A Historical Review of ESPN Power Rankings

By Ben Ulene

It’s September again, and with the major wintertime sports starting their 2016-2017 regular seasons, sports fans across the U.S. get to participate in the annual tradition of poring through expert predictions – including various outlets’ preseason power rankings.

While Vegas odds and other betting markets offer a general take on how various teams may stack up, there is something satisfying about reading power rankings reports. With written blurbs for teams that function as justifications for their rankings, sites like ESPN and Bleacher Report impart a qualitative aspect to the numbers that may mirror, or perhaps even spark, debates among fans across the country. And like professional odds-makers, many sporting news outlets update rankings as the season goes along – bookending the year with a final set of rankings leading into the playoffs – which provides a mechanism for determining how “predictable” any given regular season is.

For ease of use, I analyze ESPN’s Power Rankings in this article. With rankings from the first to last week of the regular season across all four major U.S. sports, ESPN’s rankings let us perform cross-sport comparisons to test the accuracy of predictions by different sets of “experts,” as well as dive deeper into individual sports to determine the predictability of different teams and seasons.


Cross-Sport Analysis:

Upon analyzing the past six years of rankings across MLB, NBA, NFL, and NHL, one thing is apparent: The NBA is consistently the most predictable league, and by far. As a few scatterplots show, in the NBA, Week 1 Power Rankings are much more predictive of regular season success than in any other sport:

Here, a straight diagonal line would represent perfect prediction accuracy for every team; while the NBA plot is far from perfect, it still seem to be noticeably less random than the other plots.

In fact, as a two-sided t-test shows[1], the inter-league difference in predictability (measured by the average absolute value difference for every team’s beginning ranking and their final ranking) is statistically significant between the NBA and every other league, but insignificant among the other three. In other words, the predictabilities of MLB, NFL, and NHL regular seasons cannot be proven to be different from one another – but the NBA is more predictable than all three:

League 1 Mean Difference League 2 Mean Difference p-value
NBA 4.33 MLB 6.94 1.151e-07
NBA 4.33 NHL 6.54 6.178e-06
NBA 4.33 NFL 7.52 3.242e-09
MLB 6.94 NFL 7.52 0.3327
MLB 6.94 NHL 6.54 0.4735
NFL 7.52 NHL 6.54 0.101


Why then – besides the unlikely explanation that ESPN’s NBA analysts are that much better than their analysts for other sports – is there such a drastic difference in ranking accuracy? Season length is what first comes to mind, but upon closer inspection cannot be the primary cause; not only is the NBA season easier to predict than the equally-long NHL season, but there is a noticeable lack of statistical difference between predicting the MLB (162 games) and NFL (16 games) seasons.

There are, however, a few possible explanations:

1) Fewer, more impactful players: The NBA mandates that teams carry 14 players at any given time, as opposed to the NHL’s 20, MLB’s 25, and the NFL’s 53, giving star players – who are usually apparent at the beginning of the season – more of an impact on results.

This is magnified by the nature of the game: Only in the NBA do the most impactful players consistently play for more than three quarters of the game, making it easier for talented teams to rise to the top. Pitchers in baseball can play only every five games; hockey superstars may see only 20 minutes on the ice in a game. Even in the NFL, elite quarterbacks are only on the field for offensive snaps, and the comparatively high injury rate makes it difficult to predict even the best teams.

2) Higherscoring games: The high number of possessions in NBA games, compared to the other three sports, may mean that there is less of a risk that any given NBA game is determined by chance. NBA teams possess the ball over 90 times on average in any given game[1]; even in baseball, teams will rarely send up more than 40 batters in a game[2]. Therefore, skill differences have more opportunities to manifest themselves in basketball, while mistakes can have a larger impact on the other big sports with fewer possessions.

3) Injuries: Since hockey and football are high-contact sports, teams in the NHL and NFL are much more susceptible to being gutted by injuries midseason than NBA teams. Even in baseball, a non-contact sport, pitchers – perhaps the most important players on their teams – are highly susceptible to season-ending arm injuries that can tank a team’s season.


Seasonal Analysis:

Taking the league-based differences into account, it is no surprise that six of the seven most predictable seasons in our sample are in the NBA – with the 2013 NBA season clocking in with a tiny 3.47 average difference between beginning and end rankings.


Additionally, the NBA is unique in its consistency – while other sports like the NHL vary wildly from season to season in predictability, the NBA has stayed relatively constant. The NBA has been the most predictable for each of the past six years, while no other league has repeated as least predictable – the NFL led in 2010 and 2013, MLB in 2011 and 2015, and NHL in 2012 and 2014.



Team Analysis:

Just as interesting are the numbers for different teams across sports. Not surprisingly, the Miami Heat was the most predictable team in the country over the past six years – buoyed by four years of their LeBron-powered “Big Three.” But the top of the list is not just dominated by consistently good teams – bottom-dwellers like the Philadelphia 76ers, the Edmonton Oilers, and the Houston Astros (bad until 2015) also lead in predictability. Perennially unpredictable teams like the Minnesota Vikings and Boston Red Sox dominate the bottom of the list, as well:


To conclude, what can this data tell us about predictability in American sports as a whole? For a large majority of teams across the big four U.S. sports, not a ton – moving four spots up or down in rankings can be the difference between making the playoffs and missing out. And assuming the randomness in professional sports doesn’t change anytime soon, it is probably safe to say that expert accuracy will continue along this trend for years to come.

[1] I compared the absolute value of first week–last week differences, with n=180 for every league except the NFL, which had n=192 (since the NFL has 32 teams).

[2] http://www.basketball-reference.com/leagues/NBA_stats.html

[3] https://www.teamrankings.com/mlb/stat/at-bats-per-game


Buffalo’s Big 3

By Dana Fesjian

After one week, the Bills are 0-1, but not a hopeless 0-1. Fortunately, this year unlike other years (or so they say) there are a few players that are going to bring the Bills from bad to better. The Bills’ defense has always been the stronger half of the team, and that was clear in Week One. However, there is room to improve on offense and this year’s offensive line has tremendous room for growth due to the talent that exists already. There are specifically three players whose performances matter the most, whom I like to call the “Big 3.”

The chemistry and fluidity of how Tyrod Taylor, Sammy Watkins, and LeSean McCoy play together will make or break the Bills season this year. In Week One, these three were still struggling to find their rhythm, something they’ve been trying to find all through training camp. With more practice and more games, these three will inevitably improve.

Tyrod Taylor had a pretty good game on Sunday showcasing his athleticism and agility at the QB position. Although most of his plays didn’t have successful results, Taylor has the speed and awareness on the ball to create opportunities for the Bills to have more successful plays in future games. After the saga that is finding a (good/decent/non-injured) quarterback for the Bills, Taylor is the best starter so far since this saga began with Trent Edwards and Ryan Fitzpatrick. So maybe the Bills finally have a chance.

Sammy Watkins and LeSean McCoy both work really well with Tyrod Taylor when they are playing in sync. Sammy has always been a strong WR and if he has another strong year, combined with McCoy getting more yards each game, Taylor then has two strong players he can hand off the ball to to make successful plays. McCoy has recently started to practice his skills with an Oculus Rift, so I hope he can have his VR skills become reality skills.

I may say this every year, but the Bills really do have a chance to make it to the playoffs this year. Their defense is solid and has always been their stronger half of the team, but if the Big 3 can pull it together and have three great seasons at the same time, the Bills will be back in business.

Form in soccer: not always a winning formula

By Brandon Tan

One of the most discussed statistics in soccer leading up to a match is “league form”: the results of the team’s last six games. We see this statistic referenced again and again by commentators and pundits in their match previews and analyses. The phenomenon is all over the websites of sports news outlets, such as here in the Guardian.


However, is form a statistic that we should care about? Does being “in-form” really predict match outcomes?

To answer this question, I test whether there is a significant correlation between the match outcome and league form. I compiled the fixture results from the English Premier League seasons 2010-11 to 2015-16 for each club and ran a simple linear regression with points earned (Win- 3 points, Draw- 1 point, Loss- 0 points) as the response variable and form (the average points earned over the last six matches) as the explanatory variable controlling for home advantage and the end-of-season rank of the opposing team (see Figure 1).


Figure 1: The (lack of) relationship between form and points in English Premier League soccer

What I found was that there is no statistically significant correlation (at 5% significance) between points earned and form for any club. For instance, consider the results below from running the regression on Manchester United’s fixtures (see Figure 2). Home advantage and rank are clearly significant with p-values close to zero, while form isn’t even close with a p-value of 0.837, way above the 5% significance necessary to suggest a legitimate prediction model.


Figure 2: Regression model summary in which factors form, rank, and home-field advantage predict points in English Premier League soccer

Someone might argue that 6-game form is considering too many games, so I tried running the regression on form defined as the average points earned from the last 3 games instead. Again, I found no statistically significant correlations, with the p-value from running the regression on Manchester United fixtures at 0.494.

This analysis suggests that as soccer fans we really need to stop making such a big deal out of form, because it really doesn’t tell us anything at all.


Team p-value from regression (form = average points earned from last 6 games)
Man United 0.837
Liverpool 0.094
Chelsea 0.103
Tottenham 0.945
Arsenal 0.476
Man City 0.903



Dear Rob Manfred, The Millennials Are Leaving

By Max Kaplan, “The voice of the millennial sports fan”

We millennials are losing interest and it’s not our fault.

We can’t sit through another 4-hour MLB game with 11 pitching changes and 15 walks.

We groan every time a batter steps out of the box to re-adjust his batting gloves for the third time since the last pitch. Or when the pitcher starts pacing around the mound, fondling the rosin bag.

We think “get on with it” when the manager takes a full minute to decide whether to challenge a play and then challenges it – and the fans are gifted another 3-minute stoppage.

It’s not the 10-9 slugfest that’s the problem – it’s the 3-2 game that takes 3.5 hours where nothing happens.

In a game earlier this month, “Make Baseball Fun Again” Bryce Harper faced 27 pitches and didn’t swing at a single one. Great…

The baseball establishment mocks and shames the millennials for not watching the game the “right way.” They patronize our short attention spans and our “addiction” to social media. They say we don’t “respect” the game’s tradition.

I played baseball ‘till high school, have attended over 200 MLB games across 23 different stadiums in my life.

Rob, you need me and my friends – maybe not this year, but we are your future revenue stream – and I’m telling you, it ain’t looking good.

My observed reality: college students would rather watch the English Premier League (or literally any other sport) than an unwatchable baseball game on TV.

We think baseball is getting more boring and guess what? We’re right.

Baseball Boredom Index (BBI)

Everyone knows that MLB games are getting longer and longer. But there is also way less stuff happening.

I created a new statistic, called the “Baseball Boredom Index.” Or BBI for short. It is extremely easy to understand. The BBI is how many minutes you have to wait, on average, until something happens in a baseball game.

Let’s say an “action event” is a ball in play, or a stolen base attempt. This is a low bar for excitement. It includes sacrifice bunts, dribblers to 1B, and pop-outs to SS.

How long do you have to wait between these action events? Over three minutes! That’s a full commercial break between every single moment of ‘action.’

And it has trended up ever since the dawn of the game. The last three seasons have been the slowest in MLB history. As teams incorporate sabermetrics, we are seeing record-level strikeout totals, leaving fewer balls in play and more pitches per game.



Mr. Manfred, I leave you with a bold challenge. The gauntlet has been thrown. Bring us back to 2.5 BBI. 1985 is not that long ago.

The pace of play changes in 2015 led to slightly shorter games, and a lower Baseball Boredom Index. The pitch clock experiment in the Minor Leagues proves we can cut another 10-15 minutes from time of game. It’s a start, but not enough to keep our attention. Please hurry!

Rob, the writing is on the wall. You will lose the attention of the millennials (and everyone else) unless more progress is made. In fact, I just got three text messages, a snap, six tweets, four fb notifications since you started reading this so this article is now over. Bye.

Max Kaplan, “The voice of the millennial Sports Fan”, is a graduating senior at Princeton University Engineering School majoring in Operations Research and Financial Engineering. Max’s “Curse of the Home Run Derby” article hit the front page of Yahoo.com in 2011. He has appeared on NFL.com and NFL Network. His favorite sport used to be baseball.

NFL Divisional Realignment for Earth Day

By Max Kaplan


[Late edit] I was featured in an on-air interview to defend this article on Earth Day.

Earth Day is coming up on April 22, and even the NFL can do its part to reduce its carbon footprint.

I mean, just look at the divisions. Why must the Patriots travel all the way down to Miami every year when there are over twenty teams closer? Talk about waste…

The Eagles, Giants, and Redskins are all cozy and close, but who decided to throw the Cowboys into the East?

Let’s look at the facts. Dallas isn’t in the east. Indianapolis isn’t in the south. This is not how Mother Nature intended. In the name of conservation, preservation, and environmentalism, I’ve come up with a solution!

Let’s realign the divisions. Not willy-nilly but with an eye towards protecting our environment. There’s no need for the Chiefs’ 1,500-mile annual commute to Oakland. Kansas City certainly isn’t in the west of the United States. This isn’t the age of American pioneers. We can do better.

By my calculation, the NFL could save over 165,000 gallons in jet fuel each season by realigning the divisions.

The current divisions are a legacy of the NFL-AFL merger of 1970 and while we have seen the NFL climate change over the last half-century, the warning signs have been evident and growing stronger. We cannot afford to let this problem get any worse. It is time to decommission the old and open the new clean divisions. Sustainability is all about leaving a better future for the next generation. We must act now!

Below are the geographically optimal divisions – in order to minimize overall divisional travel.

  • Southwest Division – ARI, DAL, DEN, SD
  • Pacific Division – LA, OAK, SF, SEA
  • South Division – ATL, HOU, NO, TEN
  • Heartland Division – CHI, GB, KC, MIN
  • Southeast Division – CAR, JAX, MIA, TB
  • Northeast Division – BUF, NYG, NYJ, NE
  • Atlantic Division – BAL, PHI, PIT, WAS
  • Midwest Division – CIN, CLE, DET, IND


By realigning the divisions geographically, we put teams back in their ecological niche with local rivalries. The Raiders have only played the 49ers five times since they moved to Oakland. The Jets have played the Giants only twice in the last ten years – and they share a stadium.


  • Unfortunately, no recycling. None of the divisions stayed the same.
  • But we do have hybrids. The Pacific, Northeast, and Heartland Divisions all run on three teams from the old, clunky divisions.
  • Sometimes the planet is out of equilibrium despite our best efforts. Three of the Heartland Division teams had double-digit win totals in 2015.
  • The Super Bowl is a renewable resource. The Northeast Division (Patriots, Giants) and Atlantic Division (Ravens, Steelers) account for ten of the last sixteen Super Bowl titles.

Problem Formulation

For anyone interested, I layout the NFL minimal travel problem below.


Does Order Matter? An Analysis of Round 1 vs Round 2 Picks in the NBA

By Alex Vukasin

Are teams really making use of their first round picks? Have scouts been able to pinpoint the best talent with their first round picks, or is the draft round not a significant indicator of the talent and future of players in the league?


To answer this question, I analyzed the first and second round players drafted to the NBA from 2005 to 2014. All players who were drafted and played at least one game were included in the analysis, in order to identify only the players who have had NBA experience.

Performance Variables

The response variable throughout the analysis was the draft round, while the explanatory variables were games played, years played, minutes played in total, total rebounds, field goal percentage, three-point percentage, free throw percentage, minutes per game, points, points per game, rebounds per game, assists, and assists per game.

Advanced statistics used as explanatory variables in this study were “win shares”, (the number of wins contributed to a player), win shares per 48 minutes, “box plus-minus”, (the number of points out of the past 100 possessions a player contributes to his team above the average player), and “value over replacement player”, (the number of points a player scores on average given 100 team possessions over a replacement player compared to an average team over the 82-game schedule).

These variables created all share the common rule that a higher value resulted in a better career, while a lower value resulted in a less successful career. Below is a summary of all the variables.


Correlation Analysis: Positive among Performance Indicators, Negative with Round

The method used to test whether there was a causal relationship between “round” and all of these explanatory variables began by analyzing the correlation matrix of all the variables using STATA (Figures 1a and 1b). Although all the variables have a negative correlation with “round”, none are very high, as no value exceeds -0.5. There are also positive correlation coefficients between many of the explanatory variables, so it was not possible to include all the variables in one single regression without having multi-collinearity issues.

Regression Analysis: Performance Variables to Predict Round

Next, I ran some regressions to test which performance variables could help predict the player’s draft round, which would indeed suggest a relationship between the draft round and the player’s career performance.

In Figure 2a, field goal percent, minutes per game, rebounds per game and points per game all decrease as round increases, while minutes per game is the only statistically significant value (at 0.05 significance). This result seems to be notable as it supports the negative correlations between the explanatory variables and “round” as well as the fact that the correlation between “round” and minutes per game was the highest among the relationships between explanatory and response variables. Single regression tests were then conducted between each explanatory variable and response variable “round” in order to account for the high correlation between the explanatory variables (these regressions are not shown). All of these tests result in a negative coefficient for the explanatory variable that is significant at a level of 0.05.

Due to all of these factors having negative but small correlation coefficients with “round” and negative coefficients of significance for each single linear regression, it seems probable that the round in which a player is picked has a slight relationship with how their career will turn out. Although the correlations are not extremely high, the fact that there is a common negative relationship between all of these variables and “round” leads me to believe that there could be other variables indicative of success besides those listed which could be strongly correlated with “round”, that I could study further in another analysis.


Figure 1a: Performance variables negatively correlated with Round


Figure 1b: Performance variables positively correlated with each other


Figure 2a: Regression of Round with Field Goal Percent, Minutes per Game, Rebounds per Game and Points per Game


Editor’s Note: Edits have been made for clarity.

Ode to the Great Bambino

How the Best of the Best Performed Relative to Their Time Period

By Keith Gladstone

Only the best players of a given era are inducted into the National Baseball Hall of Fame in Cooperstown, from classic names like Babe Ruth and Lou Gehrig, to the most recent nominees of Mike Piazza and Ken Griffey Jr. Since the MLB era tainted by PEDs saw unthinkable, sky-high hitting totals, the question of who deserves a seat in the Hall of Fame is open for debate. The great differences in eras alone can convolute our interpretation of the game’s statistics, so in this article I will introduce a method of comparison.  


Indeed, I did an analysis to normalize the career HR totals of all Hall of Famers based on their historical era. Babe Ruth held the career home run record at 714 upon retiring in 1935. Hank Aaron shattered the record almost 40 years years later, but what does this actually mean? Was Hank Aaron better than Babe Ruth?

I calculated a new statistic to measure a player’s HR performance relative to the era in which they played. I call it the “Home Runs to Benchmark Ratio.”

HR to Benchmark Ratio = Annual Career HR Average / HR Era Benchmark

  • A ratio of 1 means the player was an average home run hitter in his own era.
  • A ratio of 2 means the player hit twice as many HR as the average player.

Pitching dominated the game in the “Dead Ball Era,” which ended upon the emergence of Babe Ruth and the Bronx Bombers in the 1920s. 714 HR in an era when the average player hit only 100 HR in a career underscores how impressive Ruth’s prowess was.

The Home Run to Benchmark Ratio rankings below confirm this, with Babe Ruth miles above the rest, followed by other classic Yankee heroes Lou Gehrig and Joe DiMaggio. Stunningly, Hank Aaron does not even crack the top ten. His ratio is 2.48, leaving him 26th overall. The HR performances of The Great Bambino, The Iron Horse, and The Yankee Clipper relative to their contemporaries shows just how incredible they must have been to watch.

MLB HOF All-time HR Rankings – Normalized by Era

MidYear Name Career HR HR to Benchmark Ratio
1 1924 Babe Ruth 714 7.13
2 1931 Lou Gehrig 493 4.76
3 1944 Joe DiMaggio 361 4.45
25 1964 Harmon Killebrew 573 2.49
26 1965 Hank Aaron 755 2.48
27 1950 Ted Williams 521 2.43
28 1935 Earl Averill 238 2.37
29 1960 Mickey Mantle 536 2.33
30 1975 Johnny Bench 389 2.31


Below is a graph of career HR per game against the average HR per game in that era . Players that appear above the line toward the top-left have higher ratios. Babe Ruth is the top left point. 

Screen Shot 2016-04-07 at 10.15.20 AM

Explore the interactive version of this graphPlayer names revealed on mouseover.


The following assumptions were made for data collection and analysis:

  • Player performance is symmetrical over time with a peak in the middle of the player’s career
  • League averages are decent estimates of the “benchmark” over which a player could measure
  • This analysis will consider the modern era (Hall of Famers whose careers occurred mostly after 1900) and those with career batting averages above 0.250
  • Since Hall of Famers had relatively long careers, their statistics are reliable estimates of their abilities

Using the “middle year” as a barometer for a player’s peak

Since the number of players in this dataset is so large, we need a simplified way to capture a player’s top-performing year. For this analysis, we can take the player’s career totals and divide by the number of years played to get a yearly average for the player, and measure this average against the benchmark for the year (selected as the middle year of the player’s career). While this analysis is therefore not perfectly rigorous, it stills serves as a useful method for comparing players from different eras. Put another way, the performance benchmark in 1995 should be similar enough to 1997, and the benchmarks in the 1990s are different enough from those in the 1920s where a benchmark a few years off wouldn’t be a significant issue.

Data Sources