library(tidyverse)10 Multiple regression
Last chapter, we looked at correlations and linear regression to predict how one element of a game would predict the score. But we know that a single variable, in all but the rarest instances, is not going to be that predictive. We need more than one. Enter multiple regression. Multiple regression lets us add – wait for it – multiple predictors to our equation to help us get a better fit to reality.
That presents it’s own problems. So let’s get set up. The dataset we’ll use is all college football games since the 2011 season.
For this walkthrough:
We need the tidyverse.
And the data.
logs <- read_csv("data/footballlogs1120.csv")Rows: 15637 Columns: 55
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (8): HomeAway, Opponent, Result, TeamFull, TeamURL, Outcome, Team, Con...
dbl (46): Game, PassingCmp, PassingAtt, PassingPct, PassingYds, PassingTD, ...
date (1): Date
ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.One way to show how successful a footballl team was for a game is to show the differential between the team’s score and the opponent’s score. Score a lot more than the opponent = good, score a lot less than the opponent = bad. And, relatively speaking, the more the better. So let’s create that differential. Let’s also get our net yardage stat back. And because we’ll need it later, let’s add the turnover margin.
logs <- logs |> mutate(
Differential = TeamScore - OpponentScore,
NetYards = OffensiveYards - DefYards,
TurnoverMargin = DefTotalTurnovers - TotalTurnovers)The linear model code we used before is pretty straight forward. Its field is predicted by field. Here’s a simple linear model that looks at predicting a team’s point differential by looking at their net yards.
yards <- lm(Differential ~ NetYards, data=logs)
summary(yards)
Call:
lm(formula = Differential ~ NetYards, data = logs)
Residuals:
Min 1Q Median 3Q Max
-52.037 -8.743 -0.002 8.750 64.480
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.491540 0.105212 4.672 3.01e-06 ***
NetYards 0.104609 0.000588 177.899 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 13.12 on 15635 degrees of freedom
Multiple R-squared: 0.6693, Adjusted R-squared: 0.6693
F-statistic: 3.165e+04 on 1 and 15635 DF, p-value: < 2.2e-16Remember: There’s a lot here, but only some of it we care about. What is the Adjusted R-squared value? What’s the p-value and is it less than .05? In this case, we can predict 67 percent of the difference in differential with the net yardage in the game.
To add more predictors to this mix, we merely add them. But it’s not that simple, as you’ll see in a moment. So first, let’s look at adding how well the other team shot to our prediction model:
model1 <- lm(Differential ~ NetYards + TurnoverMargin, data=logs)
summary(model1)
Call:
lm(formula = Differential ~ NetYards + TurnoverMargin, data = logs)
Residuals:
Min 1Q Median 3Q Max
-39.027 -6.995 -0.026 6.926 40.812
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.4605936 0.0846094 5.444 5.3e-08 ***
NetYards 0.0965770 0.0004808 200.872 < 2e-16 ***
TurnoverMargin 4.1989070 0.0454293 92.427 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 10.55 on 15634 degrees of freedom
Multiple R-squared: 0.7862, Adjusted R-squared: 0.7861
F-statistic: 2.874e+04 on 2 and 15634 DF, p-value: < 2.2e-16First things first: What is the adjusted R-squared?
Second: what is the p-value and is it less than .05?
Third: Compare the residual standard error. We went from 13.12 to 10.55. The meaning of this is both really opaque and also simple – by adding data, we reduced the amount of error in our model. Residual standard error is the total distance between what our model would predict and what we actually have in the data. So lots of residual error means the distance between reality and our model is wider. So the width of our predictive range in this example shrank while we improved the amount of the difference we could predict. That’s good, and not always going to be the case.
One of the more difficult things to understand about multiple regression is the issue of multicollinearity. What that means is that there is significant correlation overlap between two variables – the two are related to each other as well as to the target output – and all you are doing by adding both of them is adding error with no real value to the R-squared. In pure statistics, we don’t want any multicollinearity at all. Violating that assumption limits the applicability of what you are doing. So if we have some multicollinearity, it limits our scope of application to college football We can’t say this will work for every football league and level everywhere. What we need to do is see how correlated each value is to each other and throw out ones that are highly co-correlated.
So to find those, we have to create a correlation matrix that shows us how each value is correlated to our outcome variable, but also with each other. We can do that in the Hmisc library. We install that in the console with install.packages("Hmisc")
library(Hmisc)We can pass in every numeric value to the Hmisc library and get a correlation matrix out of it, but since we have a large number of values – and many of them character values – we should strip that down and reorder them. So that’s what I’m doing here. I’m saying give me differential first, and then columns 9-24, and then 26-41. Why the skip? There’s a blank column in the middle of the data – a remnant of the scraper I used.
simplelogs <- logs |> select_if(is.numeric) |> select(-Game) |> select(Differential, NetYards, TurnoverMargin, everything())Before we proceed, what we’re looking to do is follow the Differential column down, looking for correlation values near 1 or -1. Correlations go from -1, meaning perfect negative correlation, to 0, meaning no correlation, to 1, meaning perfect positive correlation. So we’re looking for numbers near 1 or -1 for their predictive value. BUT: We then need to see if that value is also highly correlated with something else. If it is, we have a decision to make.
We get our correlation matrix like this:
cormatrix <- rcorr(as.matrix(simplelogs))
cormatrix$r Differential NetYards TurnoverMargin PassingCmp
Differential 1.000000000 0.8181275628 0.4840557093 0.03073777
NetYards 0.818127563 1.0000000000 0.1807370954 0.19266394
TurnoverMargin 0.484055709 0.1807370954 1.0000000000 -0.09282027
PassingCmp 0.030737767 0.1926639446 -0.0928202705 1.00000000
PassingAtt -0.197299921 -0.0070622350 -0.1947038338 0.88591513
PassingPct 0.424083501 0.4227014856 0.1571061824 0.50690125
PassingYds 0.222843006 0.3660930734 -0.0261683457 0.80648042
PassingTD 0.415721757 0.3777901574 0.1460542252 0.42193664
RushingAtt 0.366147066 0.4164286631 0.1949661739 -0.36957114
RushingYds 0.529414027 0.5514994757 0.1964807729 -0.32698768
RushingAvg 0.493052056 0.4889672815 0.1515509720 -0.19481231
RushingTD 0.575447906 0.4726991812 0.2628640231 -0.13360363
OffensivePlays 0.148784802 0.3853154462 -0.0099116497 0.53269592
OffensiveYards 0.589358113 0.7222177436 0.1307277553 0.39910909
OffenseAvg 0.612777821 0.6272790895 0.1638749970 0.15122077
FirstDownPass 0.176883748 0.3295436697 -0.0525717793 0.85819221
FirstDownRush 0.461030176 0.5134412933 0.1445016590 -0.24630019
FirstDownPen -0.005804627 -0.0143821648 -0.0209905463 0.15735051
FirstDownTotal 0.465369351 0.6158283311 0.0606623859 0.48945804
Penalties -0.014256447 0.0643018743 0.0251221670 0.13399082
PenaltyYds 0.017823806 0.0925787516 0.0380337438 0.12543433
Fumbles -0.144016227 -0.0001408652 -0.4542268044 0.01729726
Interceptions -0.347760026 -0.1826426810 -0.5660989685 0.09967713
TotalTurnovers -0.352523780 -0.1356792148 -0.7178615994 0.08532972
TeamScore 0.781082750 0.6370391683 0.3772962403 0.18279290
OpponentScore -0.769676830 -0.6317245372 -0.3733755376 0.13868761
DefPassingCmp -0.064368101 -0.2225621593 0.0832963630 0.08362273
DefPassingAtt 0.150903703 -0.0348030417 0.1826650975 0.07570845
DefPassingPct -0.420540317 -0.4218804949 -0.1551631995 0.03771812
DefPassingYds -0.257008122 -0.3977892433 0.0176164754 0.12705236
DefPassingTD -0.419326071 -0.3806220291 -0.1482026365 0.11209162
DefRushingAtt -0.364679806 -0.4151045731 -0.1934738938 -0.03529580
DefRushingYds -0.523353173 -0.5475061467 -0.1947469290 0.01889179
DefRushingAvg -0.486174349 -0.4868837846 -0.1472444819 0.04932196
DefRushingTD -0.561206330 -0.4637324675 -0.2585300201 0.06209874
DefPlays -0.190441765 -0.4206279645 0.0002203222 0.04186685
DefYards -0.598650533 -0.7299107656 -0.1317280381 0.11628312
DefAvg -0.618524672 -0.6394885894 -0.1614519054 0.10891950
DefFirstDownPass -0.216613706 -0.3658024956 0.0432422149 0.09125740
DefFirstDownRush -0.458561561 -0.5132897068 -0.1448412511 -0.01936969
DefFirstDownPen -0.021033906 -0.0094405902 0.0143978565 0.05194686
DefFirstDownTotal -0.486573031 -0.6326931830 -0.0664564117 0.06456859
DefPenalties 0.012883784 -0.0645926626 -0.0308257058 0.09792526
DefPenaltyYds -0.029196596 -0.1012747086 -0.0466939529 0.10848364
DefFumbles 0.150569794 0.0017932206 0.4609183161 -0.04082950
DefInterceptions 0.332705732 0.1663340665 0.5703875962 -0.02976917
DefTotalTurnovers 0.345532435 0.1249995913 0.7241396459 -0.04869267
Season -0.003878385 -0.0017905921 -0.0029299671 -0.02961025
PassingAtt PassingPct PassingYds PassingTD
Differential -0.197299921 0.42408350 0.222843006 0.415721757
NetYards -0.007062235 0.42270149 0.366093073 0.377790157
TurnoverMargin -0.194703834 0.15710618 -0.026168346 0.146054225
PassingCmp 0.885915129 0.50690125 0.806480418 0.421936640
PassingAtt 1.000000000 0.09284450 0.687316800 0.272470208
PassingPct 0.092844501 1.00000000 0.474237807 0.394851959
PassingYds 0.687316800 0.47423781 1.000000000 0.627995863
PassingTD 0.272470208 0.39485196 0.627995863 1.000000000
RushingAtt -0.467721623 0.03584624 -0.263550556 -0.059372629
RushingYds -0.450048289 0.10423452 -0.200749749 0.066534624
RushingAvg -0.303601875 0.13429002 -0.082915406 0.150662902
RushingTD -0.292721685 0.24141021 0.010666008 -0.029752708
OffensivePlays 0.553660940 0.12603088 0.435111936 0.214985872
OffensiveYards 0.207664639 0.46374173 0.653110800 0.559034001
OffenseAvg -0.083467058 0.47870518 0.504628728 0.524498271
FirstDownPass 0.746264311 0.47014196 0.883628794 0.521347879
FirstDownRush -0.367223327 0.12262166 -0.161794624 0.067316306
FirstDownPen 0.196989487 -0.01293930 0.128752737 0.102509961
FirstDownTotal 0.327548464 0.43305347 0.563278812 0.456785235
Penalties 0.141719302 0.03476302 0.151532040 0.082566511
PenaltyYds 0.119437753 0.05617415 0.151137509 0.100407689
Fumbles 0.027288146 -0.01805908 0.008760696 -0.048224087
Interceptions 0.255312890 -0.23653595 0.018058261 -0.114595347
TotalTurnovers 0.207413810 -0.18742681 0.019145808 -0.116667828
TeamScore -0.036371904 0.44813841 0.430680364 0.618452463
OpponentScore 0.272233697 -0.20691564 0.090860563 -0.019643341
DefPassingCmp 0.083282335 0.02282149 0.126240421 0.091787361
DefPassingAtt 0.057197756 0.05759184 0.144626108 0.144168720
DefPassingPct 0.078046303 -0.07302812 -0.001592122 -0.081479268
DefPassingYds 0.156063755 -0.02148430 0.154868859 0.075356141
DefPassingTD 0.171041258 -0.08319470 0.097949467 0.034306947
DefRushingAtt 0.084456819 -0.21399772 -0.036681379 -0.050879469
DefRushingYds 0.120099976 -0.17973763 -0.010091544 -0.071419629
DefRushingAvg 0.114820128 -0.11525287 0.008788627 -0.065807440
DefRushingTD 0.156005806 -0.15523374 0.028539434 -0.033296697
DefPlays 0.135037741 -0.14233101 0.108588070 0.094924415
DefYards 0.215421076 -0.15193326 0.116931355 0.007072996
DefAvg 0.175803966 -0.10697922 0.065890684 -0.058980036
DefFirstDownPass 0.108808477 -0.01049305 0.122699748 0.065231601
DefFirstDownRush 0.062733115 -0.15464608 -0.034057239 -0.067986273
DefFirstDownPen 0.049652307 0.02705658 0.079021185 0.073129558
DefFirstDownTotal 0.134220950 -0.10994466 0.083154570 0.016271698
DefPenalties 0.144504901 -0.04312251 0.092384684 0.087036309
DefPenaltyYds 0.163061597 -0.05395524 0.092101718 0.087050251
DefFumbles -0.035257824 -0.01766087 -0.037626266 0.043608120
DefInterceptions -0.068603306 0.06891426 0.007865801 0.088272589
DefTotalTurnovers -0.073984074 0.03983035 -0.018592363 0.094053467
Season -0.041775426 0.01257247 -0.005156032 0.007905151
RushingAtt RushingYds RushingAvg RushingTD
Differential 0.366147066 0.529414027 0.493052056 0.5754479058
NetYards 0.416428663 0.551499476 0.488967281 0.4726991812
TurnoverMargin 0.194966174 0.196480773 0.151550972 0.2628640231
PassingCmp -0.369571144 -0.326987677 -0.194812315 -0.1336036277
PassingAtt -0.467721623 -0.450048289 -0.303601875 -0.2927216853
PassingPct 0.035846245 0.104234516 0.134290025 0.2414102074
PassingYds -0.263550556 -0.200749749 -0.082915406 0.0106660076
PassingTD -0.059372629 0.066534624 0.150662902 -0.0297527078
RushingAtt 1.000000000 0.736306305 0.363907545 0.4905949788
RushingYds 0.736306305 1.000000000 0.871582822 0.6954129998
RushingAvg 0.363907545 0.871582822 1.000000000 0.6069527694
RushingTD 0.490594979 0.695413000 0.606952769 1.0000000000
OffensivePlays 0.477081505 0.246215936 0.040976244 0.1711530409
OffensiveYards 0.356138469 0.610734606 0.606712634 0.5461745292
OffenseAvg 0.137726057 0.576803443 0.708145937 0.5446857223
FirstDownPass -0.235462443 -0.195913314 -0.092668213 -0.0036037221
FirstDownRush 0.788585331 0.868855405 0.659384817 0.5950676324
FirstDownPen -0.002610866 -0.066896523 -0.081029439 -0.0008771748
FirstDownTotal 0.404462488 0.474548072 0.392289028 0.4319428611
Penalties -0.025070945 -0.003616931 0.018103053 -0.0256747928
PenaltyYds -0.002371028 0.033291751 0.054543977 0.0088896048
Fumbles 0.025073245 -0.027999174 -0.057804419 -0.0585646763
Interceptions -0.194010111 -0.216607533 -0.172826484 -0.2331549445
TotalTurnovers -0.127597560 -0.179146307 -0.166173466 -0.2114571250
TeamScore 0.343515192 0.571464139 0.560294996 0.6983293091
OpponentScore -0.223000591 -0.245986897 -0.200380832 -0.1884700826
DefPassingCmp -0.044444025 0.002547929 0.033539228 0.0431451577
DefPassingAtt 0.074067555 0.099274619 0.093839056 0.1309836648
DefPassingPct -0.216525965 -0.181038883 -0.115973736 -0.1529595683
DefPassingYds -0.049850048 -0.030243336 -0.009960610 0.0054702203
DefPassingTD -0.058851496 -0.078558079 -0.070930632 -0.0440736028
DefRushingAtt -0.410601794 -0.276558525 -0.117527616 -0.1963830525
DefRushingYds -0.279191271 -0.224659772 -0.131223074 -0.1962937077
DefRushingAvg -0.121473758 -0.133636020 -0.107575642 -0.1510025421
DefRushingTD -0.194642061 -0.192161132 -0.145173638 -0.1571341498
DefPlays -0.309000147 -0.159388487 -0.016763451 -0.0534880654
DefYards -0.249219953 -0.192608428 -0.106308789 -0.1426505149
DefAvg -0.119327650 -0.146094396 -0.126851539 -0.1516926770
DefFirstDownPass -0.089637192 -0.047185560 -0.008268549 -0.0067868508
DefFirstDownRush -0.317393880 -0.219849854 -0.099857008 -0.1738702217
DefFirstDownPen -0.047875380 -0.006920788 0.026459465 0.0113604598
DefFirstDownTotal -0.301802428 -0.193740061 -0.073461199 -0.1260218576
DefPenalties -0.044358538 -0.066428568 -0.057532616 0.0015101936
DefPenaltyYds -0.060502619 -0.088477801 -0.076887164 -0.0232505609
DefFumbles 0.071526298 0.023852046 -0.006854675 0.0815729450
DefInterceptions 0.143658098 0.119596138 0.077039894 0.1542031901
DefTotalTurnovers 0.153427918 0.104536716 0.052901642 0.1678066591
Season -0.007214300 0.014375807 0.028912307 0.0107538721
OffensivePlays OffensiveYards OffenseAvg FirstDownPass
Differential 0.1487848016 0.589358113 0.61277782 0.176883748
NetYards 0.3853154462 0.722217744 0.62727909 0.329543670
TurnoverMargin -0.0099116497 0.130727755 0.16387500 -0.052571779
PassingCmp 0.5326959178 0.399109095 0.15122077 0.858192210
PassingAtt 0.5536609399 0.207664639 -0.08346706 0.746264311
PassingPct 0.1260308782 0.463741727 0.47870518 0.470141964
PassingYds 0.4351119365 0.653110800 0.50462873 0.883628794
PassingTD 0.2149858720 0.559034001 0.52449827 0.521347879
RushingAtt 0.4770815054 0.356138469 0.13772606 -0.235462443
RushingYds 0.2462159365 0.610734606 0.57680344 -0.195913314
RushingAvg 0.0409762435 0.606712634 0.70814594 -0.092668213
RushingTD 0.1711530409 0.546174529 0.54468572 -0.003603722
OffensivePlays 1.0000000000 0.542021246 0.04676508 0.520188039
OffensiveYards 0.5420212464 1.000000000 0.85375467 0.562787666
OffenseAvg 0.0467650750 0.853754671 1.00000000 0.349866912
FirstDownPass 0.5201880394 0.562787666 0.34986691 1.000000000
FirstDownRush 0.3778253944 0.540847053 0.41345444 -0.176523843
FirstDownPen 0.1934115743 0.052358639 -0.04850825 0.127557487
FirstDownTotal 0.7067530216 0.822117691 0.54732219 0.632564456
Penalties 0.1172943693 0.119685962 0.06692599 0.095784956
PenaltyYds 0.1165259788 0.147897427 0.10182225 0.096127752
Fumbles 0.0507559795 -0.014562140 -0.04861711 -0.002757013
Interceptions 0.0710774491 -0.152841015 -0.22079174 0.048407099
TotalTurnovers 0.0860207172 -0.123004485 -0.19576146 0.034129166
TeamScore 0.2874768258 0.789855667 0.76082031 0.347919945
OpponentScore 0.0605888810 -0.116705845 -0.18312113 0.078320759
DefPassingCmp 0.0409367670 0.104008426 0.09430449 0.091479428
DefPassingAtt 0.1266557361 0.193638994 0.15023552 0.098615011
DefPassingPct -0.1264265905 -0.141251239 -0.09631370 0.008891843
DefPassingYds 0.1082118124 0.101800906 0.04800482 0.124829238
DefPassingTD 0.1146236054 0.018446294 -0.05356083 0.090411566
DefRushingAtt -0.3028703700 -0.243428558 -0.10790049 -0.078374674
DefRushingYds -0.1436213054 -0.181818592 -0.13406393 -0.026578333
DefRushingAvg -0.0002813871 -0.096198143 -0.11815845 0.012220090
DefRushingTD -0.0282613699 -0.125472152 -0.13806324 0.018812829
DefPlays -0.1568527102 -0.035436423 0.04784943 0.024384116
DefYards -0.0206038075 -0.054371598 -0.06184149 0.080433442
DefAvg 0.0623776236 -0.059674311 -0.11514865 0.073395293
DefFirstDownPass 0.0237393570 0.062702616 0.05343053 0.094488113
DefFirstDownRush -0.2366550850 -0.197471767 -0.09582167 -0.047869961
DefFirstDownPen 0.0042647737 0.058522280 0.06490374 0.059860743
DefFirstDownTotal -0.1508835454 -0.082547789 -0.01541490 0.043901206
DefPenalties 0.1018923824 0.023324431 -0.02935120 0.074798276
DefPenaltyYds 0.1051336326 0.006051685 -0.05191966 0.077240030
DefFumbles 0.0323306822 -0.011975338 -0.02866508 -0.048478203
DefInterceptions 0.0671333246 0.098805501 0.08046452 -0.013627929
DefTotalTurnovers 0.0709877178 0.065778716 0.04127952 -0.041645531
Season -0.0483352540 0.006944910 0.03865811 -0.020261494
FirstDownRush FirstDownPen FirstDownTotal Penalties
Differential 0.461030176 -0.0058046267 0.465369351 -0.014256447
NetYards 0.513441293 -0.0143821648 0.615828331 0.064301874
TurnoverMargin 0.144501659 -0.0209905463 0.060662386 0.025122167
PassingCmp -0.246300190 0.1573505122 0.489458037 0.133990822
PassingAtt -0.367223327 0.1969894869 0.327548464 0.141719302
PassingPct 0.122621659 -0.0129393017 0.433053465 0.034763023
PassingYds -0.161794624 0.1287527369 0.563278812 0.151532040
PassingTD 0.067316306 0.1025099605 0.456785235 0.082566511
RushingAtt 0.788585331 -0.0026108661 0.404462488 -0.025070945
RushingYds 0.868855405 -0.0668965229 0.474548072 -0.003616931
RushingAvg 0.659384817 -0.0810294393 0.392289028 0.018103053
RushingTD 0.595067632 -0.0008771748 0.431942861 -0.025674793
OffensivePlays 0.377825394 0.1934115743 0.706753022 0.117294369
OffensiveYards 0.540847053 0.0523586393 0.822117691 0.119685962
OffenseAvg 0.413454436 -0.0485082548 0.547322187 0.066925991
FirstDownPass -0.176523843 0.1275574870 0.632564456 0.095784956
FirstDownRush 1.000000000 -0.0641318871 0.578322414 -0.036954794
FirstDownPen -0.064131887 1.0000000000 0.270852432 0.131866046
FirstDownTotal 0.578322414 0.2708524323 1.000000000 0.073158288
Penalties -0.036954794 0.1318660457 0.073158288 1.000000000
PenaltyYds -0.003914431 0.1332759144 0.098075714 0.903285428
Fumbles -0.012883931 -0.0005970883 -0.010768846 -0.005811086
Interceptions -0.182588128 0.0214785180 -0.091296852 0.027221860
TotalTurnovers -0.143988031 0.0155536128 -0.074831076 0.016401015
TeamScore 0.492276701 0.0696128982 0.632633399 0.045537547
OpponentScore -0.219705545 0.0802776212 -0.083005629 0.068917067
DefPassingCmp -0.034992273 0.0554175061 0.054894754 0.102277348
DefPassingAtt 0.042935592 0.0507587613 0.115203249 0.148355604
DefPassingPct -0.156712150 0.0363078343 -0.098245000 -0.036921573
DefPassingYds -0.052773711 0.0859542906 0.073330039 0.096552884
DefPassingTD -0.072355990 0.0824503851 0.033483811 0.089465447
DefRushingAtt -0.315396095 -0.0442323619 -0.299783148 -0.045486469
DefRushingYds -0.219337776 0.0045549623 -0.180908454 -0.069631984
DefRushingAvg -0.102028419 0.0399737370 -0.058749721 -0.060058013
DefRushingTD -0.169326396 0.0293993556 -0.103441861 0.001818613
DefPlays -0.251126994 0.0089294743 -0.165281594 0.104074746
DefYards -0.206732624 0.0725064694 -0.076576066 0.025451134
DefAvg -0.107389497 0.0814999118 -0.006508286 -0.026730436
DefFirstDownPass -0.068035944 0.0654406197 0.030363996 0.078611359
DefFirstDownRush -0.224486076 -0.0169325853 -0.212823800 -0.080300783
DefFirstDownPen -0.027665937 0.0714879140 0.034910335 0.544576802
DefFirstDownTotal -0.224068251 0.0465297619 -0.122623874 0.124876699
DefPenalties -0.077839183 0.5419393396 0.124142352 0.190229864
DefPenaltyYds -0.098039476 0.6579654799 0.137890520 0.193152980
DefFumbles 0.001209747 -0.0221372452 -0.039128209 0.017532852
DefInterceptions 0.085931345 -0.0004502855 0.051527754 0.054952612
DefTotalTurnovers 0.064761271 -0.0147193348 0.012937703 0.052304098
Season 0.007784693 0.0673425838 0.004102951 0.030216760
PenaltyYds Fumbles Interceptions TotalTurnovers
Differential 0.017823806 -0.1440162271 -0.3477600256 -0.352523780
NetYards 0.092578752 -0.0001408652 -0.1826426810 -0.135679215
TurnoverMargin 0.038033744 -0.4542268044 -0.5660989685 -0.717861599
PassingCmp 0.125434327 0.0172972617 0.0996771292 0.085329720
PassingAtt 0.119437753 0.0272881459 0.2553128896 0.207413810
PassingPct 0.056174147 -0.0180590785 -0.2365359526 -0.187426813
PassingYds 0.151137509 0.0087606959 0.0180582613 0.019145808
PassingTD 0.100407689 -0.0482240874 -0.1145953471 -0.116667828
RushingAtt -0.002371028 0.0250732455 -0.1940101106 -0.127597560
RushingYds 0.033291751 -0.0279991738 -0.2166075334 -0.179146307
RushingAvg 0.054543977 -0.0578044186 -0.1728264839 -0.166173466
RushingTD 0.008889605 -0.0585646763 -0.2331549445 -0.211457125
OffensivePlays 0.116525979 0.0507559795 0.0710774491 0.086020717
OffensiveYards 0.147897427 -0.0145621396 -0.1528410146 -0.123004485
OffenseAvg 0.101822250 -0.0486171080 -0.2207917361 -0.195761462
FirstDownPass 0.096127752 -0.0027570132 0.0484070993 0.034129166
FirstDownRush -0.003914431 -0.0128839307 -0.1825881284 -0.143988031
FirstDownPen 0.133275914 -0.0005970883 0.0214785180 0.015553613
FirstDownTotal 0.098075714 -0.0107688456 -0.0912968519 -0.074831076
Penalties 0.903285428 -0.0058110858 0.0272218603 0.016401015
PenaltyYds 1.000000000 -0.0144163014 0.0153355568 0.001938904
Fumbles -0.014416301 1.0000000000 0.0201545303 0.670166444
Interceptions 0.015335557 0.0201545303 1.0000000000 0.755566974
TotalTurnovers 0.001938904 0.6701664437 0.7555669742 1.000000000
TeamScore 0.081410971 -0.0921161959 -0.2770189389 -0.266003178
OpponentScore 0.055284341 0.1316753089 0.2621523615 0.280886110
DefPassingCmp 0.111824300 -0.0396516151 -0.0184488090 -0.039675604
DefPassingAtt 0.163084881 -0.0310875854 -0.0594734620 -0.064519542
DefPassingPct -0.043214101 -0.0228701976 0.0795143505 0.044036301
DefPassingYds 0.096448222 -0.0380174026 0.0223809719 -0.008294398
DefPassingTD 0.092652431 0.0393486809 0.0992006245 0.099424170
DefRushingAtt -0.059538323 0.0712060666 0.1459827853 0.155026554
DefRushingYds -0.086795492 0.0218555987 0.1263274699 0.108100554
DefRushingAvg -0.074107080 -0.0099713949 0.0845291086 0.056210433
DefRushingTD -0.016763007 0.0762748212 0.1619374893 0.170191785
DefPlays 0.105533957 0.0355836593 0.0771562026 0.080592378
DefYards 0.012509457 -0.0141877540 0.1126254813 0.074312956
DefAvg -0.043503720 -0.0339135825 0.0944826173 0.047911401
DefFirstDownPass 0.080400150 -0.0495977245 0.0003453417 -0.032240284
DefFirstDownRush -0.095330353 0.0016592286 0.0925101726 0.069763137
DefFirstDownPen 0.655817268 -0.0192548816 0.0058728967 -0.008256072
DefFirstDownTotal 0.140712772 -0.0383893820 0.0659276055 0.023789229
DefPenalties 0.193026624 0.0220735263 0.0534219028 0.054121045
DefPenaltyYds 0.197397916 0.0219713528 0.0641562618 0.062022877
DefFumbles 0.016166609 0.0241064421 -0.0126596565 0.006396606
DefInterceptions 0.061793344 -0.0049987283 -0.0749491840 -0.058914588
DefTotalTurnovers 0.056509226 0.0119421103 -0.0640249366 -0.039705132
Season 0.044437631 -0.0772525165 -0.0412647622 -0.081249572
TeamScore OpponentScore DefPassingCmp DefPassingAtt
Differential 0.781082750 -0.769676830 -0.064368101 0.150903703
NetYards 0.637039168 -0.631724537 -0.222562159 -0.034803042
TurnoverMargin 0.377296240 -0.373375538 0.083296363 0.182665098
PassingCmp 0.182792900 0.138687606 0.083622727 0.075708445
PassingAtt -0.036371904 0.272233697 0.083282335 0.057197756
PassingPct 0.448138414 -0.206915640 0.022821493 0.057591843
PassingYds 0.430680364 0.090860563 0.126240421 0.144626108
PassingTD 0.618452463 -0.019643341 0.091787361 0.144168720
RushingAtt 0.343515192 -0.223000591 -0.044444025 0.074067555
RushingYds 0.571464139 -0.245986897 0.002547929 0.099274619
RushingAvg 0.560294996 -0.200380832 0.033539228 0.093839056
RushingTD 0.698329309 -0.188470083 0.043145158 0.130983665
OffensivePlays 0.287476826 0.060588881 0.040936767 0.126655736
OffensiveYards 0.789855667 -0.116705845 0.104008426 0.193638994
OffenseAvg 0.760820308 -0.183121129 0.094304486 0.150235522
FirstDownPass 0.347919945 0.078320759 0.091479428 0.098615011
FirstDownRush 0.492276701 -0.219705545 -0.034992273 0.042935592
FirstDownPen 0.069612898 0.080277621 0.055417506 0.050758761
FirstDownTotal 0.632633399 -0.083005629 0.054894754 0.115203249
Penalties 0.045537547 0.068917067 0.102277348 0.148355604
PenaltyYds 0.081410971 0.055284341 0.111824300 0.163084881
Fumbles -0.092116196 0.131675309 -0.039651615 -0.031087585
Interceptions -0.277018939 0.262152361 -0.018448809 -0.059473462
TotalTurnovers -0.266003178 0.280886110 -0.039675604 -0.064519542
TeamScore 1.000000000 -0.202525723 0.110705692 0.235782140
OpponentScore -0.202525723 1.000000000 0.214136044 0.004411633
DefPassingCmp 0.110705692 0.214136044 1.000000000 0.888543487
DefPassingAtt 0.235782140 0.004411633 0.888543487 1.000000000
DefPassingPct -0.205498355 0.449432186 0.527671053 0.123692569
DefPassingYds 0.056556533 0.460885709 0.810942021 0.696149740
DefPassingTD -0.027035642 0.629978452 0.431620334 0.288631775
DefRushingAtt -0.220177461 0.346803764 -0.358119934 -0.457251512
DefRushingYds -0.246346085 0.568892367 -0.304072102 -0.424485541
DefRushingAvg -0.202750810 0.555158533 -0.170796334 -0.274757828
DefRushingTD -0.184227178 0.691768961 -0.108176871 -0.261057894
DefPlays 0.027788773 0.327078018 0.543593841 0.561334735
DefYards -0.139080134 0.796651650 0.424087944 0.241608071
DefAvg -0.199605451 0.765936783 0.189854658 -0.036469447
DefFirstDownPass 0.040991911 0.381622228 0.858384763 0.750459859
DefFirstDownRush -0.221902704 0.492272660 -0.220411172 -0.338791429
DefFirstDownPen 0.060090496 0.094425396 0.166428218 0.201877092
DefFirstDownTotal -0.112644611 0.647911274 0.507516311 0.352988503
DefPenalties 0.066541317 0.047828490 0.129287516 0.138517178
DefPenaltyYds 0.044784232 0.091577186 0.124971742 0.119771459
DefFumbles 0.141038879 -0.091933095 0.015619722 0.025595221
DefInterceptions 0.250332113 -0.265828443 0.094157944 0.243961951
DefTotalTurnovers 0.278013024 -0.257642494 0.080249068 0.198258751
Season 0.005977688 0.012194161 -0.026955739 -0.040678279
DefPassingPct DefPassingYds DefPassingTD DefRushingAtt
Differential -0.420540317 -0.257008122 -0.41932607 -0.3646798064
NetYards -0.421880495 -0.397789243 -0.38062203 -0.4151045731
TurnoverMargin -0.155163199 0.017616475 -0.14820264 -0.1934738938
PassingCmp 0.037718119 0.127052362 0.11209162 -0.0352958037
PassingAtt 0.078046303 0.156063755 0.17104126 0.0844568187
PassingPct -0.073028119 -0.021484298 -0.08319470 -0.2139977160
PassingYds -0.001592122 0.154868859 0.09794947 -0.0366813791
PassingTD -0.081479268 0.075356141 0.03430695 -0.0508794692
RushingAtt -0.216525965 -0.049850048 -0.05885150 -0.4106017942
RushingYds -0.181038883 -0.030243336 -0.07855808 -0.2765585249
RushingAvg -0.115973736 -0.009960610 -0.07093063 -0.1175276158
RushingTD -0.152959568 0.005470220 -0.04407360 -0.1963830525
OffensivePlays -0.126426591 0.108211812 0.11462361 -0.3028703700
OffensiveYards -0.141251239 0.101800906 0.01844629 -0.2434285578
OffenseAvg -0.096313705 0.048004815 -0.05356083 -0.1079004931
FirstDownPass 0.008891843 0.124829238 0.09041157 -0.0783746739
FirstDownRush -0.156712150 -0.052773711 -0.07235599 -0.3153960952
FirstDownPen 0.036307834 0.085954291 0.08245039 -0.0442323619
FirstDownTotal -0.098245000 0.073330039 0.03348381 -0.2997831484
Penalties -0.036921573 0.096552884 0.08946545 -0.0454864693
PenaltyYds -0.043214101 0.096448222 0.09265243 -0.0595383233
Fumbles -0.022870198 -0.038017403 0.03934868 0.0712060666
Interceptions 0.079514351 0.022380972 0.09920062 0.1459827853
TotalTurnovers 0.044036301 -0.008294398 0.09942417 0.1550265541
TeamScore -0.205498355 0.056556533 -0.02703564 -0.2201774606
OpponentScore 0.449432186 0.460885709 0.62997845 0.3468037640
DefPassingCmp 0.527671053 0.810942021 0.43162033 -0.3581199341
DefPassingAtt 0.123692569 0.696149740 0.28863177 -0.4572515121
DefPassingPct 1.000000000 0.488760837 0.39639354 0.0331292932
DefPassingYds 0.488760837 1.000000000 0.63367353 -0.2423595169
DefPassingTD 0.396393545 0.633673530 1.00000000 -0.0474443539
DefRushingAtt 0.033129293 -0.242359517 -0.04744435 1.0000000000
DefRushingYds 0.102409466 -0.172170419 0.07787202 0.7388859674
DefRushingAvg 0.132925774 -0.057537780 0.15745657 0.3716123675
DefRushingTD 0.238512223 0.037663032 -0.01494787 0.4882259368
DefPlays 0.152972481 0.461455249 0.24068270 0.4793345862
DefYards 0.469533439 0.674872294 0.56771326 0.3586946169
DefAvg 0.483634897 0.534826925 0.53426029 0.1511943269
DefFirstDownPass 0.485612024 0.888573817 0.53252654 -0.2154397342
DefFirstDownRush 0.123723099 -0.130107645 0.08005769 0.7886334156
DefFirstDownPen 0.004343323 0.140761571 0.11532478 0.0003786557
DefFirstDownTotal 0.442339376 0.587351491 0.47035076 0.4030160447
DefPenalties 0.034741735 0.147217214 0.08072124 -0.0239812874
DefPenaltyYds 0.059174472 0.152588988 0.10343742 0.0023722250
DefFumbles -0.018411263 0.006937136 -0.05044492 0.0258540797
DefInterceptions -0.224465746 0.016870842 -0.10939176 -0.1892748746
DefTotalTurnovers -0.179078808 0.017067747 -0.11421886 -0.1241144783
Season 0.018608445 -0.002118751 0.01139349 -0.0071839390
DefRushingYds DefRushingAvg DefRushingTD DefPlays
Differential -0.523353173 -0.4861743491 -0.561206330 -0.1904417647
NetYards -0.547506147 -0.4868837846 -0.463732467 -0.4206279645
TurnoverMargin -0.194746929 -0.1472444819 -0.258530020 0.0002203222
PassingCmp 0.018891792 0.0493219599 0.062098744 0.0418668527
PassingAtt 0.120099976 0.1148201277 0.156005806 0.1350377412
PassingPct -0.179737625 -0.1152528734 -0.155233737 -0.1423310092
PassingYds -0.010091544 0.0087886271 0.028539434 0.1085880702
PassingTD -0.071419629 -0.0658074401 -0.033296697 0.0949244153
RushingAtt -0.279191271 -0.1214737584 -0.194642061 -0.3090001473
RushingYds -0.224659772 -0.1336360205 -0.192161132 -0.1593884873
RushingAvg -0.131223074 -0.1075756416 -0.145173638 -0.0167634507
RushingTD -0.196293708 -0.1510025421 -0.157134150 -0.0534880654
OffensivePlays -0.143621305 -0.0002813871 -0.028261370 -0.1568527102
OffensiveYards -0.181818592 -0.0961981429 -0.125472152 -0.0354364232
OffenseAvg -0.134063926 -0.1181584507 -0.138063242 0.0478494345
FirstDownPass -0.026578333 0.0122200897 0.018812829 0.0243841160
FirstDownRush -0.219337776 -0.1020284187 -0.169326396 -0.2511269941
FirstDownPen 0.004554962 0.0399737370 0.029399356 0.0089294743
FirstDownTotal -0.180908454 -0.0587497213 -0.103441861 -0.1652815943
Penalties -0.069631984 -0.0600580126 0.001818613 0.1040747460
PenaltyYds -0.086795492 -0.0741070803 -0.016763007 0.1055339566
Fumbles 0.021855599 -0.0099713949 0.076274821 0.0355836593
Interceptions 0.126327470 0.0845291086 0.161937489 0.0771562026
TotalTurnovers 0.108100554 0.0562104328 0.170191785 0.0805923783
TeamScore -0.246346085 -0.2027508097 -0.184227178 0.0277887731
OpponentScore 0.568892367 0.5551585335 0.691768961 0.3270780177
DefPassingCmp -0.304072102 -0.1707963335 -0.108176871 0.5435938415
DefPassingAtt -0.424485541 -0.2747578276 -0.261057894 0.5613347347
DefPassingPct 0.102409466 0.1329257742 0.238512223 0.1529724814
DefPassingYds -0.172170419 -0.0575377802 0.037663032 0.4614552492
DefPassingTD 0.077872022 0.1574565677 -0.014947867 0.2406827012
DefRushingAtt 0.738885967 0.3716123675 0.488225937 0.4793345862
DefRushingYds 1.000000000 0.8731067878 0.687728357 0.2686849660
DefRushingAvg 0.873106788 1.0000000000 0.599341514 0.0746846902
DefRushingTD 0.687728357 0.5993415139 1.000000000 0.1967054519
DefPlays 0.268684966 0.0746846902 0.196705452 1.0000000000
DefYards 0.610722051 0.6079490956 0.545467158 0.5722177961
DefAvg 0.579784008 0.7047983062 0.542409453 0.1047905677
DefFirstDownPass -0.165825447 -0.0638229969 0.024875930 0.5401012405
DefFirstDownRush 0.868275113 0.6624259285 0.587140211 0.3995445768
DefFirstDownPen -0.055648126 -0.0666170942 0.015985345 0.1995724141
DefFirstDownTotal 0.480116194 0.4045866279 0.437004237 0.7233763713
DefPenalties -0.002724418 0.0191494801 -0.021159642 0.1143778424
DefPenaltyYds 0.039415533 0.0605326372 0.018381317 0.1204025813
DefFumbles -0.026697792 -0.0543553971 -0.054016684 0.0493173209
DefInterceptions -0.208302928 -0.1616164572 -0.224805549 0.0646178779
DefTotalTurnovers -0.172427305 -0.1556441080 -0.202464353 0.0801523826
Season 0.014886088 0.0290101906 0.016506584 -0.0468280272
DefYards DefAvg DefFirstDownPass DefFirstDownRush
Differential -0.598650533 -0.618524672 -0.2166137055 -0.458561561
NetYards -0.729910766 -0.639488589 -0.3658024956 -0.513289707
TurnoverMargin -0.131728038 -0.161451905 0.0432422149 -0.144841251
PassingCmp 0.116283124 0.108919498 0.0912573991 -0.019369695
PassingAtt 0.215421076 0.175803966 0.1088084774 0.062733115
PassingPct -0.151933256 -0.106979219 -0.0104930514 -0.154646080
PassingYds 0.116931355 0.065890684 0.1226997484 -0.034057239
PassingTD 0.007072996 -0.058980036 0.0652316014 -0.067986273
RushingAtt -0.249219953 -0.119327650 -0.0896371915 -0.317393880
RushingYds -0.192608428 -0.146094396 -0.0471855598 -0.219849854
RushingAvg -0.106308789 -0.126851539 -0.0082685486 -0.099857008
RushingTD -0.142650515 -0.151692677 -0.0067868508 -0.173870222
OffensivePlays -0.020603807 0.062377624 0.0237393570 -0.236655085
OffensiveYards -0.054371598 -0.059674311 0.0627026163 -0.197471767
OffenseAvg -0.061841494 -0.115148654 0.0534305279 -0.095821670
FirstDownPass 0.080433442 0.073395293 0.0944881127 -0.047869961
FirstDownRush -0.206732624 -0.107389497 -0.0680359441 -0.224486076
FirstDownPen 0.072506469 0.081499912 0.0654406197 -0.016932585
FirstDownTotal -0.076576066 -0.006508286 0.0303639958 -0.212823800
Penalties 0.025451134 -0.026730436 0.0786113587 -0.080300783
PenaltyYds 0.012509457 -0.043503720 0.0804001497 -0.095330353
Fumbles -0.014187754 -0.033913583 -0.0495977245 0.001659229
Interceptions 0.112625481 0.094482617 0.0003453417 0.092510173
TotalTurnovers 0.074312956 0.047911401 -0.0322402835 0.069763137
TeamScore -0.139080134 -0.199605451 0.0409919112 -0.221902704
OpponentScore 0.796651650 0.765936783 0.3816222280 0.492272660
DefPassingCmp 0.424087944 0.189854658 0.8583847630 -0.220411172
DefPassingAtt 0.241608071 -0.036469447 0.7504598590 -0.338791429
DefPassingPct 0.469533439 0.483634897 0.4856120243 0.123723099
DefPassingYds 0.674872294 0.534826925 0.8885738173 -0.130107645
DefPassingTD 0.567713261 0.534260295 0.5325265422 0.080057690
DefRushingAtt 0.358694617 0.151194327 -0.2154397342 0.788633416
DefRushingYds 0.610722051 0.579784008 -0.1658254475 0.868275113
DefRushingAvg 0.607949096 0.704798306 -0.0638229969 0.662425929
DefRushingTD 0.545467158 0.542409453 0.0248759302 0.587140211
DefPlays 0.572217796 0.104790568 0.5401012405 0.399544577
DefYards 1.000000000 0.864412450 0.5900556453 0.545856277
DefAvg 0.864412450 1.000000000 0.3897732165 0.423144636
DefFirstDownPass 0.590055645 0.389773216 1.0000000000 -0.142358418
DefFirstDownRush 0.545856277 0.423144636 -0.1423584180 1.000000000
DefFirstDownPen 0.071463835 -0.025898592 0.1370785878 -0.052075270
DefFirstDownTotal 0.831806916 0.575937633 0.6536349261 0.584292108
DefPenalties 0.116299459 0.068348840 0.0919293080 -0.036048119
DefPenaltyYds 0.152185476 0.109779006 0.0989940993 0.001915398
DefFumbles -0.014423469 -0.047271438 -0.0029199677 -0.011513894
DefInterceptions -0.142482499 -0.206229864 0.0430140097 -0.176356086
DefTotalTurnovers -0.115449033 -0.184256082 0.0301262887 -0.138777101
Season 0.009448327 0.041806773 -0.0184299221 0.008887878
DefFirstDownPen DefFirstDownTotal DefPenalties DefPenaltyYds
Differential -0.0210339059 -0.486573031 0.012883784 -0.029196596
NetYards -0.0094405902 -0.632693183 -0.064592663 -0.101274709
TurnoverMargin 0.0143978565 -0.066456412 -0.030825706 -0.046693953
PassingCmp 0.0519468575 0.064568592 0.097925257 0.108483644
PassingAtt 0.0496523070 0.134220950 0.144504901 0.163061597
PassingPct 0.0270565789 -0.109944660 -0.043122514 -0.053955236
PassingYds 0.0790211848 0.083154570 0.092384684 0.092101718
PassingTD 0.0731295577 0.016271698 0.087036309 0.087050251
RushingAtt -0.0478753802 -0.301802428 -0.044358538 -0.060502619
RushingYds -0.0069207881 -0.193740061 -0.066428568 -0.088477801
RushingAvg 0.0264594652 -0.073461199 -0.057532616 -0.076887164
RushingTD 0.0113604598 -0.126021858 0.001510194 -0.023250561
OffensivePlays 0.0042647737 -0.150883545 0.101892382 0.105133633
OffensiveYards 0.0585222802 -0.082547789 0.023324431 0.006051685
OffenseAvg 0.0649037363 -0.015414902 -0.029351199 -0.051919665
FirstDownPass 0.0598607428 0.043901206 0.074798276 0.077240030
FirstDownRush -0.0276659372 -0.224068251 -0.077839183 -0.098039476
FirstDownPen 0.0714879140 0.046529762 0.541939340 0.657965480
FirstDownTotal 0.0349103351 -0.122623874 0.124142352 0.137890520
Penalties 0.5445768017 0.124876699 0.190229864 0.193152980
PenaltyYds 0.6558172682 0.140712772 0.193026624 0.197397916
Fumbles -0.0192548816 -0.038389382 0.022073526 0.021971353
Interceptions 0.0058728967 0.065927605 0.053421903 0.064156262
TotalTurnovers -0.0082560718 0.023789229 0.054121045 0.062022877
TeamScore 0.0600904963 -0.112644611 0.066541317 0.044784232
OpponentScore 0.0944253956 0.647911274 0.047828490 0.091577186
DefPassingCmp 0.1664282181 0.507516311 0.129287516 0.124971742
DefPassingAtt 0.2018770925 0.352988503 0.138517178 0.119771459
DefPassingPct 0.0043433232 0.442339376 0.034741735 0.059174472
DefPassingYds 0.1407615708 0.587351491 0.147217214 0.152588988
DefPassingTD 0.1153247810 0.470350761 0.080721243 0.103437420
DefRushingAtt 0.0003786557 0.403016045 -0.023981287 0.002372225
DefRushingYds -0.0556481262 0.480116194 -0.002724418 0.039415533
DefRushingAvg -0.0666170942 0.404586628 0.019149480 0.060532637
DefRushingTD 0.0159853449 0.437004237 -0.021159642 0.018381317
DefPlays 0.1995724141 0.723376371 0.114377842 0.120402581
DefYards 0.0714638347 0.831806916 0.116299459 0.152185476
DefAvg -0.0258985916 0.575937633 0.068348840 0.109779006
DefFirstDownPass 0.1370785878 0.653634926 0.091929308 0.098994099
DefFirstDownRush -0.0520752700 0.584292108 -0.036048119 0.001915398
DefFirstDownPen 1.0000000000 0.282830498 0.131332338 0.134294140
DefFirstDownTotal 0.2828304978 1.000000000 0.070174238 0.103037190
DefPenalties 0.1313323378 0.070174238 1.000000000 0.900787598
DefPenaltyYds 0.1342941401 0.103037190 0.900787598 1.000000000
DefFumbles -0.0030186847 -0.010305398 -0.008854950 -0.017511146
DefInterceptions 0.0194059666 -0.087469619 0.020314277 0.007791742
DefTotalTurnovers 0.0124861420 -0.071816578 0.009370146 -0.005577312
Season 0.0689030833 0.006320333 0.027973821 0.042484690
DefFumbles DefInterceptions DefTotalTurnovers Season
Differential 0.150569794 0.3327057321 0.345532435 -0.003878385
NetYards 0.001793221 0.1663340665 0.124999591 -0.001790592
TurnoverMargin 0.460918316 0.5703875962 0.724139646 -0.002929967
PassingCmp -0.040829500 -0.0297691725 -0.048692669 -0.029610254
PassingAtt -0.035257824 -0.0686033059 -0.073984074 -0.041775426
PassingPct -0.017660867 0.0689142577 0.039830347 0.012572467
PassingYds -0.037626266 0.0078658014 -0.018592363 -0.005156032
PassingTD 0.043608120 0.0882725890 0.094053467 0.007905151
RushingAtt 0.071526298 0.1436580977 0.153427918 -0.007214300
RushingYds 0.023852046 0.1195961383 0.104536716 0.014375807
RushingAvg -0.006854675 0.0770398937 0.052901642 0.028912307
RushingTD 0.081572945 0.1542031901 0.167806659 0.010753872
OffensivePlays 0.032330682 0.0671333246 0.070987718 -0.048335254
OffensiveYards -0.011975338 0.0988055011 0.065778716 0.006944910
OffenseAvg -0.028665079 0.0804645249 0.041279523 0.038658107
FirstDownPass -0.048478203 -0.0136279287 -0.041645531 -0.020261494
FirstDownRush 0.001209747 0.0859313452 0.064761271 0.007784693
FirstDownPen -0.022137245 -0.0004502855 -0.014719335 0.067342584
FirstDownTotal -0.039128209 0.0515277542 0.012937703 0.004102951
Penalties 0.017532852 0.0549526117 0.052304098 0.030216760
PenaltyYds 0.016166609 0.0617933436 0.056509226 0.044437631
Fumbles 0.024106442 -0.0049987283 0.011942110 -0.077252517
Interceptions -0.012659656 -0.0749491840 -0.064024937 -0.041264762
TotalTurnovers 0.006396606 -0.0589145881 -0.039705132 -0.081249572
TeamScore 0.141038879 0.2503321129 0.278013024 0.005977688
OpponentScore -0.091933095 -0.2658284429 -0.257642494 0.012194161
DefPassingCmp 0.015619722 0.0941579438 0.080249068 -0.026955739
DefPassingAtt 0.025595221 0.2439619508 0.198258751 -0.040678279
DefPassingPct -0.018411263 -0.2244657460 -0.179078808 0.018608445
DefPassingYds 0.006937136 0.0168708421 0.017067747 -0.002118751
DefPassingTD -0.050444915 -0.1093917599 -0.114218864 0.011393488
DefRushingAtt 0.025854080 -0.1892748746 -0.124114478 -0.007183939
DefRushingYds -0.026697792 -0.2083029281 -0.172427305 0.014886088
DefRushingAvg -0.054355397 -0.1616164572 -0.155644108 0.029010191
DefRushingTD -0.054016684 -0.2248055487 -0.202464353 0.016506584
DefPlays 0.049317321 0.0646178779 0.080152383 -0.046828027
DefYards -0.014423469 -0.1424824986 -0.115449033 0.009448327
DefAvg -0.047271438 -0.2062298639 -0.184256082 0.041806773
DefFirstDownPass -0.002919968 0.0430140097 0.030126289 -0.018429922
DefFirstDownRush -0.011513894 -0.1763560858 -0.138777101 0.008887878
DefFirstDownPen -0.003018685 0.0194059666 0.012486142 0.068903083
DefFirstDownTotal -0.010305398 -0.0874696190 -0.071816578 0.006320333
DefPenalties -0.008854950 0.0203142773 0.009370146 0.027973821
DefPenaltyYds -0.017511146 0.0077917423 -0.005577312 0.042484690
DefFumbles 1.000000000 0.0243218903 0.667876691 -0.077776623
DefInterceptions 0.024321890 1.0000000000 0.760295796 -0.045877732
DefTotalTurnovers 0.667876691 0.7602957956 1.000000000 -0.084692470
Season -0.077776623 -0.0458777320 -0.084692470 1.000000000Notice right away – NetYards is highly correlated. But NetYards’s also highly correlated with RushingYards, OffensiveYards and DefYards. And that makes sense: those things all feed into NetYards. Including all of these measures would be pointless – they would add error without adding much in the way of predictive power.
Your turn: What else do you see? What other values have predictive power and aren’t co-correlated?
We can add more just by simply adding them. Let’s add the average yard per play for both offense and defense. They’re correlated to NetYards, but not as much as you might expect.
model2 <- lm(Differential ~ NetYards + TurnoverMargin + DefAvg + OffenseAvg, data=logs)
summary(model2)
Call:
lm(formula = Differential ~ NetYards + TurnoverMargin + DefAvg +
OffenseAvg, data = logs)
Residuals:
Min 1Q Median 3Q Max
-38.259 -6.265 0.002 6.231 37.511
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.4971325 0.4288921 1.159 0.246
NetYards 0.0547248 0.0008001 68.400 <2e-16 ***
TurnoverMargin 3.8835518 0.0410088 94.700 <2e-16 ***
DefAvg -3.9332431 0.0737944 -53.300 <2e-16 ***
OffenseAvg 3.9108710 0.0728810 53.661 <2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 9.452 on 15631 degrees of freedom
(1 observation deleted due to missingness)
Multiple R-squared: 0.8285, Adjusted R-squared: 0.8285
F-statistic: 1.888e+04 on 4 and 15631 DF, p-value: < 2.2e-16Go down the list:
What is the Adjusted R-squared now? What is the p-value and is it less than .05? What is the Residual standard error?
The final thing we can do with this is predict things. Look at our coefficients table. See the Estimates? We can build a formula from that, same as we did with linear regressions.
How does this apply in the real world? Let’s pretend for a minute that you are Scott Frost, and you have a mess on your hands. Your job is to win conference titles. To do that, we need to know what attributes of a team should we emphasize. We can do that by looking at what previous Big Ten conference champions looked like.
So if our goal is to predict a conference champion team, we need to know what those teams did. Here’s the regular season conference champions in this dataset.
logs |>
filter(Team == "Ohio State" & Season == 2020 | Team == "Ohio State" & Season == 2019 | Team == "Ohio State" & Season == 2018) |>
summarise(
meanNetYards = mean(NetYards),
meanTurnoverMargin = mean(TurnoverMargin),
meanDefAvg = mean(DefAvg),
meanOffenseAvg = mean(OffenseAvg)
)# A tibble: 1 × 4
meanNetYards meanTurnoverMargin meanDefAvg meanOffenseAvg
<dbl> <dbl> <dbl> <dbl>
1 196. 0.686 5.08 6.97Now it’s just plug and chug.
(0.0547465*195.8824) + (3.8806793*0.6764706) + (-3.9374905*5.044118 ) + (3.9152803*6.908824) + 0.4960303[1] 21.03389So a team with those numbers is going to average scoring 21 more points per game than their opponent. Sound like Ohio State in the last three years?
How does that compare to Nebraska this season?
logs |>
filter(
Team == "Nebraska" & Season == 2020
) |>
summarise(
meanNetYards = mean(NetYards),
meanTurnoverMargin = mean(TurnoverMargin),
meanDefAvg = mean(DefAvg),
meanOffenseAvg = mean(OffenseAvg)
)# A tibble: 1 × 4
meanNetYards meanTurnoverMargin meanDefAvg meanOffenseAvg
<dbl> <dbl> <dbl> <dbl>
1 5 -1.38 5.44 5.54(0.0547465*5) + (3.8806793*-1.375) + (-3.9374905*5.4375) + (3.9152803*5.5375) + 0.4960303[1] -4.295411By this model, it predicted we would average being outscored by our opponents by 4.3 points over the season. Reality? We were outscored by 6.25 on average.