My initial thought was to begin this article with the traditional sob story that every last place, self-absorbed fantasy owner sings; “Everyone on my team got hurt, all my stars underperformed, and I played every team in my league on their best week.”

While all of this may be true for my 12 team head-to-head categories league team, I pretense this article with the statement above, not to gain sympathy, but to give context to the research that resulted in this article.

In this article I show what metrics have the highest correlation with the fantasy basketball player rater score and propose a linear regression that looks at an expected player rater score based off of the variables with the highest correlations.

All of the references to player rater scores in this article refer to the player rater scores that are produced by ESPN Fantasy Basketball for 12 team head to head category leagues that use these categories: points, rebounds, three pointers, field goal percentage, free throw percentage, blocks, and steals.

The population for this study looks at player rater scores from the 2015 season so far. So while the sample size is very small, it gives us a general look at what metrics, outside of the metrics that are categories themselves, correlate highly to player rater scores. I was also unable to find a centralized database that archived historical player rater data, or any value metric in general, for fantasy basketball. I also didn’t have the time to go through each season from the last decade, create z scores for each category at each position, and create the player rater scores myself. But if anyone knows where I can get my hands on this information, I would be happy to do a more conclusive study.

We also don’t want to look at player rater scores specifically; we want to look at player rater score per game. This allows for us to give credit to players like Russell Westbrook and Chris Bosh, who have been absent from play for an appreciable duration of the season, but have played exceptionally well while they’ve been on the court.

Bellow are the metrics that I looked at and their correlation to player rater score per game:

Metric Correlation to PR/GM PTS 0.813516556 FG 0.779224727 FT 0.731328749 FGA 0.704824414 FTA 0.683340911 MP 0.672800305 MP/GM 0.65573891 2P 0.64840213 2PA 0.600314706 TOV 0.558714755 STL 0.54331025 AST 0.49912851 USG% 0.461947653 DRB 0.451675677 TRB 0.356459697 BLK 0.315271298 3P 0.298185857 3PA 0.295946302 FT% 0.257915844 2P% 0.204312922 PF 0.169178919 FG% 0.168585015 3P% 0.150700146 ORB 0.113957033

The two numbers that immediately jump out are MP (minutes played) and TOV (turnovers); all of the other metrics ahead of these statistics can be discounted because they are numbers that directly contribute to one of the eight categories used in ESPN head to head category leagues.

The .672 r for minutes played and the .558 r for turnovers show a strong positive relationship with player rater score per game and are statistically significant numbers.

A week ago, before I ran a correlation on all of the metrics above, I just looked at minutes played and usage rate as stats that might correlate highly with player rater scores. To me these numbers made the most sense; minutes per game shows that you are able to get on the court enough to get the opportunity to produce, and usage rate shows that when you get the opportunity, your team incorporates you in what they do from a schematic sense.

It may be because of the small sample of player seasons that was used for this study, but it looks like minutes played and turn overs are better proxies for opportunity and incorporation than minutes per game and usage rate.

I’m still not sure why minutes played correlates more highly with player rater score per game than minutes played per game (I’d love to hear what any readers might think), but my theory is that a player of lesser skill can artificially inflate his minutes played per game by playing big minutes in blow outs or games where players ahead of him on the depth chart are hurt or in foul trouble.

Turnovers make more sense. Think about it this way. Players that get a lot of turnovers are just like guys that get caught cheating on their girlfriends multiple times and don’t get broken up with; there has to be some aspect of who they are that makes them redeeming enough to keep the girlfriend around for more; that or their girlfriend has daddy issues, low self esteem, and is in her mid thirties and is afraid that she won’t be able to find another man to start a family with—either way. In order to get a large volume of turnovers, you have to be good enough to leave you in the game after you’ve made a mistake and continue to take risks. Just like Karen let Hank Moody back into her life again and again, after mistake upon mistake, Karen, just like the team, may have thought it was worth the risk.

Below is a linear regression of expected player rater score per game, with player rater score per game as the dependent variable and minutes played and turnovers as the independent variables.

PLAYER 2015 PR PR/GM RK xPR/GM RK DIFF James Harden 17.76 0.5920 2 0.327 1 1 John Wall 12.49 0.4029 7 0.316 2 5 LeBron James 12.27 0.4231 6 0.298 3 3 Ty Lawson 6.98 0.2252 50 0.292 4 46 Damian Lillard 15.29 0.4633 5 0.291 5 0 Eric Bledsoe 11.08 0.3358 15 0.288 6 9 Brandon Knight 10.65 0.3328 16 0.282 7 9 Kobe Bryant 6.24 0.2152 52 0.274 8 44 Monta Ellis 8.97 0.2718 34 0.266 9 25 Gordon Hayward 9.92 0.3100 24 0.266 10 14 Blake Griffin 8.37 0.2616 41 0.266 11 30 Stephen Curry 17.45 0.5817 3 0.255 12 -9 Tobias Harris 8.98 0.2721 33 0.246 13 20 Kyle Lowry 12.36 0.3863 10 0.242 14 -4 Rudy Gay 9.63 0.3321 18 0.241 15 3 Marc Gasol 12.24 0.3948 8 0.239 16 -8 Tyreke Evans 4.55 0.1517 74 0.238 17 57 Chris Paul 15.7 0.4906 4 0.234 18 -14 Jrue Holiday 9.71 0.3132 22 0.228 19 3 Trevor Ariza 5.57 0.1857 60 0.225 20 40 Jimmy Butler 11.1 0.3700 11 0.224 21 -10 Kyrie Irving 9.84 0.3393 14 0.221 22 -8 Kemba Walker 7.78 0.2431 44 0.220 23 21 Carmelo Anthony 7.82 0.2697 37 0.219 24 13 Josh Smith 2.03 0.0655 138 0.218 25 113 Kevin Love 8.4 0.2710 36 0.218 26 10 Paul Millsap 9.67 0.3119 23 0.217 27 -4 Evan Fournier 2.28 0.0671 135 0.217 28 107 Mario Chalmers 4.9 0.1531 72 0.216 29 43 Rajon Rondo 3.65 0.1304 93 0.215 30 63 Mike Conley 9.53 0.3074 29 0.213 31 -2 Michael Carter-Williams 0.83 0.0361 166 0.207 32 134 Wesley Matthews 8.03 0.2433 43 0.205 33 10 Goran Dragic 7.52 0.2426 45 0.202 34 11 Darren Collison 7.41 0.2646 39 0.198 35 4 Markieff Morris 8.03 0.2433 42 0.197 36 6 Pau Gasol 9.54 0.3290 19 0.196 37 -18 Nikola Vucevic 8.43 0.2907 32 0.195 38 -6 Trey Burke 2.8 0.0875 124 0.193 39 85 Ben McLemore 3.79 0.1223 100 0.193 40 60 LaMarcus Aldridge 9.41 0.3245 20 0.191 41 -21 Solomon Hill 2.44 0.0763 130 0.191 42 88 Reggie Jackson 5.57 0.1921 58 0.190 43 15 Serge Ibaka 9.85 0.3078 28 0.190 44 -16 Deron Williams 5.87 0.2024 55 0.189 45 10 Joe Johnson 5.92 0.2041 54 0.189 46 8 DeAndre Jordan 9.61 0.3003 31 0.189 47 -16 Jeff Teague 9.53 0.3404 13 0.187 48 -35 Draymond Green 9.29 0.3097 25 0.186 49 -24 Klay Thompson 10.67 0.3679 12 0.182 50 -38 Arron Afflalo 2.61 0.0816 127 0.177 51 76 Anthony Davis 18.51 0.6170 1 0.176 52 -51 Wilson Chandler 5.37 0.1678 66 0.175 53 13 Victor Oladipo 3.59 0.1381 83 0.175 54 29 Kyle Korver 9.58 0.3090 27 0.174 55 -28 Chandler Parsons 6.54 0.2044 53 0.172 56 -3 Andrew Wiggins 0.24 0.0080 190 0.170 57 133 Channing Frye 4.45 0.1309 92 0.168 58 34 Jeremy Lin 4.29 0.1341 90 0.166 59 31 Dwyane Wade 5.63 0.2346 46 0.164 60 -14 Danny Green 10.17 0.3178 21 0.164 61 -40 Al Jefferson* 6.11 0.1909 59 0.161 62 -3 Luol Deng 5.33 0.1777 61 0.157 63 -2 Tim Duncan 8.67 0.3096 26 0.157 64 -38 Tyson Chandler 9.71 0.3034 30 0.156 65 -35 Jeff Green 5.58 0.1993 57 0.156 66 -9 Giannis Antetokounmpo 4.45 0.1391 82 0.154 67 15 Enes Kanter 4.52 0.1413 80 0.151 68 12 Andre Drummond 3.83 0.1235 99 0.151 69 30 Alec Burks* 1.89 0.0700 133 0.147 70 63 Tony Wroten 1.38 0.0600 145 0.146 71 74 Kentavious Caldwell-Pope 1.06 0.0342 168 0.145 72 96 Jarrett Jack 4.26 0.1374 85 0.143 73 12 Greg Monroe 3.02 0.1041 111 0.141 74 37 J.J. Redick 5.11 0.1597 69 0.140 75 -6 Nicolas Batum 4.54 0.1681 65 0.139 76 -11 Marcin Gortat 7.09 0.2287 48 0.137 77 -29 Nerlens Noel 1.7 0.0630 140 0.136 78 62 Brandon Jennings 3.79 0.1354 87 0.134 79 8 Jordan Hill 4.89 0.1528 73 0.133 80 -7 Chris Bosh 6.47 0.2696 38 0.132 81 -43 O.J. Mayo 1.99 0.0622 143 0.126 82 61 Derrick Favors 6.57 0.2266 49 0.126 83 -34 Dirk Nowitzki 8.4 0.2710 35 0.125 84 -49 Donatas Motiejunas 1.61 0.0537 151 0.125 85 66 Mike Dunleavy 3.41 0.1066 108 0.122 86 22 Al Horford 7.93 0.2643 40 0.121 87 -47 Steven Adams 1.56 0.0488 156 0.120 88 68 Courtney Lee 4.32 0.1543 71 0.119 89 -18 Terrence Ross 3.7 0.1156 103 0.119 90 13 Gorgui Dieng 6.91 0.2303 47 0.118 91 -44 Corey Brewer 3.59 0.1282 95 0.118 92 3 Jamal Crawford 6.26 0.2019 56 0.117 93 -37 Harrison Barnes 3.73 0.1243 97 0.117 94 3 Manu Ginobili 2.77 0.0989 115 0.117 95 20 Timofey Mozgov 4.19 0.1309 91 0.115 96 -5 Wesley Johnson 4.49 0.1403 81 0.115 97 -16 Zach Randolph* 3.51 0.1350 88 0.111 98 -10 DeMarcus Cousins 7.84 0.3920 9 0.108 99 -90 Ryan Anderson 5.07 0.1635 68 0.106 100 -32 K.J. McDaniels 3.48 0.1200 102 0.105 101 1 Zach LaVine 0.23 0.0085 189 0.103 102 87 Thaddeus Young 0.57 0.0228 176 0.101 103 73 Gerald Green 5.16 0.1564 70 0.101 104 -34 Joakim Noah 2.62 0.1048 110 0.101 105 5 Kenneth Faried 2.46 0.0848 126 0.101 106 20 Amar'e Stoudemire* 4.61 0.1646 67 0.100 107 -40 Jonas Valanciunas 5.47 0.1765 62 0.100 108 -46 Derrick Rose 1.59 0.0723 132 0.096 109 23 Matt Barnes 2.87 0.0957 117 0.094 110 7 Tristan Thompson 2.08 0.0671 134 0.094 111 23 Carlos Boozer 1.69 0.0545 150 0.093 112 38 Paul Pierce 4.05 0.1350 89 0.092 113 -24 Andre Iguodala 0.47 0.0157 186 0.092 114 72 Cory Joseph 3.16 0.1019 113 0.091 115 -2 DeMarre Carroll 2.86 0.1059 109 0.091 116 -7 Aaron Brooks 3.2 0.1000 114 0.090 117 -3 Jabari Parker* 1.4 0.0560 147 0.090 118 29 Bradley Beal 3.03 0.1377 84 0.090 119 -35 Evan Turner 2.48 0.0886 122 0.090 120 2 Roy Hibbert 3.8 0.1357 86 0.087 121 -35 Kelly Olynyk 4.87 0.1739 64 0.087 122 -58 Jared Sullinger 3.59 0.1282 94 0.086 123 -29 Avery Bradley 1.09 0.0404 164 0.086 124 40 Steve Blake 0.6 0.0182 183 0.083 125 58 Amir Johnson 3.13 0.1079 105 0.082 126 -21 Russell Westbrook 5.99 0.3328 17 0.081 127 -110 P.J. Tucker 3.2 0.1103 104 0.078 128 -24 Tony Parker* 2.26 0.1076 106 0.077 129 -23 Dion Waiters 1.31 0.0437 158 0.077 130 28 Patrick Patterson 4.65 0.1453 77 0.075 131 -54 Louis Williams 4.72 0.1475 75 0.075 132 -57 Zaza Pachulia 1.41 0.0486 157 0.073 133 24 Cody Zeller 0.76 0.0238 174 0.072 134 40 Marcus Morris 2.04 0.0618 144 0.070 135 9 Donald Sloan 0.14 0.0054 194 0.067 136 58 Luis Scola 1.35 0.0422 161 0.067 137 24 Jameer Nelson 0.56 0.0207 179 0.067 138 41 Dwight Howard 0.47 0.0261 173 0.067 139 34 Kawhi Leonard* 4.75 0.2159 51 0.067 140 -89 Henry Sims 1.98 0.0660 137 0.067 141 -4 Jerryd Bayless 2.53 0.0791 129 0.065 142 -13 Miles Plumlee 2.2 0.0667 136 0.063 143 -7 Gerald Henderson 0.9 0.0300 169 0.063 144 25 Devin Harris 2.88 0.0929 119 0.062 145 -26 Greivis Vasquez 0.25 0.0078 192 0.062 146 46 Robin Lopez* 3.09 0.1236 98 0.060 147 -49 Marvin Williams 0.69 0.0230 175 0.060 148 27 Ronnie Price 1.59 0.0513 153 0.060 149 4 Khris Middleton 2.31 0.0797 128 0.059 150 -22 Chris Kaman 1.84 0.0575 146 0.057 151 -5 Mo Williams 0.68 0.0296 170 0.057 152 18 Rodney Stuckey 0.03 0.0012 195 0.056 153 42 Omer Asik 0.19 0.0070 193 0.051 154 39 Jason Terry 1.43 0.0511 154 0.051 155 -1 Isaiah Thomas 3.04 0.1216 101 0.048 156 -55 Shawne Williams 2.79 0.0900 121 0.047 157 -36 Mirza Teletovic 0.81 0.0289 171 0.046 158 13 Tony Allen 1.57 0.0628 141 0.043 159 -18 Shane Larkin 0.85 0.0283 172 0.041 160 12 Anderson Varejao* 2.53 0.0973 116 0.041 161 -45 Lavoy Allen 2.73 0.0881 123 0.040 162 -39 Taj Gibson 1.98 0.0861 125 0.037 163 -38 Shawn Marion 0.48 0.0160 185 0.037 164 21 Kyle Singler 0.63 0.0203 180 0.036 165 15 Shabazz Muhammad 1.28 0.0427 160 0.033 166 -6 Jared Dudley 2.03 0.0634 139 0.031 167 -28 Pablo Prigioni 1.71 0.0552 148 0.030 168 -20 Kris Humphries 0.63 0.0210 178 0.028 169 9 Jose Calderon 0.31 0.0155 187 0.028 170 17 Brook Lopez 2.25 0.1071 107 0.027 171 -64 Shaun Livingston 0.58 0.0193 181 0.026 172 9 James Johnson 3.61 0.1245 96 0.024 173 -77 Rudy Gobert 4.58 0.1431 78 0.023 174 -96 Alex Len 3 0.0909 120 0.021 175 -55 Samuel Dalembert 1.13 0.0353 167 0.019 176 -9 Kevin Garnett 1.11 0.0427 159 0.019 177 -18 Patrick Beverley 0.72 0.0400 165 0.017 178 -13 Larry Sanders* 1.32 0.0489 155 0.014 179 -24 Carl Landry 0.59 0.0190 182 0.013 180 2 Nikola Mirotic 3.01 0.0941 118 0.006 181 -63 Andrew Bogut* 2.93 0.1465 76 0.005 182 -106 Anthony Morrow 1.05 0.0420 162 0.005 183 -21 Rasual Butler 2 0.0741 131 0.005 184 -53 Beno Udrih 0.64 0.0213 177 0.005 185 -8 Marreese Speights 2.97 0.1024 112 0.002 186 -74 Robert Covington 1.15 0.0548 149 0.001 187 -38 Aron Baynes 1.3 0.0406 163 -0.001 188 -25 Tyler Zeller 3.96 0.1414 79 -0.004 189 -110 Nick Young 1.37 0.0623 142 -0.012 190 -48 Brandan Wright 5.44 0.1755 63 -0.015 191 -128 Jeremy Lamb 0.4 0.0167 184 -0.020 192 -8 Kosta Koufos 0.24 0.0080 191 -0.033 193 -2 Kyle O'Quinn 1.07 0.0535 152 -0.050 194 -42 Kevin Durant* 0.08 0.0089 188 -0.082 195 -7

xPR/GM produces an r of .714 with this formula: xPR/GM =- 0.2063 + 0.0003 * MP + 0.0016 * TOV.

While I was able to produce a linear regression with minutes played per game and usage rate that yielded a correlation of .687, it appears that minutes played and turnovers are much better proxies for our formula.

I’m not sure there is much to xPR/GM other than that the concept provokes you to take a longer look at a player who steps into a meaningful role after another player on his team gets hurt, but what we can take away from this study is that minutes played and turnovers are the secondary metrics that have the highest correlation with player rater scores this year.

Devin Jordan is obsessed with statistical analysis, non-fiction literature, and electronic music. If you enjoyed reading him, follow him on Twitter