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Ole Miss was easily the most volatile of 2014's top college football teams

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Let's play with single-game percentiles! (NOTE: I updated the post to include two extra points I originally intended to make and completely forgot to actually make before hitting Publish.)

By Bill C.
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Spruce Derden-USA TODAY Sports

This year's 128-team season preview series is complete! (I even tacked on a 128-team POWER RANKINGS piece at the end, which I'm sure people will react to with calmness, tact, and measured takes.)

Now that I've got a little bit of time on my hands, I thought it would be interesting to explore one of the aspects of the previews that I found the most interesting: percentiles. In each preview, I presented something like this:

2014 Schedule & Results

Record: 6-7 | Adj. Record: 9-4 | Final F/+ Rk: 31
Date Opponent Opp. F/+ Rk Score W-L Percentile
Performance		 Adj. Scoring
Margin		 Win
Expectancy
1-Sep at Louisville 23 13-31 L 47% -1.6 13%
6-Sep Florida A&M N/A 41-7 W 91% 30.8 100%
13-Sep Arkansas State 66 41-20 W 97% 43.8 100%
20-Sep at Nebraska 30 31-41 L 62% 7.2 35%
27-Sep Duke 51 22-10 W 94% 36.3 99%
4-Oct Georgia Tech 8 17-28 L 54% 2.3 23%
11-Oct Cincinnati 47 55-34 W 99% 52.4 100%
23-Oct at Virginia Tech 33 30-6 W 99% 52.3 100%
1-Nov North Carolina 70 47-20 W 98% 48.0 100%
15-Nov Florida State 15 26-30 L 56% 3.7 32%
22-Nov at Virginia 39 13-30 L 10% -30.0 0%
29-Nov Pittsburgh 43 23-35 L 22% -18.1 1%
27-Dec vs. South Carolina 38 21-24 L 30% -12.0 10%

This was similar to the Adj. Score measure that I shared in previous years' previews, but I think it communicates a clearer message. The idea was to take the key, Five Factors-related stats from each game and, instead of presenting it as a "single-game S&P+" type of score, present it in terms of national percentiles. It's a concept most of us are familiar with because of standardized tests, and it communicates a complex set of stats in a simple, intuitive manner. I like it.

Since the percentiles ARE basically a single-game S&P+ score, there's a very strong correlation between a team's average percentile performance and its full-season S&P+ rating. But I thought it would be interesting to break these percentiles out a bit further.

Below, you'll find teams' maximum, minimum, median, and mean percentile scores, along with each team's week-to-week variance. These numbers will give you a pretty good explanation of how each team finished where it finished.

Here are the correlations between each of these numbers and a team's full-season S&P+ rating:

Max 0.774
Min 0.774
Median 0.972
Mean 0.993
Variance -0.008

As you would expect, the mean matches up nearly perfectly with the full-season number. The only reason the correlation isn't a perfect 1.000 is that each game has a different number of plays, and the full-season number is still based in part on play-by-play data.

But looking at max, min, and median tells us some interesting things about certain teams (like, say, Ole Miss). Here's the complete team list, sorted by S&P+ rank:

Team Max Rk Min Rk Median Rk Mean Rk Variance Rk Overall S&P+ Rk
Ohio State 100% 1 49% 3 95% 1 90% 2 2% 3 30.2 1
Alabama 100% 2 51% 1 94% 5 90% 1 2% 1 28.3 2
Oregon 99% 23 46% 5 95% 3 85% 3 3% 17 23.7 3
Auburn 99% 11 46% 4 88% 8 85% 4 3% 9 23.6 4
Arkansas 100% 3 37% 11 88% 9 80% 8 5% 37 23.1 5
Ole Miss 100% 6 11% 50 95% 2 79% 9 9% 114 23.0 6
Georgia 99% 14 29% 16 94% 4 82% 5 5% 41 22.6 7
TCU 100% 5 34% 12 89% 6 80% 6 3% 18 19.4 8
UCLA 99% 21 42% 7 81% 16 78% 11 4% 21 19.0 9
Georgia Tech 97% 36 49% 2 86% 12 80% 7 3% 13 18.7 10
Michigan State 99% 20 45% 6 87% 10 79% 10 4% 26 18.6 11
Mississippi State 99% 24 29% 15 83% 14 78% 13 5% 43 17.8 12
Oklahoma 100% 7 23% 22 82% 15 75% 15 6% 66 17.7 13
Baylor 98% 31 30% 14 86% 11 78% 12 5% 32 17.2 14
Stanford 98% 28 28% 17 88% 7 75% 17 7% 81 16.6 15
LSU 99% 10 14% 41 84% 13 73% 20 9% 109 16.5 16
Clemson 100% 4 27% 18 70% 33 72% 21 6% 64 15.5 17
Boise State 99% 19 18% 31 75% 28 74% 18 6% 62 15.4 18
Tennessee 99% 12 18% 32 70% 34 69% 28 7% 87 14.2 19
USC 100% 9 21% 27 77% 23 71% 23 7% 82 14.2 20
Marshall 95% 47 39% 10 78% 20 75% 16 3% 16 14.1 21
Florida State 95% 48 40% 9 80% 17 76% 14 2% 5 13.7 22
Missouri 99% 26 20% 29 77% 21 71% 22 6% 58 13.0 23
Louisville 96% 45 42% 8 76% 24 73% 19 3% 14 12.9 24
Wisconsin 98% 29 2% 113 77% 22 70% 24 8% 98 12.8 25
Team Max Rk Min Rk Median Rk Mean Rk Variance Rk Overall S&P+ Rk
Miami-FL 99% 18 10% 52 62% 46 66% 32 10% 121 12.7 26
Notre Dame 98% 30 5% 75 75% 27 70% 25 7% 86 12.1 27
Kansas State 98% 35 22% 23 73% 31 69% 27 6% 49 11.9 28
Florida 96% 43 21% 26 69% 35 69% 26 6% 59 11.6 29
Texas A&M 98% 32 4% 86 60% 51 66% 35 9% 111 10.4 30
Nebraska 94% 54 9% 57 79% 18 68% 30 8% 94 10.3 31
Arizona State 94% 56 13% 45 79% 19 68% 29 8% 95 10.2 32
Texas 99% 15 14% 40 75% 26 65% 37 8% 107 10.0 33
Louisiana Tech 99% 13 5% 81 68% 36 64% 40 10% 120 9.9 34
Arizona 96% 46 16% 37 64% 39 66% 33 7% 71 9.5 35
Minnesota 99% 17 21% 25 59% 52 64% 38 6% 54 9.1 36
Virginia Tech 93% 58 8% 59 75% 25 66% 31 7% 74 8.9 37
Cincinnati 96% 42 7% 68 73% 30 66% 34 7% 83 8.8 38
Boston College 90% 77 25% 20 65% 38 66% 36 4% 27 8.4 39
West Virginia 99% 25 31% 13 62% 48 63% 41 4% 22 8.0 40
Utah 98% 33 15% 39 64% 40 63% 42 7% 88 8.0 41
Virginia 98% 34 26% 19 62% 49 63% 43 6% 55 7.9 42
South Carolina 95% 52 23% 21 73% 32 64% 39 6% 50 7.9 43
Pittsburgh 99% 16 17% 34 54% 60 62% 44 7% 77 7.9 44
Michigan 100% 8 9% 54 58% 55 58% 50 10% 116 6.8 45
Penn State 97% 39 7% 62 59% 53 60% 47 7% 76 6.1 46
BYU 95% 50 13% 43 62% 45 61% 46 7% 72 6.1 47
Navy 99% 22 19% 30 54% 62 58% 48 7% 78 5.7 48
Memphis 91% 69 4% 88 66% 37 61% 45 6% 60 5.1 49
NC State 93% 57 1% 114 74% 29 58% 49 11% 124 4.0 50
Team Max Rk Min Rk Median Rk Mean Rk Variance Rk Overall S&P+ Rk
Western Kentucky 97% 41 7% 69 62% 47 57% 52 7% 84 3.9 51
Utah State 94% 53 4% 87 56% 57 58% 51 8% 89 3.6 52
Maryland 93% 61 8% 60 63% 41 57% 53 8% 91 3.3 53
Air Force 82% 98 8% 61 63% 43 55% 55 6% 57 2.2 54
North Carolina 97% 37 7% 67 57% 56 54% 57 8% 104 2.1 55
Colorado State 91% 74 4% 90 59% 54 55% 56 8% 103 2.0 56
Georgia Southern 85% 90 2% 108 61% 50 55% 54 7% 79 2.0 57
Kentucky 93% 62 5% 84 56% 58 53% 58 11% 127 1.5 58
Arkansas State 96% 44 8% 58 50% 73 51% 60 8% 102 1.0 59
UL-Lafayette 89% 80 5% 79 63% 44 52% 59 9% 108 0.4 60
California 93% 60 21% 24 50% 72 50% 69 4% 25 0.3 61
Western Michigan 92% 66 7% 70 48% 75 50% 64 8% 100 0.1 62
Oklahoma State 91% 70 7% 66 51% 69 50% 62 8% 101 0.0 63
Texas Tech 85% 93 20% 28 48% 74 50% 66 4% 23 0.0 64
Illinois 91% 71 13% 47 52% 67 50% 70 8% 99 -0.1 65
Temple 92% 65 7% 63 52% 68 50% 71 8% 105 -0.3 66
Toledo 86% 89 13% 46 53% 64 50% 63 6% 52 -0.3 67
Washington State 87% 86 14% 42 47% 77 49% 73 6% 70 -0.5 68
Rutgers 92% 63 6% 72 50% 71 50% 65 10% 119 -0.6 69
Iowa 95% 49 2% 105 54% 63 50% 61 10% 118 -0.6 70
Central Florida 91% 73 4% 93 55% 59 50% 68 8% 97 -0.8 71
East Carolina 87% 85 17% 33 53% 65 48% 74 5% 29 -0.9 72
Duke 91% 72 3% 101 54% 61 50% 67 6% 63 -1.0 73
Oregon State 93% 59 13% 44 45% 80 47% 76 8% 93 -1.1 74
Washington 85% 91 10% 51 51% 70 48% 75 8% 92 -1.3 75
Team Max Rk Min Rk Median Rk Mean Rk Variance Rk Overall S&P+ Rk
Rice 90% 75 4% 91 63% 42 49% 72 11% 126 -1.5 76
Colorado 85% 92 10% 53 45% 79 47% 77 5% 30 -1.9 77
Syracuse 98% 27 16% 36 37% 90 43% 87 5% 45 -2.0 78
Purdue 87% 82 15% 38 47% 78 46% 78 6% 61 -2.1 79
Northern Illinois 90% 76 12% 48 42% 84 45% 81 5% 36 -2.2 80
Nevada 78% 108 16% 35 42% 85 45% 82 4% 19 -2.2 81
South Alabama 97% 40 3% 99 43% 83 46% 79 10% 122 -2.8 82
San Diego State 87% 84 5% 83 47% 76 45% 80 6% 51 -2.9 83
UAB 88% 81 7% 64 35% 93 44% 84 9% 112 -3.0 84
Northwestern 94% 55 3% 97 44% 82 43% 85 8% 106 -3.9 85
Indiana 92% 67 6% 74 52% 66 45% 83 10% 117 -3.9 86
Middle Tennessee 82% 97 11% 49 40% 88 42% 90 6% 53 -4.3 87
UTEP 97% 38 1% 116 41% 87 42% 88 11% 125 -4.5 88
Central Michigan 84% 94 1% 123 36% 92 43% 86 7% 85 -5.4 89
Houston 81% 102 1% 122 41% 86 42% 89 6% 56 -5.8 90
New Mexico 79% 103 9% 55 31% 97 38% 92 5% 46 -6.5 91
Kansas 92% 64 4% 95 30% 100 38% 91 9% 113 -7.1 92
Tulane 84% 95 7% 65 29% 103 36% 94 6% 68 -7.5 93
UL-Monroe 79% 104 1% 115 44% 81 37% 93 5% 28 -8.0 94
Iowa State 78% 106 5% 76 37% 91 35% 96 5% 40 -8.3 95
Bowling Green 86% 87 4% 92 31% 98 34% 100 6% 67 -9.1 96
Florida Atlantic 87% 83 3% 98 32% 96 35% 97 7% 75 -9.1 97
Ohio 92% 68 4% 94 29% 102 34% 99 8% 96 -9.4 98
Miami-OH 68% 118 5% 77 34% 94 32% 104 3% 12 -9.6 99
Fresno State 73% 111 3% 104 39% 89 36% 95 8% 90 -9.7 100
Team Max Rk Min Rk Median Rk Mean Rk Variance Rk Overall S&P+ Rk
Kent State 78% 105 2% 112 32% 95 34% 101 5% 44 -9.7 101
Old Dominion 66% 120 5% 80 31% 99 31% 107 4% 20 -10.6 102
Southern Miss 71% 115 5% 78 28% 105 31% 106 5% 34 -10.7 103
Akron 86% 88 2% 109 16% 119 33% 102 9% 115 -10.9 104
Vanderbilt 73% 110 3% 103 28% 104 31% 105 5% 38 -10.9 105
Texas State 82% 99 5% 85 22% 112 30% 108 6% 69 -11.0 106
Wyoming 89% 79 9% 56 18% 118 29% 111 7% 73 -11.2 107
Georgia State 77% 109 3% 100 27% 106 30% 109 5% 47 -11.5 108
Idaho 67% 119 6% 71 27% 107 27% 114 2% 7 -11.6 109
UTSA 95% 51 1% 126 30% 101 33% 103 9% 110 -12.1 110
Florida International 71% 114 2% 110 19% 116 30% 110 6% 65 -12.3 111
Wake Forest 62% 122 6% 73 26% 108 28% 113 3% 15 -12.4 112
Appalachian State 83% 96 0% 128 25% 110 35% 98 11% 123 -12.5 113
San Jose State 72% 113 3% 102 26% 109 28% 112 5% 48 -13.6 114
South Florida 54% 124 3% 96 22% 111 25% 117 3% 11 -13.7 115
Ball State 72% 112 4% 89 18% 117 26% 116 5% 35 -14.2 116
UNLV 45% 126 5% 82 20% 114 22% 120 2% 2 -15.0 117
Tulsa 45% 127 2% 107 22% 113 23% 119 2% 6 -15.5 118
Connecticut 78% 107 2% 111 15% 120 22% 121 5% 33 -16.3 119
Massachusetts 68% 117 1% 121 14% 121 22% 123 4% 24 -17.5 120
Troy 70% 116 1% 117 14% 122 22% 122 5% 42 -18.1 121
Buffalo 81% 101 1% 125 19% 115 25% 118 7% 80 -18.8 122
Hawaii 52% 125 2% 106 13% 123 18% 126 2% 8 -18.8 123
SMU 55% 123 1% 119 13% 124 18% 125 3% 10 -19.3 124
Army 64% 121 1% 118 6% 126 20% 124 5% 31 -19.8 125
North Texas 90% 78 0% 127 6% 127 26% 115 12% 128 -20.5 126
New Mexico State 44% 128 1% 124 10% 125 15% 127 2% 4 -21.4 127
Eastern Michigan 81% 100 1% 120 5% 128 14% 128 5% 39 -24.6 128

52 teams hit the 95th percentile at least once, which is more than I would have expected. Even more interesting and/or maddening: of these 52 teams, 15 also played at least one game at the 10th percentile or lower: Arkansas State, Cincinnati, Iowa, Louisiana Tech, Miami, Michigan, North Carolina, Notre Dame, Penn State, South Alabama, Texas A&M, UTEP, UTSA, Western Kentucky, and Wisconsin.

Meanwhile, while most of the teams at the top and bottom of the rankings had pretty low variance overall (which is why they ended up on one end or the other on the bell curve), a few bucked that trend. At the high end, Ole Miss, Oklahoma, Stanford, and LSU had pretty crazy levels of variance, as did Tennessee and USC. Meanwhile, at the lower end, teams like Appalachian State (which improved dramatically at the end of the year), Buffalo, and North Texas experienced pretty high highs to go with steady lows.

What does this mean for 2015? Well ... I'm not sure. This is a pretty new concept, but it will be interesting to keep working with this to see if the volatile teams are easier or (more likely) harder to project the next season, and if something like median is more effective in projections than mean.

UPDATE: Two more points I originally intended to make.

1. As mentioned at Tomahawk Nation, consistency saved Florida State. The Seminoles never really put together a perfect performance and were stuck in the teens in terms of both median and mean, but their extreme consistency bailed them out. They were in the 80th to 85th percentile seemingly every single week and didn't lay an outright egg until the Rose Bowl.

2. The fact that 78 different teams hit the 90th percentile at least once (including North Texas, UTSA, and, yes, Kansas), and every team hit the 51st percentile or lower at least once, reminds us why head-to-head results are a bit overrated. College football teams are bipolar, and just because you were better than a team one week doesn't mean you would be the other 13 or so. Head-to-head is a good conference tie-breaker, but that's about it.

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