There is No Place Like Home

By Jeffrey Gleason

Nine weeks into the NFL season, no teams remain unbeaten. This could’ve actually been said after eight weeks, after seven weeks, and after six weeks as well. Week 5 was the last time an unbeaten team remained, when both the Cardinals and Bengals were sitting at 3-0.

However, after these same nine weeks, five teams remain unbeaten at home. The Patriots, Broncos, Eagles, Packers, and Cardinals have yet to lose on their own turf.

Home field advantage is a phenomenon that gets a lot of traction in sports. Experts often use it to justify their predictions and betting lines usually reflect the perceived advantage of the home side. However, people often generalize home field advantage with a “one size fits all” approach, acknowledging its presence, but assuming it displays a constant impact across different situations.

With five unbeaten NFL home teams and the recent impetus of a road team finally winning Game 7 of the World Series (the Giants topped the Royals on October 29th to capture their third championship in five years), I was interested in how home field advantage was quantitatively different in different situations. How does it vary across sports? Do both good teams and bad teams experience the same advantage? Is it magnified in the postseason? What about differences in earlier eras? These are the questions I set out to resolve.

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Age in the NBA: Do older teams “find ways to win games”?

By: Patrick Harrel

Tune in to any NBA team’s local broadcast, and you will be sure to hear a litany of clichés from the commentators. Most are quick to praise older players, noting on occasion that “veteran teams just know how to win games.” The San Antonio Spurs, for example, are lauded for their ability to defy expectations, winning another NBA title last year despite Tim Duncan and Manu Ginobili closing in on 40 and Tony Parker getting well into his 30’s. Like most musings from broadcasters, these assertions are driven by little more than perception—completely unfounded points made to maintain conversation in a long season.

But could there be some merit to these thoughts? There is no doubt that NBA teams are looking for any edge they can get, and do veteran players give them an advantage? Do older teams in the NBA truly “find ways to win games” like so many claim? That’s what we aimed to find out in this research.

To look at this issue, we consider an expected wins model first constructed by Bill James for baseball and later adapted by Daryl Morey for use in basketball. James dubbed his formula for expected wins the “Pythagorean expectation” because of its similarity to the Pythagorean theorem, and it relies on the well-established principle that point differential is a better estimator of team performance than raw Win-Loss data. James’ formula for the Pythagorean expectation of winning percentage is as follows:

eq1

The adapted NBA formula which we have used is the following:

eq2

Using this formula, we built a database with each team season for the last 20 years (excluding lockout years, which had odd statistical trends) with their Pythagorean expectation of wins. Using that figure, we compared the actual wins for every team to their expectation, and generated a residual figure for each individual team season. A positive residual means that a team won more games than their point differential would forecast, and a negative residual means the opposite.

The other major metric used in this section of the research is minutes-weighted age. Averaging all the ages of players on the roster does not give an accurate representation of a team’s effective age as it fails to distinguish the impact of a player like Tim Duncan, who played over 2000 minutes for the Spurs in 2013-14 at the age of 37, versus Steve Nash, who played all of 313 minutes in that same season. However, by weighting the average by the amount of minutes a player has played, we get a much stronger metric for the effective age of an NBA team. We then normalized the weighted age values to zero using the league average for each season to account for changing ages in any given year.

With these two metrics in mind, we compared the residual values of expected versus actual wins to a team’s age vs. the league average, using a linear regression, and came up with the following results:

eq3

With the regression model above, we found that there was no significant relationship between a team’s minutes weighted age and their residual wins. Because the residual wins value was centered on 0, there is no intercept term, and the only thing that remains in the regression is the slope value times the explanatory variable, age. That slope value was essentially zero, with no statistical significance whatsoever.

graph1

If you are interested, the data was as follows:

eq4

As you can see, the data yielded no statistically significant results with respect to a relationship between older teams outperforming or underperforming their expected wins. In fact, looking at publicly available data for the last 20 years, there were no apparent trends for teams outperforming their expected wins. Faster paced teams, teams that shot a lot of threes, won a lot of games, or got to the free throw line a lot all did not see a statistically significant improvement in outpacing their Pythagorean expectation.

Perhaps this is not a groundbreaking result, but it highlights the effectiveness of Pythagorean expectation that not only is it an unbiased estimator of a team’s winning percentage regardless of age, it is unbiased regardless of virtually any factor you can check. Teams that scored a lot, very little, or in the middle all tended to match their Pythagorean expectation on average. This unbiased nature of the Pythagorean estimator has its roots in the derivation of it. Research has shown point differential to be a better indicator of a team’s performance than winning percentage, and this further investigation supports that research.

This is just one way of evaluating whether veteran teams get an edge, but at least in this sector of our research, it is clear that older teams do not have any advantage. Older teams might play slower, shoot more threes, or dunk less, but they will match their Pythagorean expectation over time.

KO is OK

By Dana Fesjian

Four week update on the Kyle Orton experiment! When Doug Marrone replaced EJ Manuel at quarterback, I wasn’t sure what to expect from the offense. I went into these past four games with a little bit of hope but mostly just doubt. This ambivalence was best captured by Orton’s career record of an even 35-35. So it seemed to me that the best-case scenario was mediocrity and the worst case was, well…

His first game against the Lions was full of emotions. I was in lab (yes, lab on a Sunday afternoon during football season) and I was getting updates from ScoreCenter that the Bills were down 14-3 at halftime. Why didn’t they just leave EJ in? But after KO (does anyone call him this? If not I’m starting it) led the Bills to his 8th career game winning drive and Dan Carpenter won it with a 58-yard field goal, I was ecstatic and praising Doug Marrone.

KO2

However, I didn’t want to speak too soon and automatically go into an “I love KO” rant without seeing how well the 31-year old played for a few more games because the long term is what matters for the Bills. And I was right to not immediately praise KO because the next week they had a disappointing sixth-straight loss to the Patriots.

The last two games against the Vikings and the Jets were fantastic. Unfortunately we lost our two best running backs, CJ Spiller and Fred Jackson, in the first half of the game versus the Vikings. I was crushed when I found out both would miss significant time. But not all was bad. After KO’s 2nd game winning drive of the season against the Vikings, only Tony Romo and Nick Foles had more game winning drives on the season, and that’s considering KO didn’t even play until Week 5.

NFL: Buffalo Bills at Chicago Bears

With the thin running game, I assumed that this meant Sammy was going to get many more opportunities to fill the void. And that’s basically what happened on Sunday’s blowout game versus the Jets, which I was lucky enough to attend! That was such a great game. Even without CJ and Fred, the Bills scored 43 points thanks to an all around effort from the stonewall defense forcing 6 turnovers and from KO’s chemistry with Sammy.

In comparing KO to EJ, we see that in four games EJ has 838 yards and KO has 1,128 yards. KO also has an NFL-best 73.0% Comp Pct. in 3rd down passing, whereas EJ has the NFL’s 2nd-worst (50.0%). If the Bills keep KO at quarterback and don’t decide to bring EJ back, KO can approach his career-best 2009 season stats…in 4 fewer games.

All I can say is it’s amazing what happens when you have a quarterback you can count on. Let’s see how KO continues.

Catching Kareem

By Neil Rangwani

With opening night for the NBA regular season one week away, one storyline that isn’t getting much attention is Kobe Bryant’s pursuit of greatness. Already one of the greatest players of all time, Kobe enters this season with five championships, two Finals MVP Awards, a regular season MVP Award, fifteen All-NBA selections, two scoring championships, and innumerable comparisons to the G.O.A.T. However, one often overlooked career milestone is total points, in which Kobe is fourth, all-time, with 31,700 career points. The all-time leader, of course, is Kareem Abdul-Jabbar, with 38,387 points. With no top-tier teammates this year and in the foreseeable future to share the ball with, Kobe is uniquely positioned to make a run at the points record.

However, this past season certainly did not go according to plan for Kobe, who played in only 6 games as he recovered from injury. Now 35 years old, with 18 NBA seasons under his belt, and still recovering from a series of injuries, popular opinion is that Kobe’s chances of catching Kareem are slim. After reading this article, I decided to analyze Kobe’s chances of catching Kareem.

For reference, here’s a table of some of the top scorers in NBA history:

1

Although Kobe is pretty far from Kareem, he’s closing in on Michael Jordan, so I added Jordan’s 32,392 points as a benchmark in the analysis. I’ve also included some of the other leading scorers in the NBA: LeBron James, Carmelo Anthony, and Kevin Durant, to see if they have any chance of reaching the upper echelon of NBA scorers.

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The MLB Division Series Should Be 1,101 Games Long

By Max Kaplan

The baseball playoff system is messed up. It’s a statistician’s worst nightmare. As both an Angels diehard and a statistician, I have descended into despondency.

After six months and 162 games of baseball, a 5-game coin flip decides the fate of the eight playoff teams. The Los Angeles Angels, considered by many to be the best team in baseball and considered by most to be a better team than the Kansas City Royals, were knocked out in only three games after leading the league with 98 regular season wins. That’s three games – the same length as the common regular season sweep.

I’m going to try to “fix” the randomness and unfairness of a short playoff series. And by doing so, I hope to resurrect the Angels 2014 World Series hopes.

How many games would we need in a playoff series to be fairly confident that the better team moves on? According to my calculations below, that number is 1,101.

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Betcha Can’t Choose Just One

By Dana Fesjian

I started writing this article after the Bills went 1-3 in the preseason. But after they won their first two regular season games I thought Buffalo’s quarterback quandary had been resolved. Unfortunately I was wrong.

Last November I also wrote an article about the uncertain future of Bills’ backup quarterbacks. Now that very same uncertainty has enveloped EJ Manuel. You’d think after a year the Bills would have solved their problem of having a solid quarterback and decent back up quarterbacks.

Unfortunately they haven’t moved on from the problem at hand. The Bills still don’t have the offense they need in order to win enough games to be in the running for the extremely weak AFC East, where 7 wins might be enough to make the playoffs. At least the Bills can look to make history in becoming the first NFL team to finish with the same record in 4 straight seasons.

After EJ Manuel’s multiple knee injuries last season, the Bills were left with Jeff Tuel and Thad Lewis at quarterback. Fast-forward a full year and the question of “Who’s your quarterback?” is still valid. Although EJ was healthy during the preseason, one disappointing moment was August 23rd’s game against Tampa Bay. EJ should have stood out from his backups Thad Lewis and Jeff Tuel. Unfortunately that wasn’t the case. He had 1 interception, 1 fumble, and got sacked 4 times. This didn’t bode well for Manuel’s starting job heading into this season.

thadlewis  jefftuel  jordanpalmer  ejmanuel  kyleorton

Then the regular season started and hope skyrocketed (at least for me). EJ led the Bills to an undefeated 2-0 start. Being able to say the Bills were undefeated was a literal dream come true. However, it didn’t last long enough. Watching EJ Manuel and the offense try to score points the past two weeks has been brutal. As Ron Jaworski of ESPN said, EJ’s accuracy is just not at the level it should be to be the starter as evidenced by his 47.7% completion rate and 2 interceptions in last week’s game.

That leads us to the next decision made by Doug Marrone and Doug Whaley: to bench EJ and put in veteran Kyle Orton. I don’t know about you, but I’m having some major déjà vu! Let’s not forget how just over a month ago the Bills signed Jordan Palmer to replace Thad Lewis and then let him go. The Bills need to make a decision on whom they want at quarterback and stick with it!

They drafted EJ Manuel in the first round for a reason and although Kyle Orton has experience, I’m not sure I know how I feel about this decision yet. We will just have to wait until we see Orton start on Sunday. But one thing’s for sure, the question of “Who’s your quarterback?” is still the most relevant question within the Buffalo Bills organization.

Assessing NBA Scoring Champions Relative to League Average

A Historical Study

by Aqeel Phillips

http://i2.cdn.turner.com/nba/nba/dam/assets/130415230043-041513-kevin-durant-vs-kings.main-video-player.jpg

With just a few weeks left in the regular season, some of us are left without much to root for anymore. HEAT fans remain optimistic in the surprisingly competitive battle for the first seed, and Suns, Mavs, and Grizzlies fans are biting their nails short in hopes that their teams can grab a playoff spot. However, a good percentage of us basketball fans now realize we have little to root for anymore (or if you’re a Sixers fan like me, you realized in about August), and are just waiting to see the final playoff seedings and end-of-season awards before the playoffs get underway. Besides the MVP, one of the most notable awards each year is the Scoring Title. Last season, we were treated with a thrilling ending as the battle for the Scoring Title came down to the wire between Kevin Durant and Carmelo Anthony.

This season, Kevin Durant aka the Slim Reaper has made things less interesting, currently scoring 32.2 points per game (PPG) over 2nd place Melo’s 28.0 PPG. Durant is the only player to average 30 points since he did in the 2009-10 season. The NBA has had a notable drop in scoring lately, a trend first starting when hand checking was instituted in the early 2000’s and extended as many teams have embraced sharing the ball throughout the team in order to better find open looks, namely threes, rather than relying on singular scorers. Durant’s current season widens eyes at first glance — averaging 4 points more than his next closest competitor will do that. But I find that PPG by itself doesn’t tell the full picture. Elgin Baylor averaged over 38 points in 1961-62, but that was over 50 years ago in a completely different league. So who had the most impressive season: 2014 Durant? 1962 Baylor? 2006 Kobe? We’ve witnessed plenty of monstrous seasons, and this study examines them in relation to the rest of the league at the time to contextualize the simple PPG marks.

League Scoring Average (Season)

To get a better comparison between scoring performances, we can divide a player’s PPG by their minutes per game (MPG) marks to see how they’re scoring with regard to the opportunities they’re being given. This is especially useful in calculating a league average scoring mark. We don’t want end bench players that average 0.6 PPG to drag down the entire league scoring average, most importantly because they outnumber the talented, 20+ PPG scorers in the league. Dividing PPG by MPG for each player across the league levels the playing field, and also accounts for the possibility that in any given season the league as a whole significantly played more or less bench/low-scoring players for whatever reason (for example, in the ‘60s there were much fewer players in the league and more minutes and points to go around).

For reference, here are the Points Per Minute values for the current league leaders in scoring:

League Leaders

(For those wondering about a full list of the league leaders in PPM, see the appendix)

In terms of points scored per time played, you can see that Durant is not just scoring at an average rate while playing more minutes, he is scoring more efficiently than the players below him on the list (shown by a higher PPM value than his competitors). It’s interesting to note that Melo averages more minutes than Durant, but Durant makes much better use of his time, scoring-wise, than Melo (Durant is also more efficient with his shot attempts – averaging 20.7 field goal attempts per game to Melo’s 21.5). This gives more evidence to Durant’s case for “best scorer in the league” – not only does he have the sheer output, but he also has the efficiency.

Next, we’ll calculate the average PPM value for the entire league, and compare each individual player to that average, to see how much better they score than the average replacement.

Unlike other studies I’ve done, I haven’t artificially subtracted out all of the players that aren’t contributing much (<20 MPG, <30 GP in previous articles), as using PPM should even out all contributions.

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