by Vincent Verhei

The Kansas City Chiefs defeated the Jacksonville Jaguars on Sunday, and as you could tell from the 40-26 final score, there are many, many differences between the two teams. Beyond history, geography, color schemes, mascot, coaches, and players, though, I want to focus on how each squad distributed the ball in the passing game. Even with Tyreek Hill leaving the game due to injury, the Chiefs tended to force the ball to a small handful of players. Sammy Watkins led the team with 11 targets, while Travis Kelce had eight and Damian Williams had six; nobody else had more than two. The Jaguars spread things around much more evenly; six players had at least four targets, but none had more than seven.

What's the best way to measure each team's target distribution? For more than a century now, economists have been using Gini coefficients (developed by Italian statistician Corrado Gini) to measure the wealth distribution of various nations, among other things. In a nutshell, Gini coefficients measure the difference between actual financial distribution a perfectly even distribution. If every citizen in a given nation had exactly equal net worth, that nation's Gini coefficient would be 0.000; if one citizen had 100% of that nation's worth, the Gini coefficient would be 1.000. No, we are not going to discuss income inequality in this space (or, please, in the comments), but we can use these same principles to analyze each team's approach to the passing game.

Before we begin, I should note that I am a writer who knows how to use Excel. I am neither a mathematician nor an economist. Everything I know about Gini coefficients I learned from this Wikipedia page and this YouTube video. Gini coefficients go beyond cocktail napkin math, and it's entirely possible I'm calculating them incorrectly. However, I have checked the most extreme results with each team's target list, and they make intuitive sense.

Take that Chiefs-Jaguars game, for example. The Chiefs came out of that game with a Gini coefficient of 0.494, highest in the league (not counting the Monday night games). The Jaguars had the lowest Gini coefficient at 0.208. No team concentrated its targets around a small group of players as tightly as Kansas City, while no team spread its targets around more evenly than Jacksonville.

Other teams that used Kansas City's focused approach include Detroit, Chicago, and Carolina. For the Lions, Danny Amendola had 13 targets and Kenny Golladay and T.J. Hockenson had nine each, while nobody else had more than four. The Bears threw 13 passes to Allen Robinson, 10 to Tarik Cohen and seven to Mike Davis, but not more than five to anyone else. The Panthers had a trio of players (Christian McCaffrey, D.J. Moore, and Greg Olsen) with at least nine targets, but nobody else had more than four.

On the other hand, even target circulation appears to be a Florida thing -- the Jaguars were followed in this category by their in-state rivals, the Buccaneers (six players with at least four targets, none more than six) and Dolphins (seven players with at least three targets, none more than seven). The Steelers also spread things around quite a bit: Donte Moncrief had 10 targets and Juju Smith-Schuster had nine, while five of their teammates had four to six targets each.

These are the results from just one weekend, however, and perhaps random noise. A full season's worth of information should give us more meaningful info. The following table shows each team's Gini coefficient in 2018.

NFL Gini Coefficient Target Distributions, 2018 Team Gini

Coefficient Total

Targets Leader Targets Share MIN 0.659 599 19-A.Thielen 154 25.7% PHI 0.622 600 86-Z.Ertz 157 26.2% ATL 0.614 613 11-J.Jones 173 28.2% CHI 0.614 516 12-A.Robinson 102 19.8% NO 0.611 524 13-M.Thomas 155 29.6% LAR 0.610 552 17-R.Woods 134 24.3% PIT 0.605 686 84-A.Brown 170 24.8% KC 0.597 571 87-T.Kelce 152 26.6% SEA 0.585 410 89-D.Baldwin 76 18.5% BUF 0.583 487 11-Z.Jones 104 21.4% DAL 0.582 521 21-E.Elliott 95 18.2% CLE 0.574 563 80-J.Landry 150 26.6% OAK 0.568 535 87-J.Cook 103 19.3% GB 0.567 623 17-D.Adams 171 27.4% NE 0.558 564 28-J.White 123 21.8% CAR 0.558 552 22-C.McCaffrey 124 22.5% TEN 0.550 432 84-C.Davis 117 27.1% TB 0.548 627 13-M.Evans 140 22.3% DET 0.547 571 19-K.Golladay 124 21.7% HOU 0.541 500 10-D.Hopkins 165 33.0% IND 0.538 644 13-T.Hilton 126 19.6% SF 0.534 524 85-G.Kittle 139 26.5% BAL 0.533 551 15-M.Crabtree 104 18.9% NYG 0.531 583 13-O.Beckham 129 22.1% MIA 0.529 441 80-D.Amendola 79 17.9% ARI 0.528 478 11-L.Fitzgerald 113 23.6% WAS 0.515 495 86-J.Reed 84 17.0% LAC 0.510 508 13-K.Allen 137 27.0% JAX 0.505 527 12-D.Westbrook 102 19.4% CIN 0.503 539 83-T.Boyd 108 20.0% NYJ 0.469 506 11-R.Anderson 94 18.6% DEN 0.414 572 10-E.Sanders 99 17.3%

Minnesota leads the way here -- no team leaned on its top guys more than the Vikings. Adam Thielen and Stefon Diggs had over 150 targets each. Tight end Kyle Rudolph was a distant third with 83, and nobody else had even 60. The Eagles are next in line, led by the 157 targets of Zach Ertz. Alshon Jeffery and Nelson Agholor had more than 90 targets apiece, but nobody else in Philadelphia had 50. Julio Jones led the NFL with 173 targets, nearly double any of his teammates, so it's no surprise to see Atlanta third here. Nobody else in Atlanta had even 100 targets; Calvin Ridley and Mohamed Sanu were both in the 90s, while Austin Hooper just missed with 89.

It's clear to see that injuries and other personnel moves can affect a team's Gini coefficient when looking at the teams at the bottom of the table. Denver had the lowest Gini coefficient in the NFL; Emmanuel Sanders led the team with just 99 targets, making them one of six teams with no 100-target players. However, eight Broncos had 40 targets or more. Things looked a lot different in Denver in the middle of the year. Through Week 8, Sanders had 65 targets and Demaryius Thomas had 56, but nobody else had even 40. Then Thomas was traded and Sanders got hurt and everything changed. Nobody on the Jets had 100 targets either, in part because Robby Anderson, Jermaine Kearse, and Quincy Enunwa each missed a handful of games. Running back Elijah McGuire missed half the season, but still had 31 targets. For Cincinnati, Tyler Boyd had 108 targets, while A.J. Green was second with 77 (in only nine games) and four other players had 48 or more.

The most surprising team in this table is the Houston Texans. DeAndre Hopkins led the NFL with 33% of his team's targets -- nobody else was even at 30% -- yet the Texans had a lower Gini coefficient than most teams. This is not an error on our part, just a bit of a statistical fluke; the targets that did not go to Hopkins were scattered all over the place. Nobody else on the Texans had even 50 targets, but three were in the 40s, two were in the 30s, and four were in the 20s. This is another reflection of the Demaryius Thomas trade, as well as injuries -- in this case, to Will Fuller and Keke Coutee.

The correlation between Gini coefficient and pass offense DVOA last year was .366 -- generally, teams that spread the ball around did not do as well as those who concentrated on smaller groups of players. Correlation does not mean causation, however. Teams that have superstars are going to feed them as often as possible, and those superstars will raise both the Gini coefficient and the DVOA. Teams that lose all their receivers to injury, meanwhile, will have the opposite results.

Quarterbacks Rk Player Team CP/AT Yds TD INT Sacks Total

DYAR Pass

DYAR Rush

DYAR Opp 1. Dak Prescott DAL 25/32 405 4 0 0 273 265 8 NYG Yes, Prescott threw four touchdowns, each within New York's 30-yard line ... but he was even better at the other end of the field. He threw 10 passes within the Dallas 40, and eight of them resulted in first downs. The other two were a 6-yard gain on first down and an incompletion on second-and-4. Those nine completions produced a total of 216 yards. 2. Lamar Jackson BAL 17/20 324 5 0 1 201 204 -3 MIA Jackson would have made the top 10 in this table based on his first quarter alone: 6-of-6 for 163 yards and two touchdowns. And then his first pass of the second quarter was his third touchdown, a 33-yarder. He's only below Prescott in these tables because Prescott threw almost 50 percent more passes. 3. Patrick Mahomes KC 25/33 378 3 0 0 168 174 -6 JAX Mahomes was also a monster in the first quarter: 8-of-9 for 211 yards and two touchdowns. He was much more quiet in the second half, when only two of his 13 dropbacks gained 10 or more yards, none more than 15 yards. 4. Case Keenum WAS 30/43 380 3 0 1 151 151 0 PHI Big first quarters were the theme this week, apparently. Keenum's first 15 minutes: 9-of-11 for 132 yards and a touchdown. His first pass of the second quarter was a 69-yard touchdown, but then he too cooled off. As Washington turned a 10-point lead into a 9-point deficit, Keenum went nine straight dropbacks without picking up a first down, padding his stats with 11-yard gains on second-and-25 and third-and-20 in the process. 5. Derek Carr OAK 22/26 259 1 0 0 139 141 -2 DEN 6. Tom Brady NE 24/36 341 3 0 1 139 139 0 PIT In his first game post-Gronkowski, Brady only threw two passes to tight ends, both to somebody identified as "85-R.Izzo" in the play-by-play. One was incomplete; the other was caught for a 3-yard gain on second-and-13. So, way to go, Steelers. You totally shut that dude down. 7. Carson Wentz PHI 28/39 313 3 0 1 123 119 5 WAS Wentz's first third-down pass was incomplete. He nailed every third-down throw after that, completing all 12 of them for 197 yards and nine conversions, including seven in a row at one point, with three touchdowns. 8. Drew Brees NO 32/41 370 2 1 1 105 105 0 HOU 9. Matthew Stafford DET 27/43 385 3 0 3 96 85 11 ARI Stafford's DYAR is worse than you might think because he fumbled twice. The Lions recovered one, but the other was lost to Arizona on first down just outside the red zone. That happened in the first quarter and might have gone overlooked in all the excitement at the end of the game, but it's a big reason Detroit ended with a tie and not a win. 10. Gardner Minshew JAX 22/25 275 2 1 1 83 82 2 KC Minshew's debut was fantastic, better in relief than most starters this week, but we must point out that his gaudy completion percentage was padded by a lot of dumpoffs. He had eight failed completions in three quarters and change; Ben Roethlisberger and Matt Ryan led the league with 10 failed completions each this week. Minshew completed all five of his third-down throws, but only two resulted in first downs. 11. Deshaun Watson HOU 20/30 268 3 1 6 71 51 21 NO 12. Philip Rivers LAC 25/34 333 3 1 4 46 40 5 IND On deep passes, Rivers went 6-of-7 for 129 yards and a touchdown. Rk Player Team CP/AT Yds TD INT Sacks Total

DYAR Pass

DYAR Rush

DYAR Opp 13. Marcus Mariota TEN 14/24 248 3 0 4 37 29 8 CLE Mariota's three touchdowns came on three consecutive throws over the third and fourth quarters, producing a total of 89 DYAR between them. His other 25 dropbacks were pretty bad. Obviously, if you take away any quarterback's best plays, his numbers are going to look worse, but it's kind of stunning how useless Mariota was outside his explosion. His average completion gained a league-high 12.4 yards after the catch. 14. Nick Foles JAX 5/8 75 1 0 0 33 33 0 KC Foles' career in Jacksonville lasted less than 10 minutes of game time before he broke his clavicle. He'll be back in a few months, assuming Gardner Minshew hasn't Brady-Bledsoed him by then. We're a long way from that, but "lost his job to a sixth-round rookie with a moustache" would be a fitting end to the bizarre tale of Foles' career. 15. Eli Manning NYG 31/44 306 1 0 1 31 30 1 DAL Manning played well over most of the field, but struggled in the red zone: 4-of-6 for 22 yards, just one touchdown, one sack-fumble, recovered by the Cowboys. 16. Joe Flacco DEN 21/31 268 1 0 3 29 33 -5 OAK 17. Russell Wilson SEA 14/20 196 2 0 4 21 21 0 CIN Here's a perfect summary of how hot-and-cold Wilson's day was: seven of his eight first downs (including both touchdowns) came in the second and fourth quarters. In the first and third quarters, he went 6-of-7 for 63 yards but just the one first down, while also being sacked three times. In the second and fourth, he went 8-of-13 for 133 yards with just one sack, plus a 4-yard DPI. 18. Kirk Cousins MIN 8/10 98 1 0 1 19 30 -11 ATL According to Over The Cap, Cousins is being paid $29 million this year in salary and bonuses. That's an average of $1.8 million over 16 game checks. That means Cousins earned more than $150,000 for each of his 12 dropbacks (ten passes, one sack, one DPI) in this game. The Vikings, of course, will be perfectly happy writing those checks as long as they win by multiple touchdowns every week. 19. Jacoby Brissett IND 21/27 190 2 0 2 18 15 3 LAC Brissett completed seven of eight passes thrown to his right. That sounds good, but those seven completions gained only 46 yards and one first down. 20. Andy Dalton CIN 35/51 418 2 0 5 10 10 0 SEA Dalton was best throwing down the middle against Seattle's defense, going 9-of-12 for 142 yards and a touchdown, with a 13th throw resulting in a 15-yard DPI. Where have you gone Earl Thomas? (Oh. Right. Baltimore.) 21. Jimmy Garoppolo SF 18/27 166 1 1 1 -1 -1 0 TB Red zone passing: 2-of-4 for 8 yards, no touchdowns, with a sack that gave those 8 yards back. A total of five plays that went absolutely nowhere. 22. Aaron Rodgers GB 18/30 203 1 0 5 -6 -6 0 CHI Rodgers had 13 dropbacks between the 40-yard lines, and only one of those plays resulted in a first down. All told, he went 3-of-11 for 21 yards with two sacks in the middle of the field. Rk Player Team CP/AT Yds TD INT Sacks Total

DYAR Pass

DYAR Rush

DYAR Opp 23. Ryan Fitzpatrick MIA 14/29 185 1 1 2 -11 -16 5 BAL A very bad day throwing to his right, where Fitzpatrick went 2-of-8 for 9 yards with an interception. 24. Matt Ryan ATL 33/46 304 2 2 4 -32 -39 7 MIN Ryan's splits were like Wilson's but even more extreme. In the first and third quarters, he went 11-of-19 for 84 yards (plus a 26-yard DPI) with two sacks and two interceptions, finishing last in DYAR. In the second and fourth quarters, he went 22-of-27 for 220 yards (plus a 9-yard DPI) with two sacks and two touchdowns, finishing third in DYAR behind Dak Prescott and Matthew Stafford. 25. Ben Roethlisberger PIT 27/47 276 0 1 1 -46 -48 2 NE In the first 59 minutes of Sunday night's loss to New England, Roethlisberger threw for exactly 1 yard on New England's half of the field. "Yard." Singular. All told, he went 4-of-17 for 36 yards with one sack and one interception after crossing the 50. 26. Jared Goff LAR 23/39 186 1 1 1 -57 -55 -2 CAR Goff did not complete a deep pass against Carolina, going 0-for-5 with an interception. He did gain 16 yards on a deep-ball DPI to Robert Woods. 27. Sam Darnold NYJ 28/41 187 1 0 4 -81 -81 0 BUF Darnold did not complete a deep pass either, going 0-for-4. His deepest completion was caught 12 yards downfield by Robby Anderson, who promptly ran backwards 4 yards, then fumbled the ball away. Darnold's average pass traveled 5.4 yards downfield, and his average completion was caught 2.5 yards downfield, both the worst marks for any starter this week. 28. Josh Allen BUF 24/37 254 1 2 1 -81 -91 10 NYJ Allen did not have a single dropback in the red zone. In the front zone -- the area between New York's 20- and 40-yard lines -- he went 4-of-9 for 64 yards with one touchdown, one sack-fumble, and one fumble on an aborted play. 29. Cam Newton CAR 25/37 239 0 1 3 -83 -57 -26 LAR Newton did not have a dropback in the red zone either. Throwing down the middle, he went 4-of-6 for all of 17 yards with no first downs and one interception. 30. Kyler Murray ARI 29/54 308 2 1 5 -88 -85 -3 DET By DYAR, Murray was the worst quarterback in the first quarter, third-worst in the second, and second-worst in the third ... but then the best in the fourth quarter and overtime. In those 25 minutes, he went 20-of-29 for 238 yards with two touchdowns and a sack. Only two of his dropbacks in this game came from under center. He was sacked on the first one and threw an incompletion on third-and-4 on the other. 31. Mitchell Trubisky CHI 26/45 228 0 1 5 -93 -95 2 GB On Green Bay's side of the 50, Trubisky went 6-of-14 for 29 yards with only one first down to go with one interception and one sack. 32. Baker Mayfield CLE 25/38 285 1 3 5 -101 -101 0 TEN Through three quarters, Mayfield was comfortably among the top 10 passers of the week, but he was far and away the worst passer in the fourth quarter/OT. In the last 15 minutes, he completed six of his nine official pass attempts: three to his own team (for 21 total yards) and three to Tennessee. He also gained 16 yards on a DPI but lost 16 yards on a pair of sacks. 33. Jameis Winston TB 21/36 194 1 3 3 -222 -227 5 SF It's not just that Winston threw three interceptions, it's where he threw them. At or inside the Tampa Bay 25 -- you know, where most drives begin -- he went 3-of-7 for 22 yards (plus a 16-yard DPI) with a fumbled snap and ALL THREE interceptions, including two pick-sixes. Winston put together the following four-play stretch just before and just after halftime: completion to O.J. Howard, who fumbled the ball away (not Winston's fault, but still); interception on another pass to Howard; fumbled snap; pick-six.

Five Best Running Backs by DYAR (Total) Rk Player Team Runs Rush

Yds Rush

TD Rec Rec

Yds Rec

TD Total

DYAR Rush

DYAR Rec

DYAR Opp 1. Christian McCaffrey CAR 19 128 2 10/11 81 0 85 61 25 LAR Five runs for 10-plus yards with three shorter first downs, including two red zone scores. He was stuffed for no gain or a loss just twice, and one of those was on third-and-12 so it barely mattered. Six of his 10 catches were successful (a good rate for a running back), including three first downs. 2. Austin Ekeler LAC 12 58 1 5/8 96 2 79 19 60 IND Only two stuffs, with four first downs, including gains of 19 and 13 yards. In addition to his 5-96-2 receiving statline, he also drew a 3-yard DPI to convert a first-and-15. 3. Derrick Henry TEN 19 86 1 1/2 75 1 54 24 30 CLE Four first downs on the ground, with gains of 18 and 16 yards, with only two stuffs. His 75-yard touchdown reception included 80 yards after the catch. 4. Marlon Mack IND 25 174 1 0/0 0 0 54 54 0 LAC Eleven big first downs on the ground, four more than anyone else this week, including a 63-yard touchdown and gains of 25 and 10 yards, with only two stuffs. 5. Mark Ingram BAL 14 107 2 0/0 0 0 47 47 0 MIA Each of Ingram's carries gained at least a yard, and his shortest runs both went for touchdowns or they would have gained more. He had two other first downs, the longest a 49-yard gain.

Five Best Running Backs by DYAR (Rushing) Rk Player Team Runs Rush

Yds Rush

TD Rec Rec

Yds Rec

TD Total

DYAR Rush

DYAR Rec

DYAR Opp 1. Christian McCaffrey CAR 19 128 2 10/11 81 0 85 61 25 LAR 2. Marlon Mack IND 25 174 1 0/0 0 0 54 54 0 LAC 3. Mark Ingram BAL 14 107 2 0/0 0 0 47 47 0 MIA 4. Carlos Hyde HOU 10 83 0 1/1 2 0 30 34 -4 NO 5. Devin Singletary BUF 4 70 0 5/6 28 0 32 33 -2 NYJ Usually when you see a guy gain 70 yards on four carries, you'd assume he had a 50- or 60-yarder in there, but no -- EACH of Singletary's carries gained at least 12 yards and a first down. Only Christian McCaffrey has more 12-plus-yard runs than Singletary (not counting Monday night), and it took McCaffrey 14 more total carries to do it.

Worst Running Back by DYAR (Total) Rk Player Team Runs Rush

Yds Rush

TD Rec Rec

Yds Rec

TD Total

DYAR Rush

DYAR Rec

DYAR Opp 1. Miles Sanders PHI 11 25 0 1/2 2 0 -47 -32 -15 WAS 19 yards and a first down on one carry, 6 yards (and six stuffs!) on his other 10 runs. He lost yards on first- and second-and-goal from the 3, as well as second-and-5. His two targets were a 2-yard gain on first-and-10 and an incompletion on second-and-1.

Worst Running Back by DYAR (Rushing) Rk Player Team Runs Rush

Yds Rush

TD Rec Rec

Yds Rec

TD Total

DYAR Rush

DYAR Rec

DYAR Opp 1. Miles Sanders PHI 11 25 0 1/2 2 0 -47 -32 -15 WAS

Five Best Wide Receivers and Tight Ends by DYAR Rk Player Team Rec Att Yds Avg TD Total

DYAR Opp 1. Sammy Watkins KC 9 11 198 22.0 3 89 JAX Watkins had more DYAR in the first quarter than any other receiver had in an entire game this week. His first five targets: 68-yard touchdown on third-and-3; 21-yard gain on first-and-10; 13-yard gain on first-and-15; 49-yard touchdown; 22-yard gain on second-and-7. His next six targets produced only 25 total yards, but two first downs, including another score. 2. DJ Chark JAX 4 4 146 36.5 1 65 KC His four targets: 7-yard gain on second-and-11; 35-yard touchdown on third-and-8; 69- and 35-yard gains on first-and-10. 3. Michael Gallup DAL 7 7 158 22.6 0 64 NYG Five of Gallup's catches gained at least 12 yards and a first down, the longest a 62-yarder. The others were both 6-yard gains on first-and-10. 4. Marquise Brown BAL 4 5 147 36.8 2 59 MIA Brown's first quarter was almost as explosive as Watkins': 47- and 83-yard touchdowns, plus a 14-yard gain on second-and-5. He didn't pick up another first down the rest of the game, but who cares? 5. Phillip Dorsett NE 4 4 95 23.8 2 53 PIT Four targets: 8-yard gain on third-and-5; 25-yard touchdown; 4-yard gain on first-and-10; 58-yard touchdown on third-and-10.