NBA Comeback Clutchness: Real or Just Noise? Sandy Huang and Toa Lohe

Similar documents
NBA Comeback Clutchness. Sandy Huang Toa Lohe

BOSTON Shamrocks. Totals 67,500,000 61,550,000 46,760,000 31,410,000 28,530,000 16,500,000

NBA IN REVIEW

Card Set Number Player Team Seq.

Cavaliers James Jones Jerseys Prizms Blue Mojo 7 Cavaliers n/a James Jones Jerseys Prizms Blue Mojo Prime 7 Cavaliers 10 Joe Harris Jerseys Prizms Blu

Playoff Contenders Basketball Group Break Checklist Yellow Hightlight = Autograph; (Premium Edition + Retail not included) 76ERS

Guard USA n/a Guard,Forward USA Center USA n/a

C Howard, Dwight Cha F Green, Draymond GS G Lillard, Damian Por

Panini Revolution Basketball Checklist (No Parallels Listed) - Highlighted in Yellow - Autographs 76ERS

Panini Gala Basketball Team Checklist

2011 Panini Preferred Basketball (Hobby)

Past & Present Basketball Group Break Hits Checklist

Panini Ascension Basketball Team Checklist Green = Autograph 76ERS. Player Set Card # Team Print Run

266 Players with Cards 7 of those players have 6 cards or under, 11 Players only have Diamond Cards (Nash and Dennis Johnson only have 6) Relic Total

Analyzing NBA Champions and the Player Efficiency Rating

NBA Sticker Collection Final Checklist

Portland Trail Blazers Team salaries

2012NBAAllStarScoring Drills

Court Kings Basketball Team Checklist 76ERS

Lillard has a good matchup in a competitive, high-scoring game at MIN - who ranks 21st vs PGs.

KINGS FRANCHISE PLAYOFF HISTORY

Math SL Internal Assessment What is the relationship between free throw shooting percentage and 3 point shooting percentages?

by John Smallwood SCHOLASTIC INC.

Playoff Contenders Basketball Checklist

Impeccable Basketball Team Checklist

What Should Your Salary Be? Using Statistical Graphs to Compare Data - Grade 10

SACRAMENTO KINGS 2004 PLAYOFF GUIDE 133

S E A S O N

Panini Hoops Team Checklist

Harvard Talk Wayne Winston Kelley School of Business

Regular Season Coverage to Culminate with 22 Games in 20 Days, March 19- April 7

Panini Status Basketball HITS Checklist 76ERS Player Set Card # Team Print Run

McDONALD S ALL AMERICAN GAMES

CONTENTS. 142 Season Review 144 Regular Season Statistics 145 Breakdown/ Individual Highs. 146 Team Highs & Lows

76ERS Panini Grand Reserve Basketball Team Checklist Green = Auto or Relic

Panini Absolute Basketball Checklist Orange = Insert/Base

Are the 2016 Golden State Warriors the Greatest NBA Team of all Time?

Got It! Need It Edition Item # UPC Code Description Series League Team Name Last Name Est Release Status Generation Active P-NBAGEN00-G1LE

GAME NOTES PROBABLE STARTERS POS. PLAYERS STATS AND NOTES. AVERAGES: 5.1 Pts 4.1 Rebs 0.3 Asts. #33 Jonas Jerebko Kinna, Sweden

Elena Delle Donne ( 08), Kyrie Irving ( 10), Ben Simmons ( 15) FACT SHEET McDONALD S ALL AMERICAN GAMES

Men s Basketball BIG 12 RECORD BOOK -- MEN S BASKETBALL. ANNUAL STANDINGS (# - Indicates NCAA Tournament participant; $ - Final Four; ^ - NIT)

SEASON REVIEW Roster

2014/15 UD Lettermen

On Estimating the Ability of NBA Players

INDIVIDUAL CAREER RECORDS (as of 10/25/18)

ADMIN PLAYERS FACILITIES MEDIA COMMUNITY SEASON TRADITION PLAYOFFS NBA

SET INSERT/SUBSET # PLAYER 2012 Panini Base (12-13) Basketball Panini Rookie Signatures 26 Norris Cole 2013 Panini Gold Standard (13-14) Basketball

2005 NBA Mock Draft # Wednesday, May 25 th, 2005 BY MATTHEW HATFIELD

Ken Griffey Jr. Cal Ripken Frank Thomas Ken Griffey Jr. Cal Ripken Panini Immaculate Collection Baseball Immaculate Triple Signatures 1

SEASON REVIEW

INVESTIGATION OF THE EFFECTS OF 4-POINT SHOOTING RULES APPLIED IN BIG 3 BASKETBALL ORGANIZATION ON COMPETITION RESULTS IN NBA PLAY-OFFS

SET SUBSET/INSERT # PLAYER 2015 Panini Immaculate Collection (15-16) Basketball Shadowbox Signatures 22 Mason Plumlee 2015 Panini National Treasures

Blake Griffin's tomahawk dunk sets off a list of NBA's all-time most exciting players

SILENT AUCTION. 6 pm 10 pm. (Items as of )*

PLAYING GENERAL MANAGER: A SPORT FINANCE EXPERIENCE. Mike Mudrick Sport Management June 7, 2016

SACRAMENTO KINGS 2004 PLAYOFF GUIDE 63

Harvey Pollack s STATISTICAL YEARBOOK. sixers.com

Individual Career Records. End of

DEKALB DUGOUT CLUB 2017 FIRST TEAM ALL-COUNTY BASEBALL

GOODWIN SPORTS MANAGEMENT

GOODWIN SPORTS MANAGEMENT

2015 Donruss Base Brand Donruss (15-16) Basketball Elite Dominator Signatures 23 Kyrie Irving

Most Total Points, Career Most Total Points, Season Most Rebounds, Career

NEW MEXICO - STOPS DRILL

SET SUBSET/INSERT PLAYER

West Montgomery Team Records (Individual)

SEASON REVIEW

MISCELLANEOUS RECORDS

Select Basketball Group Break Checklist Green = Auto, Auto Relic, or Relic 76ERS

Draft Board Decoder. FantasyDrafthelp.com/ hoops.html

Totally Certified Basketball Team Checklist Green = HITS - Auto or Relic 76ERS

20 Duke players have been selected in the first round of the NBA Draft in the Coach K era, including 12 in the last nine years

3/17/2013 Los Angeles Clippers vs. New York Knicks

elton INJURIES Streaks Overall: Lost 1 Home: Won 1 Road: Lost 2 Tim Thomas (personal reasons) is NOT WITH TEAM

2013 USA Basketball Men s National Team Mini-Camp. July 22-25, 2013 Las Vegas, Nevada

Panini Court Kings HITS Checklist (Condensed)

LAFAYETTE BOYS SOCCER HISTORY

Injury Report: 12/29/18 05:30 PM

MSXC Round #3 SHANE O BANION MAKES IT TWO IN A ROW!

Extreme Shooters in the NBA

Year-by-Year. Hornets Year-by-Year

OKLAHOMA CITY THUNDER at MIAMI HEAT

elton INJURIES Streaks Overall: Won 1 Home: Won 1 Road: Won 1 Tim Thomas (personal reasons) is NOT WITH TEAM

Iowa Wesleyan University Men s Basketball Records

2015 Panini Immaculate Collection (15-16) Basketball

CAVS HIGHEST POINTS PER GAME ALL-TIME (SINGLE SEASON)

MGT 233 Homework #1, Fall 2017

TORONTO RAPTORS NBA DRAFT INFORMATION

FLORENCE SPEEDWAY Union, Kentucky

SET INSERT/SUBSET # PLAYER 2011 Panini Dominion (11-12) Hockey Rookie Ensigns 56 Yann Sauve 2011 Panini Crown Royale Hockey Rookie Royalty Signatures

Copyright BallersInstitute.com. All rights reserved.

Wilt Chamberlain s 100 point game - March 2, 1962

Avoca Football Club Season

NBA TVs Comprehensive Preseason Coverage to Feature 30 Live Game Telecasts, NBA Real Training Camp and Media Day Reports From Around the League

The Impact of Star Power and Team Quality on NBA Attendance THESIS

Scoring Summary (Final) Arkansas State vs Texas A&M (Aug 30, 2008 at College Station, TX)

Evaluating NBA Shooting Ability using Shot Location

Wildcats Season Top Ten

Forward Dirk Nowitzki PPG RPG APG SPG BPG TPG FG% 3PT% FT% #41 7-0/

FIRST ROUND VS. DETROIT

Transcription:

1 NBA Comeback Clutchness: Real or Just Noise? Sandy Huang and Toa Lohe Introduction In his last NBA game, Kobe Bryant famously scored 60 points against the Utah Jazz to lead the Los Angeles Lakers to a 101-96 victory. The game was entertaining not just because Kobe scored lots of points but because of how he scored those points. Let us set the scene. With about three minutes remaining in the 4 th quarter, the Lakers were down 10 points, and it seemed that Kobe would likely end his career with a loss despite having already scored 45 points. He, however, surprised us all by proceeding to score 15 straight points for the Lakers, a brilliant capstone performance to end a legendary 20-year career in the NBA. 1 At the end of the night, Kobe reminded everyone of why many of us watch sports in the first place: to feel the emotional suspense of seeing people struggle against and sometimes even overcome seemingly improbable odds. 2 This ability to overcome seemingly improbable odds is what we often nebulously call clutchness. Inspired by Kobe s last game, our final project quantified the clutchness of NBA players. In particular, we were interested in situations in which a player s team was either behind by 5 points (or less) or tied (but not ahead) in the last 5 minutes of the 4 th quarter (or overtime). Let us refer to this particular subset of clutchness as comeback clutchness. In contrast to comeback clutchness is escape clutchness when a player s team is either ahead by 5 points (or less) or tied (but not ahead) in the last 5 minutes of the 4 th quarter (or overtime). We made this particular distinction between comeback clutchness and escape clutchness because of both our assumption that there is a psychological difference between these two scenarios that significantly impacts how players perform and the fact the NBA does not provide data on situations where teams are only behind/ahead and not tied. Finally, one of the main aims of our project is to find out whether special comeback clutchness performances (e.g. Kobe s last game) can be repeated or if their manifestations are just noise (i.e. random). Background Previous work on NBA clutchness has been done by 82games 3 and Liberty Ballers 4 (a SB Nation blog for the Philadelphia 76ers). The first study done by 82games focused on the most clutch players in terms of field goals attempted, points scored, effective field goal percentage, foul drawing ability, and free throw shooting. The second study done by 82games focused on plusminus, win-loss record, rebounding, passing, and shot creation (based on unassisted field goals made per 48 minutes). The third study done by 82games focused on the difference between nonclutch and clutch moments, PER (Player Efficiency Rating), and opposing player PER. Lastly, the study done by Liberty Ballers focused on clutch shooting. None of these four studies, however, focused on comeback clutchness. 1 For the sake of Kobe s mythology, let s ignore the officiating shenanigans at the end (e.g. the Laker s Julius Randle setting hilariously illegal screens on the Jazz s Gordon Hayward). 2 Seth Partnow of VICE Sports more eloquently defined it as [t]hat anticipation, the moment just before the roller coaster tips over the crest of the big drop [...] the thrill that keeps us coming back. https://sports.vice.com/en_au/article/kobe-bryant-majored-in-drama-not-math 3 http://www.82games.com/clutchplayers.htm http://www.82games.com/clutchplay2.htm http://www.82games.com/clutchplay3.htm 4 http://www.libertyballers.com/2012/2/29/2832299/lebron-james-kobe-bryant-dwyane-wade-clutch-nba-playoffs-4th-quarter

2 Methods By using Clutch Traditional Stats 5 and Clutch Advanced Stats 6 provided by the NBA, we formulated a comeback clutchness version of Justin Kubatko s Win Shares statistic (i.e. the estimated number of wins a player produces for his team). 7 Below are all the necessary conditions for a player s stats to be included in our analysis: 1) The statistic is accumulated in the last 5 minutes of the 4 th quarter (or overtime). 2) The player s team is either behind by 5 points (or less) or tied (but not ahead). 3) The player has played in at least a total of 50 minutes. In order to normalize for the total number of minutes played by each player, we also calculated comeback clutchness Win Shares Per 48. 8 To calculate Win Shares, Offensive Win Shares are added to Defensive Win Shares. Below are the details of calculating Offensive Win Shares and Defensive Win Shares: Player Points and Defensive Rating are already included in the player data provided by the NBA. 9 Additionally, Team Minutes 10 and Team Pace 11 are already included in the team data provided by the NBA. Below is a table detailing how to calculate the other statistics: Statistic Calculation Player Possessions Player Pace 12 48 Minutes Played Usage Rate 13 Team Defensive Possessions Opponent s Total Points 14 Team Defensive Rating 15 100 League Points Per Possession Total League Points Sum of Each Team s (Pace 48 Minutes Played) League Points Per Game Total League Points (Total Minutes Played 48) League Pace Sum of Each Team s (Pace 48 Minutes Played) (Total Minutes Played 48) 5 Comeback clutchness traditional player filter for analysis of 2015-2016 season: http://stats.nba.com/league/player/#!/clutch/?cf=min*ge*50&season=2015-16&seasontype=regular%20season&aheadbehind=behind%20or%20tied&permode=totals 6 Comeback clutchness advanced player filter for analysis of 2015-2016 season: http://stats.nba.com/league/player/#!/clutch/advanced/?season=2015-16&seasontype=regular%20season&aheadbehind=behind%20or%20tied&cf=gp*ge*10 7 http://www.basketball-reference.com/about/ws.html 8 Divide by the total number of minutes played and then multiplying by 48 9 See footnotes 5 and 6 10 Comeback clutchness traditional team filter for analysis of 2015-2016 season: http://stats.nba.com/league/team/#!/clutch/?season=2015-16&seasontype=regular%20season&permode=totals&aheadbehind=behind%20or%20tied 11 Comeback clutchness advanced team filter for analysis of 2015-2016 season: http://stats.nba.com/league/team/#!/clutch/advanced/?season=2015-16&seasontype=regular%20season&aheadbehind=behind%20or%20tied 12 See footnote 6 13 See footnote 6 14 Comeback clutchness opponent team filter for analysis of 2015-2016 season: http://stats.nba.com/league/team/#!/clutch/opponent/?season=2015-16&seasontype=regular%20season&aheadbehind=behind%20or%20tied&permode=totals 15 See footnote 11 and Wikipedia: https://en.wikipedia.org/wiki/defensive_rating

3 In addition to this first analysis of comeback clutchness, we also conducted subsequent analysis on the value of comeback clutchness, the difference between comeback clutchness and escape clutchness, the difference between comeback clutchness and regular performance, and the repeatability of comeback clutchness. The value of comeback clutchness was measured as the differential between comeback clutchness Win Shares Per 48 and regular season Win Shares Per 48. The difference between comeback clutchness and escape clutchness was measured by using F-tests and t-tests, and the same method was used for the difference between comeback clutchness and regular performance. Finally, the repeatability of comeback clutchness was measured as the year-to-year correlation. We did these analyses for every season since the 2001-2002 season and also looked at comeback clutchness plus-minus and PIE (Player Impact Estimate). 16 Results Comeback clutchness for the 2015-2016 season: Top 10 Comeback Clutchness (WS/48) Bottom 10 Comeback Clutchness (WS/48) 1) Andre Drummond (1.10) 1) Isaiah Canaan (-0.92) 2) Stephen Curry (1.06) 2) Brandon Knight (-0.59) 3) Draymond Green (1.06) 3) Al-Farouq Aminu (-0.45) 4) Klay Thompson (0.90) 4) Mason Plumlee (-0.41) 5) Dirk Nowitzki (0.87) 5) Trevor Booker (-0.33) 6) LeBron James (0.85) 6) Damian Lillard (-0.29) 7) Deron Williams (0.79) 7) Rajan Rondo (-0.28) 8) Chandler Parsons (0.78) 8) PJ Tucker (-0.27) 9) Jeff Green (0.70) 9) Khris Middleton (-0.23) 10) Danilo Gallinari (0.69) 10) Robert Covington (-0.22) Value of comeback clutchness for the 2015-2016 season: Top 10 Differential (WS/48) Bottom 10 Differential (WS/48) 1) Andre Drummond (0.97) 1) Isaiah Canaan (-0.95) 2) Draymond Green (0.87) 2) Brandon Knight (-0.64) 3) Klay Thompson (0.76) 3) Mason Plumlee (-0.55) 4) Stephen Curry (0.75) 4) Al-Farouq Aminu (-0.54) 5) Dirk Nowitzki (0.73) 5) Damian Lillard (-0.46) 6) Deron Williams (0.71) 6) Trevor Booker (-0.45) 7) Chandler Parsons (0.67) 7) Rajan Rondo (-0.36) 8) Jeff Green (0.64) 8) Russell Westbrook (-0.36) 9) LeBron James (0.61) 9) Khris Middleton (-0.33) 10) Jeremy Lin (0.60) 10) Serge Ibaka (-0.32) 16 PIE s explanation can be found here: http://stats.nba.com/help/glossary/

4 Comeback clutchness for the past 15 seasons: Top 5 Players by Comeback Clutchness Win Shares Per 48 2015-2016 Andre Drummond Stephen Curry Draymond Green Klay Thompson Dirk Nowitzki 2014-2015 Pau Gasol Joakim Noah Roy Hibbert Zach Randolph Jimmy Butler 2013-2014 Greivis Vasquez Mike Conley James Harden Dirk Nowitzki Damian Lillard 2012-2013 Chris Bosh Paul Pierce Jeff Green Ray Allen LeBron James 2011-2012 Andrew Bynum Joe Johnson Udonis Haslem Roy Hibbert Zaza Pachulia 2010-2011 Mo Williams Dirk Nowitzki Tyson Chandler Manu Ginobili Serge Ibaka 2009-2010 LeBron James Kobe Bryant Dirk Nowitzki Marc Gasol Chauncey Billups 2008-2009 Pau Gasol Dwight Howard Kobe Bryant Jason Terry Tony Parker 2007-2008 LeBron James Stephen Jackson Chris Paul Amar'e Stoudemire Jeff Green 2006-2007 Josh Howard Dirk Nowitzki Jason Terry Samuel Dalembert Jason Kapono 2005-2006 Keith Bogans Chauncey Billups Chris Kaman Rasheed Wallace Earl Boykins 2004-2005 Ben Gordon Chauncey Billups Tyson Chandler Kirk Hinrich Kenny Thomas 2003-2004 Kobe Bryant Shaquille O'Neal Reggie Miller Metta World Peace Gary Payton 2002-2003 Tony Battie Tony Delk Jason Terry Chauncey Billups Shareef Abdur-Rahim 2001-2002 Raef LaFrentz Ervin Johnson Dirk Nowitzki Ryan Bowen Antonio Davis Bottom 5 Players by Comeback Clutchness Win Shares Per 48 2015-2016 Isaiah Canaan Brandon Knight Al-Farouq Aminu Mason Plumlee Trevor Booker 2014-2015 Tim Hardaway Jr. Jeremy Lin Rudy Gay Jordan Hill Wayne Ellington 2013-2014 Trey Burke Gordon Hayward Ricky Rubio Ben McLemore Zaza Pachulia 2012-2013 Greivis Vasquez Andrea Bargnani Arron Afflalo Jared Dudley Evan Turner 2011-2012 Brandon Jennings Kris Humphries Tayshaun Prince Monta Ellis Brandon Knight 2010-2011 Kirk Hinrich Stephen Curry Dorell Wright Luke Ridnour Monta Ellis 2009-2010 George Hill Tyreke Evans Manu Ginobili Tayshaun Prince Mike Bibby 2008-2009 Jason Richardson Peja Stojakovic Steve Nash Andrea Bargnani Rasheed Wallace 2007-2008 Rashad McCants Tim Thomas Anthony Parker Carlos Delfino Chris Kaman 2006-2007 Dahntay Jones Jarvis Hayes Luther Head Adam Morrison DeShawn Stevenson 2005-2006 Luke Ridnour Donyell Marshall Steve Blake Jumaine Jones Rashard Lewis 2004-2005 Tim Thomas Jarvis Hayes Keith Bogans Tony Parker Carlos Boozer 2003-2004 Bobby Simmons Toni Kukoc Michael Finley Damon Jones Doug Christie 2002-2003 Lamar Odom Corey Maggette Andre Miller Elton Brand Jason Richardson 2001-2002 Bob Sura Bryon Russell Mark Jackson Larry Hughes Erick Dampier

5 Value of comeback clutchness for the past 15 seasons: Top 5 by Comeback Clutchness Win Shares Per 48 Differential 2015-2016 Andre Drummond Draymond Green Klay Thompson Stephen Curry Dirk Nowitzki 2014-2015 Joakim Noah Roy Hibbert Pau Gasol Zach Randolph Jimmy Butler 2013-2014 Greivis Vasquez Mike Conley Taj Gibson Paul Pierce Klay Thompson 2012-2013 Jeff Green Paul Pierce Chris Bosh Ray Allen Avery Bradley 2011-2012 Andrew Bynum Joe Johnson Udonis Haslem Roy Hibbert Zaza Pachulia 2010-2011 Mo Williams Dirk Nowitzki Tyson Chandler Manu Ginobili Jeff Green 2009-2010 Kobe Bryant LeBron James Dirk Nowitzki Marc Gasol Jared Jeffries 2008-2009 Jason Terry Pau Gasol Tony Parker Rashard Lewis Raja Bell 2007-2008 LeBron James Stephen Jackson Jeff Green Baron Davis Nick Collison 2006-2007 Josh Howard Dirk Nowitzki Jason Terry Samuel Dalembert Jason Kapono 2005-2006 Keith Bogans Chris Kaman Earl Boykins Rasheed Wallace Carmelo Anthony 2004-2005 Ben Gordon Tyson Chandler Chauncey Billups Kenny Thomas Kirk Hinrich 2003-2004 Kobe Bryant Shaquille O'Neal Metta World Peace Al Harrington Alvin Williams 2002-2003 Tony Battie Tony Delk Jason Terry Antoine Walker Glenn Robinson 2001-2002 Raef LaFrentz Ervin Johnson Ryan Bowen Antonio Davis Dirk Nowitzki Bottom 5 by Comeback Clutchness Win Shares Per 48 Differential 2015-2016 Isaiah Canaan Brandon Knight Mason Plumlee Al-Farouq Aminu Damian Lillard 2014-2015 Rudy Gay Jeremy Lin Andre Drummond Chris Paul Jordan Hill 2013-2014 Ricky Rubio Gordon Hayward Trey Burke Ramon Sessions Ben McLemore 2012-2013 Greivis Vasquez Ryan Anderson Jared Dudley Blake Griffin John Wall 2011-2012 Brandon Jennings Kris Humphries Tayshaun Prince Monta Ellis Greg Monroe 2010-2011 Kirk Hinrich Stephen Curry Dorell Wright Luke Ridnour Monta Ellis 2009-2010 George Hill Manu Ginobili Tyreke Evans Deron Williams Mike Bibby 2008-2009 Jason Richardson Steve Nash Chris Paul Peja Stojakovic Nate Robinson 2007-2008 Rashad McCants Anthony Parker Carlos Delfino Tim Thomas Chris Kaman 2006-2007 Dahntay Jones Amar'e Stoudemire Luther Head Jarvis Hayes DeShawn Stevenson 2005-2006 Luke Ridnour Donyell Marshall Steve Blake Rashard Lewis Jumaine Jones 2004-2005 Tim Thomas Tony Parker Kobe Bryant Carlos Boozer Jarvis Hayes 2003-2004 Bobby Simmons Toni Kukoc Michael Finley Damon Jones Jason Kidd 2002-2003 Lamar Odom Corey Maggette Elton Brand Andre Miller Gilbert Arenas 2001-2002 Bob Sura Bryon Russell Mark Jackson Andrei Kirilenko Mike Miller

6 Difference between comeback clutchness and escape clutchness (includes past 15 seasons): F-Test Two-Sample for Variances Escape Clutchness Comeback Clutchness Mean 0.399744153 0.314479098 Variance 0.116108959 0.115400413 Observations 1630 1630 df 1629 1629 F 1.006139892 P(F<=f) one-tail 0.450852491 F Critical one-tail 1.084946995 t-test: Two-Sample Assuming Equal Variances Escape Clutchness Comeback Clutchness Mean 0.399744153 0.314479098 Variance 0.116108959 0.115400413 Observations 1630 1630 Pooled Variance 0.115754686 Hypothesized Mean Difference 0 df 3258 t Stat 7.154521473 P(T<=t) one-tail 5.16225E-13 t Critical one-tail 1.645321462 P(T<=t) two-tail 1.03245E-12 t Critical two-tail 1.960692388 Since F < (F Critical one-tail), the variances of the two samples are equal, and, since (t Stat) >> (t Critical two-tail) and the p-value << 0, player performance in comeback clutchness situations is significantly different from that of escape clutchness situations. Difference between comeback clutchness and regular performance (includes past 15 seasons): F-Test Two-Sample for Variances Comeback Clutchness Regular Performance Mean 0.283649742 0.11589044 Variance 0.120707021 0.002725993 Observations 1862 1862 df 1861 1861 F 44.28001294 P(F<=f) one-tail 0 F Critical one-tail 1.079261758 t-test: Two-Sample Assuming Unequal Variances Comeback Clutchness Regular Performance Mean 0.283649742 0.11589044 Variance 0.120707021 0.002725993 Observations 1862 1862 Hypothesized Mean Difference 0 df 1945 t Stat 20.60443832 P(T<=t) one-tail 8.74521E-86 t Critical one-tail 1.645637431 P(T<=t) two-tail 1.74904E-85 t Critical two-tail 1.961184408 Since F >> (F Critical one-tail) and the p-value = 0, the variances of the two samples are unequal, and, since (t Stat) >> (t Critical two-tail) and the p-value 0, player performance in comeback clutchness situations is significantly different from that of regular performance situations.

7 Year-To-Year Correlation using comeback clutchness WS/48: R 2 = 0.02 (no correlation) Year-to-Year Correlation using comeback clutchness WS/48 differential: R 2 = 0.01 (no correlation)

8 Discussion Looking at our results, we seem to have produced some pretty intuitive results and also some very counterintuitive results. For instance, in the 2015-2016 season, Andre Drummond had both the highest comeback clutchness Win Shares Per 48 (1.10) and the highest comeback clutchness Win Shares Per 48 differential (0.97). To be clear, this means Drummond s regular season Win Shares Per 48 was 0.13. 17 This is a very counterintuitive result given that opposing teams often hack Drummond near the end of games (i.e. foul him on purpose to send him to the free throw line where he shoots an abysmal 37.1%). It could be the case, however, that Drummond s comeback clutchness is so high because teams who are ahead may be less likely to employ the hacking strategy and thus Pistons coach Stan Van Gundy is not forced to take Drummond out of the game. It could also be the case that Drummond is often taken out of the game immediately after the first hacking foul and thus his comeback clutchness numbers are inflated. Other counterintuitive results include random appearances in the top five by some very marginal players 18 and bottom-five appearances by some marquee players in their prime like Damian Lillard (2015-2016 season), Chris Paul (2014-2015 season), Manu Ginobili (2009-2010 season), and Kobe Bryant (2004-2005 season). 19 In contrast to these counterintuitive results, we produced very intuitive ones like Stephen Curry, Draymond Green, and Klay Thompson being in the top five for both comeback clutchness Win Shares Per 48 and comeback clutchness Win Shares Per 48 differentials. Teams like the Dallas Mavericks who repeatedly won close games were also rewarded in our rankings (e.g. Dirk Nowitzki, Deron Williams, and Chandler Parsons) while an awful team like the Philadelphia 76ers was represented by their point guard Isaiah Canaan. Finally, the ever efficient LeBron James appears in both of our 2015-2016 rankings. Conclusions Comeback clutchness is just noise (i.e. rarely repeatable) given its non-existent year-toyear correlation. It is, however, significantly different from both regular season performance and escape clutchness. The latter result confirms our assumption that there probably exists a psychological difference between playing behind and playing ahead that significantly impacts player performance, especially when it comes to clutch situations. Extensions of our project include performing the same kinds of analyses but with adjusted plus-minus and PIE. By using adjusted plus-minus, one could better account for differences in competition. By using PIE, our hypothesis is that more intuitive results can be gained (i.e. less random appearances in the top five by very marginal players), at least according to our preliminary analysis 20 of PIE. A downside, however, to using adjusted plus-minus and PIE is that neither statistic really tells you how many wins a player can produce for their team (although one could potentially argue that this is also true of Win Shares Per 48). 17 1.10 0.97 = 0.13 18 Specifically: Greivis Vasquez, Udonis Haslem, Zaza Pachulia, Jason Kapono, Keith Bogans, Earl Boykins, Kenny Thomas, Tony Battie, Tony Delk, Raef LaFrentz, Ervin Johnson, Ryan Bowen, Antonio Davis, Jared Jeffries, Nick Collison, and Alvin Williams 19 Along with Steve Nash (2008-2009 season), Rashard Lewis (2005-2006 season), Tony Parker (2004-2005 season), Carlos Boozer (2004-2005 season), Michael Finley (2003-2004 season), Lamar Odom (2002-2003 season), Elton Brand (2002-2003 season), John Wall (2012-2013 season), Brandon Jennings (2011-2012 season), Deron Williams (2009-2010 season), and Mike Miller (2001-2002 season) 20 Looking at the top players for each of the last fifteen seasons

9 Appendix Top 5 Players by Comeback Clutchness Offensive Win Shares Per 48 2015-2016 Stephen Curry Kevin Durant Andre Drummond Jeremy Lin Jamal Crawford 2014-2015 Anthony Davis Dirk Nowitzki LaMarcus Aldridge James Harden Danny Green 2013-2014 Mike Conley James Harden Damian Lillard Chris Bosh Iman Shumpert 2012-2013 Dirk Nowitzki Ray Allen Jeff Green Jarrett Jack Jimmy Butler 2011-2012 Andrew Bynum Kyrie Irving Kobe Bryant Nene Dwight Howard 2010-2011 Dirk Nowitzki Mo Williams Eric Gordon Manu Ginobili Jason Richardson 2009-2010 Kobe Bryant LeBron James Joe Johnson Steve Nash Dirk Nowitzki 2008-2009 Zach Randolph Jason Terry Kobe Bryant Tony Parker Paul Pierce 2007-2008 LeBron James Stephen Jackson Manu Ginobili Tim Duncan Vince Carter 2006-2007 Mehmet Okur Zach Randolph Chauncey Billups Jason Kapono Dirk Nowitzki 2005-2006 Jason Terry Earl Boykins Primoz Brezec Chauncey Billups Dwyane Wade 2004-2005 Ray Allen Ben Gordon Earl Boykins Larry Hughes Chauncey Billups 2003-2004 Kevin Garnett Kobe Bryant Yao Ming Metta World Peace Shareef Abdur-Rahim 2002-2003 Shaquille O'Neal Derek Anderson Jason Terry Dirk Nowitzki Chris Webber 2001-2002 Bonzi Wells Dirk Nowitzki Pat Garrity Ray Allen Antoine Walker Top 5 Players by Comeback Clutchness Defensive Win Shares Per 48 2015-2016 Draymond Green Andre Drummond Jeff Green Reggie Jackson LeBron James 2014-2015 Derrick Rose Joakim Noah Roy Hibbert Zach Randolph Luc Mbah a Moute 2013-2014 Greivis Vasquez Joakim Noah Kirk Hinrich Taj Gibson Courtney Lee 2012-2013 Chris Bosh Kevin Garnett Paul Pierce Rajon Rondo Avery Bradley 2011-2012 Udonis Haslem Roy Hibbert Zaza Pachulia Jeff Teague Mario Chalmers 2010-2011 Mo Williams Tyson Chandler Jason Kidd Tim Duncan Serge Ibaka 2009-2010 Andrew Bogut Marc Gasol Jared Jeffries Lamar Odom Mike Conley 2008-2009 Hedo Turkoglu Pau Gasol Dwight Howard Rashard Lewis Lamar Odom 2007-2008 Jeff Green Shaquille O'Neal Chris Paul Nick Collison Daniel Gibson 2006-2007 Josh Howard Dirk Nowitzki Jason Terry Monta Ellis Andre Miller 2005-2006 Keith Bogans Chris Kaman Elton Brand Marcus Camby Chauncey Billups 2004-2005 Tyson Chandler Kirk Hinrich Ben Gordon Stephen Jackson Ben Wallace 2003-2004 Shaquille O'Neal Kobe Bryant Al Harrington Reggie Miller Jermaine O'Neal 2002-2003 Tony Battie Tony Delk Antoine Walker Darius Miles Christian Laettner 2001-2002 Ryan Bowen Raef LaFrentz James Posey Ervin Johnson Vin Baker

10 Bottom 5 Players by Comeback Clutchness Offensive Win Shares Per 48 2015-2016 Robert Covington Derrick Rose Khris Middleton Isaiah Canaan Brandon Knight 2014-2015 Derrick Rose Bradley Beal Rudy Gay Michael Carter-Williams Steven Adams 2013-2014 Brandon Jennings Dion Waiters Ramon Sessions Ben McLemore Gerald Green 2012-2013 John Wall Carlos Delfino Jared Dudley Luis Scola Byron Mullens 2011-2012 Brandon Jennings O.J. Mayo Jameer Nelson Nicolas Batum Jason Kidd 2010-2011 Luke Ridnour Vince Carter Tony Parker Brandon Jennings DeMarcus Cousins 2009-2010 Rodney Stuckey Corey Brewer Eric Gordon Jamal Crawford Aaron Brooks 2008-2009 Metta World Peace Rasheed Wallace Baron Davis LaMarcus Aldridge Jason Richardson 2007-2008 Kirk Hinrich Gerald Wallace Antonio McDyess Chris Kaman Dwyane Wade 2006-2007 Luther Head Randy Foye Jason Kidd Hedo Turkoglu Jameer Nelson 2005-2006 Jumaine Jones Anthony Johnson Mark Blount Raef LaFrentz Deron Williams 2004-2005 Keith Bogans Kobe Bryant David Wesley Tony Delk Speedy Claxton 2003-2004 Allen Iverson Toni Kukoc Michael Finley Eric Williams Jamal Crawford 2002-2003 Darius Miles Larry Hughes Scottie Pippen Troy Hudson Kenyon Martin 2001-2002 LaPhonso Ellis Bryon Russell Derrick Coleman Baron Davis Terry Porter Bottom 5 Players by Comeback Clutchness Defensive Win Shares Per 48 2015-2016 Isaiah Canaan Mason Plumlee CJ McCollum Damian Lillard Brandon Knight 2014-2015 Jeremy Lin Tim Hardaway Jr. Jordan Hill James Harden Marcin Gortat 2013-2014 Trey Burke Gordon Hayward Corey Brewer Ricky Rubio Zaza Pachulia 2012-2013 Ben Gordon Ryan Anderson Chris Paul Jamal Crawford Anthony Davis 2011-2012 Kris Humphries Monta Ellis Greg Monroe Brandon Jennings Brandon Knight 2010-2011 Kirk Hinrich Stephen Curry Dorell Wright Monta Ellis DeMar DeRozan 2009-2010 Tyreke Evans Mike Bibby George Hill Jason Richardson Beno Udrih 2008-2009 Jason Richardson Steve Nash Chris Paul Peja Stojakovic Rasual Butler 2007-2008 Rashad McCants Anthony Parker Carlos Delfino Ryan Gomes Al Jefferson 2006-2007 Amar'e Stoudemire LaMarcus Aldridge Dahntay Jones DeShawn Stevenson Jarvis Hayes 2005-2006 Donyell Marshall Rashard Lewis P.J. Brown Luke Ridnour Steve Blake 2004-2005 Tim Thomas Carlos Boozer Manu Ginobili Josh Childress Jarvis Hayes 2003-2004 Bobby Simmons Ray Allen Damon Jones Brad Miller Steve Nash 2002-2003 Lamar Odom Corey Maggette Charlie Ward Andre Miller Elton Brand 2001-2002 Bonzi Wells Bob Sura Bryon Russell Erick Dampier Ron Mercer