Looking at Strength of Schedule: An Analysis of the Early Top 10

There are a number of pre-season rankings for the 2019 college football season that released their post-spring rankings. I was curious as to which teams, based on one of these rankings (https://www.sportingnews.com/us/ncaa-football/news/college-football-rankings-sns-pre-preseason-top-25-for-2019/1r9osjd86wpdr1alq91g458llh) was looking at the toughest schedule, at least as it appears now.

Team Rank
Alabama 1
Clemson 2
Georgia 3
Oklahoma 4
Ohio State 5
Texas 6
LSU 7
Florida 8
Michigan 9
Notre Dame 10
Texas A&M 11
Penn State 12
Oregon 13
Washington 14
Mississippi State 15
Auburn 16
Army 17
Washington State 18
Syracuse 19
Stanford 20
Wisconsin 21
UCF 22
Iowa State 23
Northwestern 24
Nebraska 25

I then assigned a value to each of the top 25 teams in the Sporting News’ rankings. This point value was simply inverse to their ranking (the 25th ranked team was worth 1 point to play, the top-ranked team is worth 25 points to play). Then, I took the top ten teams and looked at their upcoming schedule and tallied up the number of points their opponents are worth. Any opponent not ranked in the current top 25 is worth zero points. Charting the totals in a histogram shows that the point system is approximately normally distributed (i.e., similar to a bell-shaped curve).

histogram

To understand the degree of difficult beyond ordinal rankings, I standardized each teams’ overall point total relative to the other top ten teams. What we end up with is a pretty close look at how tough a schedule each of these top ten teams has compared to each other.

chart

The outcome shows that LSU is looking at a very tough schedule, while Clemson has a cake-walk ahead of them. The column on the far right displays each teams’ overall difficulty in terms of standard deviations from the group (top ten teams) average.

Notes:

I considered penalizing teams for home games and non-P5 opponents, but it wouldn’t change the outcome, so I chose not to complicate the analysis. Furthermore, if any of these teams are to make the playoffs, how they do against top 25 competition will be key.

A 5-star bias? A case study.

247 sports, a college football recruiting heavyweight, just released their top 25 running backs list for the 2019 college football season. They also included 10 ‘Honorable Mentions’.  Here is the list (Honorable mentions in blue, all tied for 26th rank):

Rank Player Team HS Year HS Rating HS Stars
26 Stevie Scott Indiana 2018 0.8402 3
26 Brian Robinson Alabama 2017 0.9361 4
26 Isaiah Bowser Northwestern 2018 0.8639 3
26 Larry Rountree III Missouri 2017 0.8435 3
26 Kylin Hill  Mississippi State 2017 0.9184 4
26 Jordan Cronkrite USF 2015 0.8853 3
26 Anthony McFarland Maryland 2017 0.9537 4
26 Master Teague Ohio State 2018 0.9132 4
26 Chuba Hubbard Oklahoma State 2017 0.8868 3
26 Trey Sermon Oklahoma   2017 0.9232 4
25 Zack Moss Utah 2016 0.8389 3
24 Spencer Brown UAB 2017 0.758 2
23 Pooka Williams Kansas 2018 0.9055 4
22 Darrynton Evans Appalachian State 2015 0.7519 2
21 Joshua Kelley UCLA 2015 0.7667 2
20 Rakeem Boyd Arkansas 2018 0.8467 3
19 Ben LeMay Charlotte 2016 0.8273 3
18 Lamical Perine Florida 2016 0.8699 3
17 Salvon Ahmed Washington 2017 0.9476 4
16 Ricky Slade Penn State 2018 0.9853 5
15 Cam Akers FSU 2017 0.9984 5
14 CJ Verdell Oregon 2017 0.8752 3
13 Ke’Shawn Vaughn Vanderbilt 2015 0.8953 4
12 Michael Warren II Cincinnati 2017 0.8707 3
11 J.J. Taylor Arizona 2016 0.8396 3
10 Kennedy Brooks Oklahoma 2017 0.9159 4
9 Jermar Jefferson Oregon State 2018 0.8619 3
8 Greg McCrae UCF 2016 0.8135 3
7 Najee Harris Alabama 2017 0.9984 5
6 J.K. Dobbins Ohio State 2017 0.9791 4
5 D’Andre Swift Georgia 2017 0.9838 5
4 AJ Dillon Boston College 2017 0.8803 3
3 Eno Benjamin Arizona State 2017 0.94 4
2 Jonathan Taylor Wisconsin 2017 0.8854 3
1 Travis Etienne Clemson 2017 0.9171 4

There’s nothing on the list that I really care to disagree with. As a Gator fan, I would Perine number one, but there may be some bias occurring there. I certainly think he is better than 18th, but I digress…

5starscores

The 2018 statistics were taken for each player on the list and analyzed. Of note, only the stats for those players who were in the top 290 in performance last year were included (because this is how many were available at my source). In the above table, the production for each of the players on 247’s list is displayed. There were four 5-star players on the list and three 2-stars, comprising 11% and 8 % of the list, respectively. The key statistic here is where each of the star categories averaged their rank on the list. The 5-stars averaged the 11th (10.8) overall ranking and the 2-stars averaged 22nd (22.3).  4-stars were ranked evenly with 3-stars on average, 16.9 to 17.0.

When we take each of these categories and ranking them from 1 to 4 (1 being the highest), here is what we get:

5staravgs

The 5-star running backs averaged the best ranking, number of receptions, and receiving touchdowns. However, they were last in rushing yards, rushing touchdowns, plays from scrimmage, total yards, and total touchdowns. Overall, their production was barely better than that of the 2-stars (2.8 to 2.9) on average across the categories.

For the statistics folks, the difference between the 2-star averages in terms of where they are ranked on the list and that of the 5-star averages is statistically significant:

An independent-samples t-test was conducted to compare the rank of 2-star and 5-star players. Given a violation of Levene’s test for homogeneity of variances, (F= 32.775, p = .002), a t-test not assuming homogeneous variances was calculated. There was a significant difference in the scores for the 2-stars (M=22.33, SD=1.528) and 5-stars (M=10.75, SD=5.560) conditions; t(3.58)= 3.436, p= 0.02. The size of this effect (d = 2.84), as indexed by Cohen’s (1988) coefficient d was found to exceed the convention for a large effect size (d = 0.80).

These results suggest that 5-star players were ranked significantly higher on this list than were 2-star players. But did the production between the two groups warrant the disparity in the ranking?

An independent-samples t-test indicated that total yards were not significantly higher for
5-stars (M = 995.66, SD = 304.93) than for 2-stars (M = 1319.0, SD = 102.22), t(4) = 1.741,
p = .157, d = 0.35. Equal variances were assumed. 

Ricky Slade from Penn State was not included in the statistical comparison of yards because he wasn’t among the top 290 performers last year. His low production scores would’ve drug the 5-stars overall average down. (Did he redshirt last year?).

So why the disparity? 5-star running backs are given the highest ranking, but overall had the lowest production (if you included Slade) of each of the groups? I think there was certainly a bias for those players in effect in this particular ranking. When we look at each player’s high school year and average them out per star ranking, we can see the 5-stars are typically newer. This goes down the line:

Stars Avg HS yr
5 2017.3
4 2017
3 2016.8
2 2015.7

As you can see, the lower the star ranking, the more likely the player was to have been in college longer. This players ranking was likely on potential and subjective opinion.

Disclaimer because some college football fans get upset about everything:

This is just a case study of one list that was put out by 247 sports. Their list may be complete garbage and invalid in every way, not representative of the population, etc. I know. The point here was to take a micro-level look at the potential bias that occurs when sports reports, journalists, etc do these rankings.

Yes, the 5-star players play against tougher competition than the typical 2-star. Yes, that matters. But they don’t play against tougher competition than the 4-stars and most of the 3-stars.

Also: Alabama (Brian Robinson and Najee Harris) and Ohio State (Master Teague and JK Dobbins) have 2 players each on the list. Florida has 2 players it recruited on the list (LaMical Perine and Jordan Cronkite), but Cronkite transferred (now as USF).

2018 Teams with 5-stars and their win %

Here is some data on how all teams who had at least one 5-star player on their rosters faired in 2018 (regular season only).

2018 chart 5 stars.winP

This chart above is neat because you can see the contrast levels between the number of 5-stars and winning percentage clearly. Notre Dame, for instance, had a low number of 5-stars (1) and a high winning percentage (100%).

2018 5 star regression

2018 5 star histogram

2018 5 star regression statistics

The R square (yellow highlight) explains the variance attributed to the number of 5-stars on a team’s roster. The significance (blue highlight) shows the likelihood of the relationship is due to randomness. The Multiple R (not highlighted) shows the correlation between the number of 5-stars on the roster and win %.

Because the data isn’t normally distributed (doesn’t take a bell-shaped curve in the histogram above), quartiles are a preferred method of looking for outliers:

Teams w 5-star No. of 5-Star Win % 5-starsOutlier Win% Outlier
Georgia 14 0.92 Yes No
Alabama 12 1.00 Yes No
Ohio State 11 0.92 Yes No
Clemson 9 1.00 Yes No
USC 8 0.42 No No
FSU 7 0.42 No No
UCLA 5 0.25 No No
LSU 4 0.75 No No
Michigan 4 0.83 No No
Penn State 4 0.75 No No
Oklahoma 3 0.92 No No
Stanford 3 0.64 No No
Texas 2 0.75 No No
Florida 2 0.75 No No
Auburn 2 0.58 No No
Tennessee 2 0.42 No No
Ole Miss 2 0.42 No No
Maryland 2 0.42 No No
ND 1 1.00 No No
Texas A&M 1 0.67 No No
Miami 1 0.58 No No
Washington 1 0.77 No No
Miss State 1 0.67 No No
Arkansas 1 0.17 No No
Pittsburgh 1 0.54 No No
Oklahoma St 1 0.50 No No
West Virginia 1 0.73 No No
Iowa 1 0.67 No No
Houston 1 0.67 No No

 

Recruiting and its statistical success to college football in the only metric that matters – winning.

I find the fan fascination with recruiting fascinating. While you’ll never hear me argue against recruiting’s importance – after all, the coaches put so much emphasis on it and they are the true experts – I also don’t subscribe to the theory that it is all about the Jimmy’s and Joe’s and not the X’s and O’s. I think, based on every detailed analysis I and others have done on recruiting, that coaching is the key factor in winning. Not the only factor, but the number one key.

The purpose of this analysis is not to explain every single variable that contributes to winning (SOS, Coaching, home field, randomness, etc.). The point is to isolate the discussion on recruiting across several dimensions. It is often helpful to isolate a variable in order to understand how it is part of a bigger system.

That being said, recruiting is strongly correlated with winning percentage. I analyzed the direct linear relationship between 57 Power 5 teams since the from 2005 through 2017. I tallied up each year’s recruiting data. Then, I parsed each year for each team out along these dimensions: Number of players in year’s class, 3-star players in class, 4-star players in class, 5-star players in class, Blue Chip percentage (calculated by taking the percentage of 4 and 5-star players relative to all of the players recruited in a class), and the average rating of those players. Next, I averaged each team’s scores across each of those dimensions over the time span. First up, Blue Chip percentage (BCp):

BCp no line

The scatterplot above shows the winning percentage for each team on the vertical (y) axis and the BCp on the horizontal (x) axis. A quick visual of this chart indicates that higher BCp is associated with more winning at the P5 level. It looks as if there is a strong positive linear relationship. Next, I added a fit line to the graph:

BCp w line

In this second chart, the line confirms the initial suspicion: As BCp goes up, winning will go up as well.  The regression equation here shows that if you were to have, say a BCp of 79%, the model would predict you to win 78% of your games (y=0.44+0.43*.79, y= 0.7797). Beyond that, however, the model was statistically significant (p = .000, a= 0.05, R= .699, R2= .488). For the non-stats crowd, these numbers basically mean that there is less than a 1% chance that these findings are due to random chance, and that about 49% of winning percentage experienced in this sample is attributable to BCp and other unknown factors accounting for the other 51%. So, we have a strong positive relationship and we know how much of that relationship is due to BCp. So far, so good.

But, there was something about this chart (look at the first one without the line) that immediately caught my eye- there is an obvious curve in the lower quadrant. This lets us know that BCp and, its relationship with winning, is different for different teams. It looks to me like the strongest correlation occurs when a team is above 50 BCp or so. When we apply smoothing (LOESS), we can see this visually:

loess BCp

Things get loose in the 30- 40 range. They look chaotic to me when BCp drops below 30%:

BCp under 30

When BCp gets low, it only accounts for 15% of winning percentage (in this sample, which is 34 team averages over a 13-year period). Intuitively, this makes sense. How can blue-chip players help you win if you don’t have any? That doesn’t mean you can’t win:

Wisconsin

That little guy way up there is Wisconsin. They’ve won 76% of their games with an average BCp of 17%. Props, Badgers. There’s a flip side to that as well… UCLA has had an average BCp of 50% while winning only 54% of their games on average. I’m sure things will get better with Chip running the show…

A Better Recruiting Metric 

While BCp has a clear and strong relationship to winning percentage, the individual recruit rating (RR) using 247 Composite is even better (R=.722, R2= .522, p=.000, a=0.05). Where the BCp model accounted for 48% of the variance and correlated with winning percentage at 69.9%, average rating accounts for 52.2% of the variance and is positively correlated with winning percentage at 72.2%.  Here is that chart with a LOESS curve applied. loess rating

An Even Better Model

Having looked at recruiting’s relationship to winning percentage along these two dimensions (Blue Chip percentage, and recruit rating), I wanted to look at the variables that comprise these two dimensions. In this attempt, I used multiple linear regression. The dependent variables used are (range averages) number of recruits in the class, 3-stars in class, 4-stars in class, and 5-stars in class. What I found was even better than the previous two simple linear models (all assumptions of the MLR were met).

The correlation is .755, or 75.5% positive, with 54.6% of the variance (adj. R2). The table below shows how each variable scored:

pearsons

All 57 Teams

Here is how all of the teams included stacked up.

all teams regression

Teams that were at or near the line generally performed as one would expect given their average RR. Since that chart is a bit cluttered, here are all the teams in list format:

Team Avg Rating Average W%
USC 0.9372 75%
Ohio State 0.9283 85%
Alabama 0.9198 83%
Florida 0.9166 68%
Texas 0.9165 66%
Florida State 0.9164 71%
Georgia 0.9154 72%
LSU 0.9140 75%
Notre Dame 0.9081 63%
Miami 0.9045 60%
Oklahoma 0.9033 78%
Clemson 0.9023 73%
Michigan 0.9017 61%
Auburn 0.9005 65%
UCLA 0.8972 54%
Penn State 0.8951 71%
Tennessee 0.8939 53%
Texas A&M 0.8928 59%
South Carolina 0.8863 61%
Stanford 0.8858 63%
Oregon 0.8857 74%
Ole Miss 0.8810 50%
California 0.8809 50%
Washington 0.8806 49%
North Carolina 0.8795 52%
Virginia Tech 0.8745 70%
Arkansas 0.8742 55%
Mississippi State 0.8741 55%
Michigan State 0.8736 64%
Iowa 0.8710 60%
Arizona State 0.8709 55%
Wisconsin 0.8706 76%
Virginia 0.8700 40%
Oklahoma State 0.8691 68%
Arizona 0.8687 50%
Baylor 0.8680 52%
Texas Tech 0.8675 59%
Louisville 0.8674 65%
Illinois 0.8670 35%
Missouri 0.8668 62%
West Virginia 0.8666 56%
Georgia Tech 0.8636 58%
Boston College 0.8617 54%
Utah 0.8614 59%
Colorado 0.8611 32%
Oregon State 0.8603 47%
Vanderbilt 0.8598 41%
Minnesota 0.8594 45%
Duke 0.8591 37%
Kansas 0.8586 33%
Iowa State 0.8575 36%
Northwestern 0.8575 57%
Washington State 0.8568 38%
Kansas State 0.8560 58%
Syracuse 0.8556 36%
Indiana 0.8533 37%
Wake Forest 0.8529 46%

 

 

 

 

Florida’s Feleipe Franks performance variance in 2018.

Franks ended the 2018 season playing well. This graphic shows how he did throughout the season relative to his own performance, game by game.

ffchart1

The blue line through the middle is the average for Feleipe across several categories of passer statistics. Games with results below the line were below average (for FF). Used here were attempts, completion percentage, yards, touchdowns, and interceptions. The number of completions wasn’t included, as they would be redundant with the completion percentage. Each category was standardized, with each total standard score summed to give a full picture of how FF did game to game.

fftable1

The column on the far right is Franks’ total score for that game when standardized against his full-season performance. The scores bolded are for games against relatively crappy teams, so it puts some of his performance in context.

Also, no rushing stats are used here- only passing. I would use rushing stats, but since college football counts sacks against the rushing total, it messes it up. Lost yardage to sacks should be a completely different statistic and not count against passing or rushing in my view, but I digress…

 

Breaking down the 2020 recruiting class- March

This is a continuation of last month’s breakdown. To get an understanding, I am tracking the changes in recruiting leans (from 247 composite CB/commits) over the next 12 months to record the amount of fluctuation that occurs in a recruiting season. Here are this month’s tables:

march19RRchanges

50.21

51.plus

The list above depicts the 71 teams that are considered a ‘lean’ by 247 Crystal Ball predictions for at least one of the top rated 1000 players in the 2020 high school football class. Inevitably, someone will argue that it is way too early to predict anything and that the CB forecasts are garbage. I’m not arguing against any of that. I’m interested in how much fluctuation this ‘market’ undergoes throughout the year. This way I’ll know when handwringing (which I don’t do) over a recruit’s decision to play college football is appropriate.

Here is a current look at how the leans favor Florida:

marchGATORSleans

One interesting thing I noticed is that the Gators are trending for 100% of the 5-stars from the state of Florida. There’s only one (Bowman), but whatever. I would think more would be from Florida. Here is how the numbers look by state:

march5star

march4star

popchart

Interesting stuff. To me anyways…

Breaking down the 2020 recruiting class

Now that 2019 is in the books, let’s take a look at how 2020 is shaping up. Obviously, class metrics will change considerably. The benefit to charting how things are looking now versus how they shape up a year from now will provide insight as to how much fluctuation occurs, and maybe provide some relief for fans experiencing angst over their school’s recruiting efforts before the classes are signed. I expect lots of change between now and this time next year, but here is how things are shaping up for next year’s class at the moment.

Overall Summary:

TOTAL N 5-stars N 4-stars N 3-stars
1000 34 309 657
Tot Leaning home 5-star leaning home 4-star leaning home 3-star leaning away
257 15 129 113
Tot Leaning away 5-star leaning away 4-star leaning away 3-star leaning home
211 17 119 75
% Leaning Home % 5-star leaning home % 4-star leaning home %3-star leaning home
26% 44% 42% 17%
% Leaning Away % 5-star leaning away % 4-star leaning away %3-star leaning away
21% 50% 39% 11%

The above chart shows the breakdown of how the top 1000 recruits (247 Composite) are leaning. Many aren’t leaning toward a school yet. Out of the 34 five-star recruits, 15 are leaning toward an in-state school while 17 are leaning toward an out-of-state school. The 2019 class saw 65% of the five-stars leave their home state. Right now, that figure is at 50%.

By Team:

College lean No. of leans No. 5-star No. 4-star No. 3-star Avg. Rate of lean
UCLA 3 1 2 0 0.9568
Georgia 12 3 7 2 0.9458
Ohio State 27 6 18 3 0.9441
Clemson 17 3 13 1 0.9437
USC 13 3 9 1 0.9368
Notre Dame 12 0 11 1 0.9365
LSU 23 2 19 2 0.9360
Penn State 14 3 9 2 0.9356
Alabama 15 2 10 3 0.9338
Oklahoma 14 1 10 3 0.9298
Stanford 9 1 7 1 0.9289
Florida 18 1 13 4 0.9282
Miami 18 0 14 4 0.9220
Washington 7 1 3 3 0.9219
Texas 15 0 10 5 0.9213
N.C. State 7 1 4 2 0.9185
West Virginia 1 0 1 0 0.9149
Louisville 3 0 2 1 0.9143
Tennessee 8 0 5 3 0.9117
Arizona 2 0 1 1 0.9090
Texas A&M 22 3 8 11 0.9076
Florida State 16 1 9 6 0.9074
South Carolina 12 0 8 4 0.9056
Auburn 10 0 7 3 0.9055
Oregon 11 0 8 3 0.9041
Ole Miss 7 0 4 3 0.9041
UTSA 1 0 1 0 0.9020
Michigan 15 0 10 5 0.8963
Arizona State 2 0 1 1 0.8943
North Carolina 4 0 3 1 0.8921
Wisconsin 7 0 2 5 0.8866
Nebraska 2 0 1 1 0.8863
Mississippi State 8 0 4 4 0.8835
Virginia Tech 5 0 2 3 0.8832
California 4 0 1 3 0.8818
Minnesota 5 0 1 4 0.8795
Fresno State 1 0 0 1 0.8789
Arkansas 10 0 1 9 0.8785
TCU 2 0 1 1 0.8781
Michigan State 10 0 2 8 0.8743
Kentucky 4 0 0 4 0.8736
Duke 3 0 0 3 0.8703
Purdue 3 0 1 2 0.8670
Oregon State 3 0 1 2 0.8668
Maryland 2 0 0 2 0.8667
Northwestern 4 0 0 4 0.8663
Iowa 8 0 1 7 0.8634
Utah 3 0 0 3 0.8626
Oklahoma State 4 0 1 3 0.8608
N/A 532 2 61 469 0.8605
Brigham Young 5 0 1 4 0.8596
Missouri 5 0 0 5 0.8576
Baylor 5 0 0 5 0.8569
Iowa State 5 0 0 5 0.8561
Boston College 6 0 1 5 0.8527
Rutgers 1 0 0 1 0.8527
Texas Tech 3 0 0 3 0.8520
Cincinnati 2 0 0 2 0.8477
Tulsa 1 0 0 1 0.8477
Virginia 2 0 0 2 0.8445
Colorado 1 0 0 1 0.8427
Vanderbilt 2 0 0 2 0.8366
UAB 1 0 0 1 0.8366
UCF 1 0 0 1 0.8333
Wake Forest 1 0 0 1 0.8333
Indiana 1 0 0 1 0.8316

The above table is a breakdown of how each school is doing in recruiting among the top 1000 players currently. Florida currently is 16th in terms of average talent rating for recruits committed/leaning toward them with a score of .9282. UCLA has the highest average, but they only have 3 leans.

By Position:

Position Offense Defense Skill Pos Total 5-stars 4-stars 3-stars Avg. rating
SDE No Yes No 54 3 16 35 0.8803
RB Yes No Yes 73 5 24 44 0.8895
ILB No Yes No 35 2 8 25 0.8765
OLB No Yes No 75 2 27 46 0.8824
WR Yes No Yes 162 5 61 96 0.8895
OT Yes No No 98 3 33 62 0.8870
PRO Yes No Yes 46 1 12 33 0.8798
ATH Yes No Yes 85 1 23 61 0.8788
CB No Yes Yes 78 4 21 53 0.8814
OG Yes No No 43 1 11 31 0.8759
DT No Yes No 66 1 28 37 0.8908
WDE No Yes No 38 3 11 24 0.8864
APB Yes No Yes 13 1 3 9 0.8829
DUAL Yes No Yes 33 1 6 26 0.8718
TE Yes No No 34 1 5 28 0.8692
OC Yes No No 10 0 1 9 0.8688
S No Yes Yes 57 0 19 38 0.8766

This table breaks down the class by position. There are 73 running backs in the top 1000 players, 5 of which are 5-stars, 24 are 4-stars, and 44 are 3-stars. The overall average rating for the position group is .8895. The skill position designation is subjective. Feel free to let me know if you disagree and why. I will gladly take input on that.

The University of Florida Gators:

future gators

This table depicts how Florida’s class is looking now. So far, so good.

By State:

2020collegestate

This map shows how many recruits from this sample are leaning/committed to schools in various states. 53 of them are leaning toward Florida teams, with Florida and Miami each having 18, FSU having 16, and UCF having 1.

By Home State:

2020homestate

This map depicts where the top 1000 recruits for 2020 are from. Of note, 3 are from Canada and not depicted here. Florida and Texas are doing a lot of the heavy lifting, however, Georgia is producing some great players. Here is how the per capita breakdown looks:

State 2018 Population Players produced Per Capita lean (by 10,000)
Hawaii 1420491 18 78.9
Georgia 10519475 105 100.2
Alabama 4887871 45 108.6
Louisiana 4659978 39 119.5
Tennessee 6770010 41 165.1
Florida 21299325 117 182.0
Wisconsin 1805832 9 200.6
Texas 28701845 139 206.5
Nevada 3034392 11 275.9
Missouri 6126452 22 278.5
Kentucky 4468402 16 279.3
Arizona 7171646 25 286.9
Maryland 6042718 19 318.0
Michigan 9995915 30 333.2
Ohio 11689442 33 354.2
South Carolina 5084127 13 391.1
Oklahoma 3943079 10 394.3
Utah 3161105 8 395.1
Virginia 8517685 21 405.6
California 39557045 88 449.5
North Carolina 10383620 23 451.5
Nebraska 1929268 4 482.3
Washington 7535591 15 502.4
Iowa 3156145 6 526.0
Kansas 2911505 5 582.3
Arkansas 3013825 5 602.8
Indiana 6691878 10 669.2
Pennsylvania 12807060 16 800.4
Minnesota 5611179 7 801.6
Colorado 5695564 7 813.7
Oregon 4190713 5 838.1
Illinois 12741080 15 849.4
Massachusetts 6902149 7 986.0
Connecticut 3572665 3 1190.9