of the championships that are currently up for grabs, it would rightfully gain the right to call itself “TitleTown.”
We wanted to take a look at this possibility, and be able to quantify the probability of Boston holding three or four major professional sports championships at the same time this year. To do this, we simulated the remainder of the NBA and NHL playoffs 100,000 times using a Glicko model fit separately for the NBA and NHL that has been used to generate predictions showcased here and here. The ratings for each team have been updated to reflect the game results in the first round. Thus, we consider the Columbus Blue Jackets to be a stronger team than we did in our previous simulations. If you are interested in learning about the technical details of this Glicko model, please reach out to me on Twitter @andrew_puopolo or by email at andrewpuopolo@college.harvard.edu.
The first thing we wanted to take a look at was each of the two team’s current probability of reaching the subsequent three rounds of the playoffs:
The distributions for both teams are quite different. In each series, the Bruins are considered favorites and the Celtics are considered underdogs.
Next, we will take a look at the conditional probability of the Bruins and Celtics winning the Championship given they advance to each round of the playoffs.
What this table tells us is that the Celtics would have a 28.4% chance of winning the NBA Finals if they win the Eastern Conference. The first row of the table is the same as the last row of the previous table, as they both measure the current title odds. These probabilities are not exact, and are dependent on opponents in subsequent rounds. For example, if the Celtics were to beat the Bucks, their title odds are likely to be greater than 10% if their Eastern Conference Finals opponent is the Philadelphia 76ers, and less than 10% if the opponent is the Toronto Raptors.
Finally, we will take a look at Boston’s path to potential dominance, and how the probability of Boston holding 3 or 4 championships at the same time changes as each team progresses through the playoffs. Since the NHL playoffs are generally a week ahead of the NBA playoffs, each Bruins series is likely to wrap up before the Celtics series, and we will consider six distinct “steps” between Boston and history, namely each series in each sport. If either team is eliminated, then the probabilities of Boston winning a third championship are the same as the relevant probability in the previous chart. Each Celtics probability assumes that the Bruins have already won their series in the current round.
These probabilities represent Boston’s chances of attaining Titletown status after each “step” of the process.
Overall, the chances of Boston taking home a championship in either basketball or hockey this year is still relatively low, as the Celtics are unlikely to raise Banner 18. However, this storyline is an interesting one to follow if both Boston teams get past their second round opponents.
If you have any questions or comments, please reach out to Andrew on Twitter @andrew_puopolo or by email at andrewpuopolo@college.harvard.edu.
On Saturday, April 13, Chris Davis ended the drought. He had gone 54 at bats, 62 plate appearances, and 210 days without a hit, besting Eugenio Vélez’s old MLB record of 46 consecutive hitless at bats. Finally, at bat number 55, he laced a single into right field for his first hit since September. To put Davis’ struggles into context, nearly 600 players recorded hits in that time, including fearsome sluggers like Jon Lester, Greg Allen, and David Price. Anthony Rendon and Christian Yelich each tallied 43 hits, and Khris Davis clubbed 16 home runs over the course of the drought. The disparity between the two Davises was most apparent in last week’s series between the Orioles and A’s. Chris went 0 for 9, while Khris hit .368 and crushed 4 home runs in 4 games.
It wasn’t supposed to be this dark for Chris Davis and the Orioles. In 2012, he guided Baltimore to the postseason, and he followed that up by leading the league in home runs in both 2013 and 2015. As a result, the Orioles rewarded him with a 7-year, $161 million contract during the 2016 offseason. However, after one solid year under the new deal, he struggled in 2017. Last year was even worse, as Davis recorded one of the worst years in MLB history. He hit only .168, which is the worst qualified batting average ever. In addition, his FanGraphs WAR of -3.1 suggests that he cost the Orioles 3 wins, even as he accounted for nearly 20% of the team’s payroll.
Although Davis did not live up to the hype of his contract, the hitless streak was not all on him. Over the course of his drought, he was quite unlucky. In his record-breaking at bat, he crushed a pitch 346 feet, but Robbie Grossman caught it at the warning track. In Friday’s game against the Red Sox, Davis hit a line drive to right field, which Statcast predicted would fall for a hit 97% of the time. However, Boston had the shift on, and Eduardo Núñez calmly gloved it for the final out of the game.
This inspired us at HSAC to consider how unlucky Davis was over the course of his hitless streak, and how many hits he “deserved”. One way to examine how unexpected Davis’ hitting drought was is to examine the probability that a hitter of his caliber would record an out in 54 consecutive at bats. Prior to the streak starting, Chris Davis’ 2018 batting average was .175. This provides a baseline for Davis’ initial talent level. To figure out how unlikely it would be for Davis to not get a hit in 54 straight at bats, one can subtract his batting average (updating before each at bat) from 1 and then multiply these results together. This is similar to subtracting the initial batting average from 1 and putting that number to the 54th power, which gives a probability of about 1 in 34,000. Updating prior to each at bat gives a slightly more accurate estimate, and this calculation puts the odds around 5.41 x 10^{-5}. Since the odds of a given .175 hitter recording 54 consecutive outs are about 1 in 18,000 (smaller than the odds of a complete amateur making a hole in one), Davis appears to be very unlucky. However, even this probability doesn’t fully reflect Davis’ bad luck.
Another measurement that’s useful for determining how many hits a player “deserves” is expected batting average (xBA). Using the launch angle and exit velocity of a given ball in play, Statcast predicts how likely it is that the ball will be a hit. If a line drive has an xBA of 0.800, one would expect it to result in a hit 80% of the time. It would take an excellent defensive play (or good positioning) to prevent a hit in this situation. To find out how unlucky Davis was during his hitting drought, we gathered the expected batting average of each of the balls Davis put into play. Next, we added the 30 strikeouts he accumulated over the hitless streak, which each have an xBA of zero. Finally, we computed Davis’ average expected batting average during the streak, as well as the probability that he would go hitless for these 54 consecutive at bats. This probability was calculated by subtracting each xBA from 1, and then finding the product of each of these answers.
First, here are some of the balls from Chris Davis’ hitting drought with the highest expected batting average. He hit several pitches very hard, but they either went right into the shift or hung up at the warning track. For more detail on these pitches and Chris Davis’ hitting, check out these results from Baseball Savant.
Chris Davis’ Unluckiest Non-Hits
At Bat Number | Pitcher | Exit Velocity (mph) | Distance (feet) | xBA |
54 | Ryan Brasier | 74.9 | 177 | .970 |
17 | Lance Lynn | 109.2 | 210 | .880 |
35 | Joe Biagini | 105.0 | 313 | .680 |
25 | J. A. Happ | 102.0 | 396 | .670 |
51 | Aaron Brooks | 105.1 | 382 | .650 |
The following graph shows Chris Davis’ cumulative expected batting average throughout his streak. Many peaks and valleys populate the graph, as a result of Davis’ high number of strikeouts (which have an xBA of 0). However, as demonstrated by the rising trend, Davis was getting better and better chances as his hitless drought carried on. By the end of the drought, his xBA peaked at .142. Nevertheless, this xBA was still well below the 2019 MLB average, which is around .244.
The next graph demonstrates the probability of Chris Davis going hitless for a certain number of at bats in a row, based on the expected batting average of each at bat. The sharp decline at the 17th at bat is due to the line drive Chris Davis hit off Lance Lynn (2nd at bat listed in the first table) on September 22. Although Statcast expected a ball with a comparable exit velocity and launch angle to become a hit 88 percent of the time, it did not account for the shift. Gleyber Torres was stationed right where he needed to be and was able to make the catch for the final out.
As the graph demonstrates, Davis’ streak was very unlikely. Based on the balls he put in play, it was improbable that he would have 25 consecutive at bats without a hit, let alone more than twice that. Overall, the odds that Davis would go 54 at bats in a row without a hit were approximately 0.000000882, or 1 in 1.13 million. Just writing this number out doesn’t completely reflect how remarkable Chris Davis’ streak really was. To provide some framing for these astronomical odds, one would have almost twice the probability of being dealt a royal flush (1 in 649,740) and would be 90 times more likely to make a hole-in-one (1 in 12,500). In 2012, former HSAC president Andrew Mooney calculated that the odds of an average pitcher throwing a perfect game were 0.00000983, or more than 10 times more likely than Chris Davis’ streak.
While Chris Davis might not be as talented as he once was, he was very unlucky to not record a hit at some point over the course of 210 days. Finally, his luck changed on Saturday. Davis stepped up to the plate with the bases loaded, and on a 1-0 pitch, knocked a single into right to score two runs. Overall, he enjoyed a good series against the Red Sox, racking up 4 hits (including one with an xBA of only .140), and had his first home run since August. Things may finally be looking up in Baltimore.
If you have any questions for Danny about this article, please feel free to reach out to him at dblumenthal@college.harvard.edu
]]>In recent years, the formats for the playoffs in both the NBA and NHL have come under increasing scrutiny. In the NBA, there have been numerous complaints about the imbalance of the two conferences. An Eastern Conference team without Lebron as its star player have only won 3 championships since 2000, and none since 2008. As a result, there have been calls to make the playoff bracket go from 1 to 16, disregarding conferences altogether.
The main argument behind this format change is to create fairness and ensure that the best two teams reach the NBA Finals. This was readily apparent in last year’s NBA playoffs. The two best teams in the league were clearly the Golden State Warriors and the Houston Rockets. However, under the current playoff format, these two teams meet in the Western Conference Finals. Meanwhile, a team from the weaker Eastern Conference (either the Cleveland Cavaliers or the Boston Celtics) had chance to make it to the NBA Finals. Although both Conference Finals series went to a full seven games, the Eastern Conference Champion Cavaliers were overmatched by the superior Warriors in the Finals, and were swept in four games, providing a bit of an anticlimax.
There is a similar phenomenon occurring in the NHL. In 2014, the NHL decided to partition their playoff format even more through the creation of divisions. As a result, teams could (mostly) only play teams within their seven or eight team division in the first two rounds of the playoffs. Thus, it is possible for the two best teams in the league to face off in only the second round of the playoffs. This year, the Tampa Bay Lightning and Boston Bruins have the two best records in the NHL, and although they both lost the first game of their best of seven Eastern Conference Quarterfinal Series, and since they both play in the Atlantic Division would meet in the second round of the playoffs.
This creates the same dilemma as to what the NBA is going through. While there are many arguments for why the current playoff formats are the way they are and should remain the same, I wanted to look into the fairness argument. If the NBA and NHL adopted “fairer” playoff formats, how would that affect individual team’s chances of winning the title or reaching the championship series?
Fortunately, using a similar methodology to the one used to predict the NHL playoffs that I published earlier this week, we are able to estimate these effects through simulation. For this analysis, we used the 2017/18 NBA playoffs (as this year the conferences are more equal) and the 2018/19 NHL playoffs. For each of these two seasons, we simulated the playoffs 250,000 times using two different seeding formats using our estimate for a team’s Glicko rating and rating deviation. For the NBA, we will simulate first using the current playoff format and then simulate using the proposed 1-16 format. For the NHL, we will simulate using the current playoff format and then simulate using the format used before 2014. The format before 2014 was the same as the format that the NBA currently employs, where the top 8 teams from each conference are seeded 1-8 regardless of their division. To make the simulations simpler, we will not reseed teams in the second round. As it turned out, this year’s NHL Western Conference shook out as a “true bracket” where 1 plays 8, 2 plays 7 etc., so for the purposes of this analysis we will focus on the Eastern Conference. It is important to note that the model used to predict future outcomes only relies on past game results and their timing (and nothing else). Thus, our model is very similar to the pure 538 Elo, and fails to take into account things like “Playoff Lebron,” which their Carmelo Model takes into account. For the technical details on the underlying model, please email andrewpuopolo@college.harvard.edu or reach out to me on Twitter @andrew_puopolo.
If we look at last year’s NBA playoffs, a true 1-16 bracket would have looked like this:
We now have what is desired, which is the Rockets and Warriors on opposite sides of the bracket.
Using the results of our two simulations, we wanted to compare every team’s chances of making it to the NBA finals as well as their chances of winning it.
In order to get a sense of our predictions, we will first look at the probabilities for each team reaching the NBA Finals under the current playoff format, given that they had at least a 1% chance of making it to the NBA Finals:
Obviously, since the model does not take into account factors other than game results, the Cavs and Warriors have a low probability of reaching the Finals, while the teams that dominated the regular season (Raptors and Rockets) have a higher chance. This plot is only intended to serve as a baseline so that the next plot can be put into context.
Next, we will take a look at the change in percent probability of each team reaching the NBA Finals under a 1-16 playoff format:
These results are exactly what we’d expect. Since the Warriors would not have needed to go through the Rockets to make the NBA Finals, their probability of reaching the Finals skyrockets. In addition, since the Celtics and 76ers have to now go through the Rockets and the Raptors have to go through the Warriors, their chances plummet. In fact, we see every single Eastern Conference team’s chances go down and every single team in the Western Conference has their chances go up.
This would seem to imply that a playoff change is needed. However, we will next take a look at the probability of a team winning the NBA Finals in order to see if the current playoff format is truly unfair.
While our plot looks incredibly similar to the previous plot, we see that the scale has changed drastically. In our previous plot, the Warriors chances of reaching the Finals increased from 21 to 40%, while their chances of winning the NBA Finals only increased from 13 to 15%. A similar story can be painted for the other teams. This is likely since the teams required to defeat en route to winning the NBA Finals does not change that drastically. The Warriors still likely would have needed to face the Rockets and Raptors in order to win the Championship, just in a slightly different order.
Next, we’ll take a look at this year’s NHL Eastern Conference. This year, three of the top four teams are in the same division. The Boston Bruins finished with the second record in the East, and in order to reach just the Eastern Conference Finals will likely have to defeat the 5th best team in the East (the Toronto Maple Leafs) and the runaway Presidents Cup winners (Tampa Bay Lightning). In a true 1-8 format, they would have faced the 7th place Carolina Hurricanes and 3rd place Washington Capitals.
If the Eastern Conference playoffs were seeded 1-8, this is what the bracket would look like:
We will go through a similar process to the NBA. However, we will examine one round earlier since the NHL partitions its playoffs into four groups instead of two. Thus, qualifying for the Eastern Conference Finals is most likely to change under the revised format.
First, we will take a look at each team’s chances of reaching the Eastern Conference Finals under the current format.
Here, we see that despite the fact that the Bruins finished 7 points ahead of the Penguins in the regular season, their chances of reaching the Eastern Conference Finals are 5% lower given that they likely must face the Tampa Bay Lightning in the second round. In addition, the Maple Leafs fall from 5th to 7th as a result of having to face both the Bruins and (likely) the Lightning.
Now, let’s take a look at the change in probabilities from the current format to the traditional 1-8 format that was used prior to 2014.
As expected, the Bruins see the biggest bump in probability due to facing weaker opponent in both rounds. Similarly to the NBA, we see that all four Atlantic Division teams see their probabilities increase, while all four Metropolitan Division teams see their probabilities decrease. The Bruins’ probability increases from 22 to 30 percent, which is about a 33% increase.
Next, we will take a look at the change in the probability of reaching the Stanley Cup Finals:
We see a very similar trend to the NBA. Although the Lightning’s chance increases the most (by 2% from 38 to 40), the difference is pretty small. It is interesting to note that the Bruins’ chance only goes up by about 1%, but this is likely due to the fact that their expected opponents to reach the Finals are roughly similar, just in a slightly different order.
Given these results, we can conclude that by switching the playoff format, the best teams are more likely to win the Championship and reach the later rounds of the playoffs. This difference is profound at the “critical round” of the playoffs (the round where the current paths have differed the most). In addition, we see that these differences are much more pronounced in the NBA than in the NHL, likely due to the increased parity present in the NHL.
However, these differences are rather small and have little change when predicting the overall champion. Given that the main argument behind changing the format is for fairness and crowning the best possible champion, we find that the effects are too small compared to the numerous arguments against changing the playoff format (travel, less exciting matchups etc.) in order to justify changing the playoff format. However, if the goal for a playoff system is to ensure that the two best teams compete for the championship in a winner take all series, then changing the playoff format might be worth exploring.
Tonight, the Stanley Cup Playoffs begin when the Columbus Blue Jackets head to Florida to take on the President’s trophy winners Tampa Bay Lightning. The Lightning are heavy favorites to win the Stanley Cup this season, having finished with 21 points more than the team with the second best team in the league. In light of their dominance, how likely are the Lightning to win the Stanley Cup this season?
To answer this question, I used a Glicko rating system model to simulate this year’s Stanley Cup Playoffs 100,000 times. For those who are unfamiliar with what the Glicko rating system is, the Glicko rating system is an extension on the well known Elo rating system that dynamically updates after games. If a team wins a game, their rating goes up, if they lose a game their rating goes down. Beating a good team makes your rating go up by more than beating a bad team.
What differentiates the Glicko system from the Elo system is its ability to incorporate timing of matches into its prediction. In the Elo system, the rating changes at the same rate at the beginning and end of the season, which is problematic as the summer offseason changes the strengths of teams considerably, which should be reflected by team’s ratings moving more at the beginning of the season.
We fit our Glicko model using game results from the 2005/6 to the 2017/18 seasons. For the technical details behind fitting this model, please email me at andrewpuopolo@college.harvard.edu.
In our Glicko model, we estimated that the home team has an advantage of 33 rating points per game. This means that if two evenly rated teams face off, then the home team has a 54.7% chance of winning the game.
Our simulations are run “hot”, which means that we are constantly updating our estimate for a team’s strength throughout the (simulated) playoffs as they advance through more rounds.
First, we will look at our predictions for the first round of this year’s Stanley Cup Playoffs:
These predictions are pretty much more or less what we expected. In the Eastern Conference, the 1-4 matchups in each division (Tampa Bay vs Columbus and Washington vs Carolina) see the team with home ice advantage as heavy favorites. We also have the Boston Bruins as slight favorites over the Toronto Maple Leafs. However, it is interesting to note that the Islanders are underdogs against the Pittsburgh Penguins, despite having home ice advantage. This is due to the Penguins having a rating that is 34 points higher than the Islanders, as it incorporates some of last year’s results into the estimate for a team’s rating.
In the West, the predictions for this series are more of a toss up. The Sharks and Golden Knights have almost identical team ratings and the model gives San Jose a slight edge due to home ice advantage. There is a similar phenomenon in the Winnipeg vs St. Louis series. The other two series see the better team with about a ⅔ chances of advancing.
Next, we will take a look at our predictions for the winner of each Conference
The Lightning are overwhelming favorites in the Eastern Conference, but despite their regular season dominance, only make it to the Stanley Cup Finals in 38% of our simulations. This is a testament to the great parity of hockey. Another thing to note is that despite having the second best record in the Eastern Conference, the Bruins only make the the Stanley Cup in 12% of simulations, while the Washington Capitals who finished with three fewer points in the regular season make the Stanley Cup in 20%. There are two explanations for this. The first is that the Capitals are rated higher than the Bruins due to their Stanley Cup win last season. The second is that there is a higher probability that the Bruins face the Lightning en route to the Stanley Cup than the Capitals do. The Bruins have to face the Lightning in 78% of simulations, while the Capitals only have to face the Lightning in 55%. In addition, the Bruins have to face a tougher opponent in the first round than the Capitals do.
The Western Conference is much more even than the East. Only two teams (the Dallas Stars and Colorado Avalanche) have a fewer than 10% chance of qualifying, while no team has higher than a 21% chance. This shows the incredible parity that is currently present in the Western Conference.
Finally, we will look at our predictions for the probability of all sixteen teams winning the Stanley Cup:
Our results are somewhat as expected. The Lightning have a 27% chance of winning the Stanley Cup, while we see pretty strong parity across the rest of the league. We see that the East has about a 60% chance of winning the Stanley Cup over the West, which makes sense given that 3 of the top 4 teams by record came from the East.
If you have any questions for Andrew, please reach out to him at andrewpuopolo@college.harvard.edu
]]>It has long been believed that the proper way to shoot a basketball is a shot with as much arc as possible, allowing the ball to “see” as much of the hoop as possible before descending into it. This theory came into the popular eye only a few years after Sir Isaac Newton invented physics, as well as the 1-3-1 zone defense, revolutionizing a game that would not be invented for another two hundred years.
But since then, we split the atom, we discovered quantum mechanics, and we have caught a fleeting glimpse of James Harden’s quadruple stepback. With the tools we have now, shooting in basketball is due for another upgrade. With the arced method of shooting, even the slightest error in shot leads to the ball bouncing off the rim and into the hands of the opposing team. Harden’s Rockets know this inefficiency well (see: 2018 Western Conference Finals, Game 7). While basketball players spend hours perfecting their form to allow for the cleanest entry into the hoop as possible, there exists an easier way to optimize scoring and increase shooting efficiency.
Consider the following scenario: the Warriors inbound the ball to Steph Curry, down by two with five seconds remaining in the game. He slows down as he approaches the three-point arc, faced with a tough decision. He can pass the ball for an easy, game-tying layup, he could shoot a moonshot three-pointer, or he can throw the ball at the backboard so hard that it pops and falls into the basket. The standard basketball is 4.73 inches in radius at 7.5 Psi. In Measurement of the mechanical properties of the handball, volleyball, and basketball using DIC method: a combination of experimental, constitutive, and viscoelastic models, Kirimi et al (2015) calculate the maximum stress of a basketball and analyze how a basketball is deformed when external pressures are applied.
The maximum stress a basketball can take is 8.85 Psi and the elasticity modulus is 591.25×10^3 kPa, meaning it takes 591.25×10^3 Newtons of force to change the basketball’s volume one cubic meter. In order for the basketball to reach 8.85 Psi, Boyle’s Law says that it would require a change in volume of 71.98 in3. Using the information given to us, and performing the deformation calculations, the basketball would need to be launched at a speed of 275 mph, a modest speed for any professional basketball player.
Once the basketball is popped, due to conservation of mass, it flattens out, going from a sphere to a deflated shell of leather that is about three inches thick (pictured below). This new form of the basketball is 140.6 in2 in surface area and about 7 inches in radius, looking like a large pancake. The distance between the backboard and the rim is six inches, so the larger, less bouncy basketball will flop into the hoop, as the majority of its mass will be over the hoop due to the slight impulse provided by the backboard.
If Curry steps up, absolutely hurls that basketball at the backboard at 275 mph, it’s game over, Warriors win.
If you have any questions for Jackie about this article, please feel free to reach out to him at jackiemoon@aprilfools.edu
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