2010 Alabama Mr. Football Coty Blanchard THEORY OF WINNING Coaching, recruiting and spending in college football Table of Contents Introduction How to predict a win Data sources Initial Model Out of sample prediction Practical applications Next steps Jason Campbell, Auburn University Authors Introduction McDonald “Mac” Mirabile Manager of Strategic & Financial Analysis at WWF Undergraduate and graduate thesis on the predictors of a successful transition from college to NFL Prior academic publications on topics such as biases in college football polls, the NFL Rookie Cap, the Wonderlic Test, and the Peer Effect in the NFL draft Mark Witte Assistant Professor at College of Charleston Generally awesome guy Topic Introduction The importance of winning in college Shapes alumni support, attendance Influences quality of recruiting Self-enforcing cycle How to predict a win Vegas point spread, totals, and money line theoretically capture all available information under the efficient market hypothesis (EMH) Existing literature consistently enforces EMH, though there are some published examples of deviations and profitable strategies within wagering markets Within the framework of this paper, we will assume EMH holds within college football wagering markets and will measure the success of our developed models relative to the baseline Vegas model Predicting Wins with the Vegas Line Bubble chart illustrates the home team’s winning percent by the Vegas Line, with the size of the bubble based on the number of observations Predicting Wins with the Vegas Line Bar chart of home team’s winning percentage by the Vegas line The Vegas Line model Home Win (0,1) = b1*Line + error This model within our data explains 29% of the variation in wins (Pseudo R2). The line coefficient is 0.1091, with a standard error of 0.00437, and an Odds Ratio of 1.115 Interpretation: for each additional point a team is favored, their odds of winning increase by 11.5% Non-linear model shows similar results Improving the Vegas Line model Can it be done, or does the Vegas line incorporate all publically available information? To test this, we added several variables: Home, Away win and losing streaks Home, Away AP Rankings, Top 25 matchups Dummy variables for conference games, neutral field matchups, and night games Distance between schools, stadium size, rivalry information Conference dummy variables Improving the Vegas Line model Effect Line ETP HWS HLS AWS ALS Hrank Arank HNR ANR TrueT25 ConfGame Neutral Nightgame Stadium Distance Rivalry Conf DF 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 12 Wald 285.4691 1.1213 0.522 0.8024 1.8483 0.1004 0.7195 0.1588 1.591 1.5452 0.2535 0.003 0.001 0.3414 1.078 0.0145 2.0766 11.5154 Pr > ChiSq <.0001 0.2896 0.47 0.3704 0.174 0.7513 0.3963 0.6903 0.2072 0.2138 0.6146 0.9566 0.9743 0.559 0.2992 0.9042 0.3541 0.4853 • Table on left shows these additional variables and a their corresponding Wald Chi2 statistics • The Vegas line successfully incorporates all available information. • Adding more explanatory variables does not improve the model’s fit. • None of the added variables are statistically significant as their importance is already captured in the Line variable. Data Sources To develop a model of winning without utilizing the Vegas line, the authors gathered data on the following topics: Game-specific factors Institutional factors/history Team player composition/recruiting Team coach factors/history We will discuss the collection and organization of this data next Game-specific Factors Matchup data comes from Covers.com Data includes game location, time, day, conference information Each matchup (home vs away) is one observation in the dataset There are about 500 games per season Institutional Factors & History Historical team performance comes from CFBDatawarehouse.com University football team expenditure and student body size data come from the Equity in Athletics website Each of these variables is reported for a particular year (e.g., Michigan’s historical team performance through 2007 and their team expenditure data for the 2008 season would all be used as predictors for the 2008 season matchups) Team player composition and recruiting Class recruiting data comes from Rivals.com, Scouts.com, and Prepstar.com Recruiting classes in 2005 (RS-Senior), 2006 (Senior / RS-Junior), 2007 (Junior, RS-Sophomore), 2008 (Sophomore, RS-Freshman), an 2009 (Freshman) are used as predictors for the 2009 season matchups. Due to the NFL draft, transfers, and general attrition, these variables are imperfect measures of the talent comprising a team in a particular season Team coach factors and history Historical coach performance comes from CFBDatawarehouse.com Coach biographical information comes from various university athletics department websites Each of these variables is reported for a particular year (e.g., Michigan’s coach’s historical performance through 2007 would be used as a predictor for the 2008 season matchups) Summary Statistics of Model variables Variable Mean Std Dev Minimum Maximum N home_win 0.6 Stadium 55.458 Student_Body_H 17.883 cum_winpct_adf 0.008 total_expense_all_football_ldf 0.109 class_rank_scouts_l4_adf -5.843 first_year_HC_H 0.072 first_year_HC_A 0.083 coach_age_adf 0.239 coach_experience_adf 0.447 seasons_coach_adf 0.323 cum_winpct_coach_adf 0.017 nfl_years_adf -0.028 Home_Coach_Minority 0.047 Away_Coach_Minority 0.048 0.49 22.246 8.017 0.11 0.563 31.682 0.258 0.275 11.764 12.456 11.091 0.246 3.369 0.213 0.213 0 16 0.002 -0.392 -1.611 -106.25 0 0 -46 -46 -41 -0.826 -16 0 0 1 107.501 43.026 0.408 2.386 100.75 1 1 48 54 42 0.84 16 1 1 3418 3418 3304 3418 3204 3340 3418 3418 3418 3417 3418 3418 3417 3418 3418 N Miss 0 0 114 0 214 78 0 0 0 1 0 0 1 0 0 Initial Model Odds Ratio Estimates Effect Estimate Stadium Student_Body_H cum_winpct_adf total_expense_all_fo class_rank_scouts_l4 first_year_HC_H first_year_HC_A coach_age_adf coach_experience_adf seasons_coach_adf cum_winpct_coach_adf nfl_years_adf Home_Coach_Minority Away_Coach_Minority N: 2,948 R-Square: .215 1.004 1.005 1.714 2.529 0.992 0.754 1.291 0.984 1.002 1.007 6.806 0.961 0.581 1.866 95% Wald Confidence 1 1.008 0.99 1.017 0.63 4.647 2.03 3.153 0.99 0.996 0.54 1.047 0.93 1.784 0.97 0.996 0.99 1.013 1 1.019 4.43 10.45 0.93 0.99 0.38 0.892 1.16 2.997 Matchup-specific variables: • Stadium Size • Home team student size School-specific variables: • Cumulative Team Win Pct Diff • Log Diff of Total Team expenditures Team-specific variables (Difference home – away): • Scouts.com weighted average class ranking Coach-specific variables (Difference home – away) : • First year head coach Home team dummy • First year head coach Away team dummy • Coach age • Coach experience (assistant + HC) • Head coach seasons • Lifetime Coach Win Pct Diff • Years as NFL player • Home team’s head coach minority dummy • Away team’s head coach minority dummy Initial Model - Interpretations Matchup-specific variables: • Stadium Size – for every additional 10,000 seats, the home team is 4% more likely to win • (also considered game time, location, rivalry variables) School-specific variables: • Log Diff of Total Team expenditures – the odds ratio of the % difference (home/away) in team spending of 2.5 suggests that a team spending 100% more (twice as much) is 150% more likely to win, (Alternative, equivalent interpretation: odds of winning increase 15% for each 10% increase in excess of your opponent’s expenditures) Team-specific variables (all Difference home – away) : • Scouts.com average class ranking – for each unit increase in average class ranking between the home and away, the home team is 1% more likely to win Coach-specific variables (all Difference home – away) : • First year head coach dummy variables – marginally significant and coefficients in the direction one would expect • Diff in HC’s ages – for each additional year in age difference b/w the Home and Away team’s coach, the home team is 1% less likely to win • Diff in HC’s cumulative Win % – for each 1% difference in lifetime win percentage between the home team’s HC and the away team’s HC, the home team is about 6% more likely to win • Years as NFL player – for each additional year of NFL playing experience between the home team’s HC and the away team’s HC, the home team is about 4% less likely to win • Home team Head Coach Minority – minority coaches are 42% less likely to win than non-minority coaches at home • Away team Head Coach Minority – home teams are 87% more likely to win when playing against a minority coach Out of Sample prediction Analysis Variable : Vegas_Model_Correct sample Correct Incorrect % Correct In 1,450 541 72.8% Out 612 233 72.4% Analysis Variable : Our_Model_Correct sample Correct Incorrect % Correct In 1,420 648 68.7% Out 603 278 68.4% Both models have comparable in and out of sample performance Out of Sample by Line 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 11) favorite 28+ 10) favorite 21 - 27 09) favorite 14 - 20 08) favorite 7 - 13 07) favorite 3 - 6 12) favorite 0 - 2 06) underdog .5 - 2 05) underdog 3 - 6 04) underdog 7 - 13 03) underdog 14 - 20 02) underdog 21 - 27 01) underdog 28+ Vegas line does a better job predicting everything except games where the line is between -2 and +2 Home Win Our Model Vegas Model 2009 Season (SEC results) Data from 2004-2008 used to develop the model Data from 2009 used in an out-of-sample validation School Alabama Arkansas Auburn Florida Georgia Kentucky LSU Mississippi Mississippi St. South Carolina Tennessee Vanderbilt Model Actual Evaluation Wins Losses Pct Wins Losses Pct Correct Incorrect PCT 11 1 92% 12 0 100% 11 1 92% 8 4 67% 7 5 58% 11 1 92% 7 5 58% 7 5 58% 10 2 83% 12 0 100% 11 1 92% 11 1 92% 11 1 92% 7 5 58% 8 4 67% 4 8 33% 6 6 50% 8 4 67% 10 3 77% 9 4 69% 10 3 77% 5 6 45% 7 4 64% 7 4 64% 2 9 18% 4 7 36% 7 4 64% 6 5 55% 5 6 45% 10 1 91% 8 4 67% 6 6 50% 8 4 67% 3 7 30% 1 9 10% 8 2 80% Note: Non Div1A opponents not scored/modeled Practical Applications Predict 2010 season results – conference standings, national champion, before a single game has been played Next steps What can be added to the model? New sources of data (attendance, compensation/bonus – impute missing values based on relative rank of team within conference?) Additional data cleanup (game time, more years 2001-2003) Different estimation methodologies BACKUP/OLD SLIDES BEGIN HERE Who is hiring minority coaches? Analysis of Maximum Likelihood Estimates Parameter Estimate Standard Wald Pr > ChiSq Error Chi-Square Intercept 8.4961 2.1216 16.0358 <.0001 Stadium 0.0311 0.0116 7.1846 0.0074 School_Seasons_Home -0.014 0.00771 3.2851 0.0699 Cum_WinPCT_School_Home -6.9228 3.0907 5.0172 0.0251 MA5_Win_PCT_School_Home -2.1436 1.3669 2.4592 0.1168 Coach_Age_H -0.1657 0.0537 9.526 0.002 Coach_Experience_H 0.0479 0.0497 0.9289 0.3352 The coach is more likely to be young (see coach_age), belong to a historically crappy program (Cum_WinPCT_School_H) as well as belong to a recently crappy program (MA5_Win_PCT_School_H) of relatively newer schools (School_Seasons_H) and larger schools (Stadium). Predicting recruiting classes Parameter Estimate Std Error Wald 95% Chi2 Pr > Chi2 Intercept 43.38 4.49 34.58 52.17 93.4 <.0001 Prev_WinPCT_School -9.69 3.34 -16.23 -3.15 8.43 0.0037 MA5_Win_PCT_School -15.52 4.81 -24.96 -6.08 10.4 0.0013 Class_Rank_Scouts_Lag1 0.27 0.04 0.20 0.34 55.8 <.0001 Class_Rank_Scouts_Lag2 0.18 0.04 0.10 0.26 20.6 <.0001 Class_Rank_Scouts_Lag3 0.10 0.04 0.02 0.18 6.23 0.0126 Class_Rank_Scouts_Lag4 0.13 0.04 0.05 0.20 10.1 0.0015 ACC -17.79 2.96 -23.58 -11.99 36.2 <.0001 Big 12 -16.18 2.84 -21.75 -10.61 32.4 <.0001 Big East -15.02 2.84 -20.59 -9.45 27.9 <.0001 Big Ten -16.26 2.85 -21.84 -10.67 32.5 <.0001 Conf USA -7.57 2.38 -12.23 -2.90 10.1 0.0015 I-A Ind -12.09 3.73 -19.41 -4.77 10.5 0.0012 Indep -11.87 8.44 -28.41 4.68 1.98 0.1597 MAC 0.17 2.30 -4.34 4.68 0.01 0.9412 MWC -3.67 2.54 -8.66 1.32 2.08 0.149 Pac-10 -18.79 3.05 -24.78 -12.81 37.9 <.0001 SEC -21.78 3.05 -27.75 -15.80 51.1 <.0001 Sun Belt -3.33 2.68 -8.59 1.93 1.54 0.2149 WAC 0.00 0.00 0.00 0.00 . . GLM estimation of dependent variable: Scouts class ranking Previous year and 5-year MA Win % impact recruiting Previous classes are also good predictors of current year’s class ranking Conference impacts recruiting Alabama (2010) = 43.4 – (9.7*1) – (15.5*.77) + (.27*2) + (.18*1) + (.1*22) + (.13*18) – 21.8 = 3 (Actual rank 4) Auburn (2010) = 43.4 – (9.7*.615) – (15.5*.66) + (.27*16) + (.18*18) + (.1*6) + (.13*9) – 21.8 = 15 (Actual rank 5) Vanderbilt (2010) = 43.4 – (9.7*.167) – (15.5*.38) + (.27*72) + (.18*74) + (.1*87) + (.13*61) – 21.8 = 63 (Actual rank 61) 2009 out of sample (A-F) School Akron Alabama Arizona Arizona St. Arkansas Arkansas State Auburn BYU Ball State Baylor Boise St. Boston College Bowling Green California Central Michigan Cincinnati Clemson Colorado Colorado State Connecticut Duke East Carolina Eastern Michigan Florida Florida State Fresno State Model Losses Wins 4 11 4 8 8 3 7 10 4 2 10 10 5 9 7 10 10 9 6 5 2 6 1 12 9 7 Pct Wins 6 40% 2 1 92% 12 8 33% 7 3 73% 3 4 67% 7 5 38% 1 5 58% 7 2 83% 10 5 44% 2 9 18% 3 3 77% 13 2 83% 7 6 45% 5 3 75% 7 3 70% 8 2 83% 11 3 77% 8 2 82% 3 4 60% 2 7 42% 7 7 22% 3 6 50% 7 9 10% 0 0 100% 11 3 75% 6 5 58% 7 Actual Losses Pct 8 20% 0 100% 5 58% 8 27% 5 58% 7 13% 5 58% 2 83% 7 22% 8 27% 0 100% 5 58% 6 45% 5 58% 2 80% 1 92% 5 62% 8 27% 8 20% 5 58% 6 33% 5 58% 10 0% 1 92% 6 50% 5 58% Evaluation Correct Incorrect PCT 8 2 80% 11 1 92% 7 5 58% 6 5 55% 11 1 92% 6 2 75% 10 2 83% 10 2 83% 5 4 56% 8 3 73% 10 3 77% 9 3 75% 7 4 64% 6 6 50% 9 1 90% 11 1 92% 11 2 85% 5 6 45% 4 6 40% 10 2 83% 6 3 67% 11 1 92% 9 1 90% 11 1 92% 9 3 75% 8 4 67% 2009 out of sample (G-M) School Georgia Georgia Tech Hawaii Houston Idaho Illinois Indiana Iowa Iowa St. Kansas Kansas State Kent State Kentucky LSU Louisiana Tech Louisville Marshall Maryland Memphis Miami-Florida Miami-Ohio Michigan Michigan State Middle Tennessee Minnesota Mississippi Model Losses Wins 11 11 7 2 1 3 3 8 1 4 4 0 4 10 4 4 3 3 5 4 1 8 5 4 1 5 Pct Wins 1 92% 7 2 85% 10 4 64% 4 9 18% 9 12 8% 8 8 27% 2 8 27% 3 4 67% 11 10 9% 4 8 33% 4 6 40% 4 10 0% 4 8 33% 6 3 77% 9 6 40% 3 7 36% 3 9 25% 6 8 27% 1 6 45% 1 8 33% 8 9 10% 0 3 73% 4 7 42% 5 6 40% 7 10 9% 5 6 45% 7 Actual Losses Pct 5 58% 3 77% 7 36% 2 82% 5 62% 9 18% 8 27% 1 92% 7 36% 8 33% 6 40% 6 40% 6 50% 4 69% 7 30% 8 27% 6 50% 10 9% 10 9% 4 67% 10 0% 7 36% 7 42% 3 70% 6 45% 4 64% Evaluation Correct Incorrect PCT 8 4 67% 10 3 77% 6 5 55% 4 7 36% 6 7 46% 8 3 73% 11 0 100% 9 3 75% 8 3 73% 12 0 100% 8 2 80% 6 4 60% 8 4 67% 10 3 77% 7 3 70% 10 1 91% 9 3 75% 7 4 64% 7 4 64% 8 4 67% 9 1 90% 7 4 64% 8 4 67% 7 3 70% 7 4 64% 7 4 64% 2009 out of sample (M-S) School Mississippi St. Missouri NC State Nebraska Nevada New Mexico New Mexico State North Carolina North Texas Northern Illinois Northwestern Notre Dame Ohio Ohio State Oklahoma Oklahoma State Oregon Oregon St. Penn State Pittsburgh Purdue Rice Rutgers SMU San Diego State San Jose St. Model Losses Wins 2 7 3 12 7 1 0 6 1 7 5 8 5 11 10 6 8 5 9 4 6 5 9 8 5 3 Pct Wins 9 18% 4 4 64% 7 7 30% 3 2 86% 10 6 54% 8 10 9% 1 12 0% 2 5 55% 6 7 13% 1 4 64% 6 7 42% 6 3 73% 6 6 45% 7 0 100% 9 2 83% 7 6 50% 8 5 62% 10 7 42% 7 3 75% 10 6 40% 7 5 55% 4 6 45% 2 0 100% 5 3 73% 7 5 50% 3 8 27% 1 Actual Losses Pct 7 36% 4 64% 7 30% 4 71% 5 62% 10 9% 10 17% 5 55% 7 13% 5 55% 6 50% 5 55% 4 64% 2 82% 5 58% 4 67% 3 77% 5 58% 2 83% 3 70% 7 36% 9 18% 4 56% 4 64% 7 30% 10 9% Evaluation Correct Incorrect PCT 7 4 64% 9 2 82% 8 2 80% 12 2 86% 12 1 92% 9 2 82% 10 2 83% 7 4 64% 6 2 75% 8 3 73% 7 5 58% 7 4 64% 5 6 45% 9 2 82% 9 3 75% 8 4 67% 7 6 54% 8 4 67% 9 3 75% 7 3 70% 5 6 45% 8 3 73% 5 4 56% 8 3 73% 6 4 60% 9 2 82% 2009 out of sample (S-U) School South Carolina South Florida Southern Cal Southern Miss Stanford Syracuse TCU Temple Tennessee Texas Texas A&M Texas Tech Troy State Tulane Tulsa UAB UCF UCLA UL-Lafayette UL-Monroe UNLV UTEP Utah Utah State Model Losses Wins 6 5 12 6 2 2 9 4 8 13 6 8 7 0 10 0 5 11 2 0 2 5 8 2 Actual Pct Wins Losses 5 55% 5 5 50% 5 1 92% 9 6 50% 6 11 15% 8 9 18% 3 2 82% 10 4 50% 5 4 67% 6 1 93% 13 7 46% 6 4 67% 8 3 70% 6 10 0% 1 1 91% 4 11 0% 4 6 45% 6 2 85% 7 6 25% 4 8 0% 2 8 20% 4 6 45% 4 4 67% 9 9 18% 3 Evaluation Pct Correct Incorrect PCT 6 45% 10 1 91% 5 50% 8 2 80% 4 69% 8 5 62% 6 50% 8 4 67% 5 62% 7 6 54% 8 27% 8 3 73% 1 91% 8 3 73% 3 63% 7 1 88% 6 50% 8 4 67% 1 93% 14 0 100% 7 46% 11 2 85% 4 67% 8 4 67% 4 60% 9 1 90% 9 10% 9 1 90% 7 36% 5 6 45% 7 36% 7 4 64% 5 55% 10 1 91% 6 54% 7 6 54% 4 50% 6 2 75% 6 25% 6 2 75% 6 40% 6 4 60% 7 36% 8 3 73% 3 75% 11 1 92% 8 27% 8 3 73% 2009 out of sample (V-W) School Vanderbilt Virginia Virginia Tech Wake Forest Washington Washington St. West Virginia Western Michigan Wisconsin Wyoming Model Losses Wins 3 3 10 3 2 3 6 4 11 1 Pct Wins 7 30% 1 8 27% 3 3 77% 10 7 30% 4 10 17% 5 9 25% 1 6 50% 8 5 44% 2 1 92% 9 9 10% 5 Actual Losses Pct 9 10% 8 27% 3 77% 6 40% 7 42% 11 8% 4 67% 7 22% 3 75% 5 50% Evaluation Correct Incorrect PCT 8 2 80% 7 4 64% 11 2 85% 7 3 70% 9 3 75% 10 2 83% 10 2 83% 7 2 78% 10 2 83% 6 4 60% Other considerations (backup slide) Off the field model .18 On the field model .26 Are the coefficients robust? Future problems: things that recruits like – new stadiums, new weight rooms, facilities Could we do a recruiting paper modeled on NCAA football recruiting info – coach history, academic prestige, location, tv time, etc Out of Sample prediction (intercept) Analysis Variable : Vegas_Model_Correct sample Correct Incorrect % Correct In 837 315 72.7% Out 384 132 74.4% Analysis Variable : Our_Model_Correct sample Correct Incorrect % Correct In 787 365 68.3% Out 352 164 68.2% Both models have comparable in and out of sample performance Friday Meet with profs about research Present to a class Lunch Seminar presentation Dinner Models To begin, we will look at each of these data sources and its relationship to our outcome variable individually. Because each of these data sources is described with dozens of potential variables, this initial modeling will inform our final set of models where data from all possible sources are considered in development. All models are developed using a Logit function as our outcome variable, Home Win, is binary. We will discuss the resulting coefficients as Odds Ratios to aid interpretation. Model 1: Game specific factors Odds Ratio Estimates Effect Point Estimate Neutral Nightgame Stadium Conference ACC vs WAC Conference Big East vs WAC Conference Big Ten vs WAC Conference Big Twelve vs WAC Conference CUSA vs WAC Conference INDP vs WAC Conference MAC vs WAC Conference Mountain West vs WAC Conference NC vs WAC Conference Pac Ten vs WAC Conference SEC vs WAC Conference Sun Belt vs WAC day_of_week Fri vs Wed day_of_week Mon vs Wed day_of_week Sat vs Wed day_of_week Sun vs Wed day_of_week Thu vs Wed day_of_week Tue vs Wed Distance 0.804 0.868 1.018 0.573 0.741 0.444 0.665 0.576 0.554 0.789 0.766 0.992 0.483 0.347 0.955 1.184 0.662 1.407 1.103 1.686 1.727 1 90% Wald Confidence Limits 0.62 1.05 0.76 0.99 1.01 1.02 0.4 0.83 0.49 1.12 0.3 0.66 0.46 0.96 0.4 0.84 0.36 0.86 0.55 1.13 0.52 1.12 0.74 1.34 0.33 0.7 0.24 0.51 0.64 1.43 0.65 2.16 0.31 1.43 0.81 2.44 0.55 2.21 0.92 3.09 0.85 3.52 1 1 Model 1: Game specific factors Other considered variables Distance b/w schools Rivalry game (major/minor/none) Other variables to consider in the future: Game-time (need to clean some data) Model 2: Institutional factors & history Effect Odds Ratio Estimates Point Estimate Cum_Losses_School_H MA5_Wins_School_H TOTAL_EXPENSE_ALL_Fo EFMaleCount_H EFFemaleCount_H Cum_Losses_School_A MA5_Win_PCT_School_A TOTAL_EXPENSE_ALL_Fo school_seasons_ldf cum_winpct_adf total_expense_all_fo school_seasons_31t75 school_seasons_31t75 school_seasons_m101_ 1.005 1.039 0.972 1 1 0.996 0.082 1.028 0.53 185.1 3.366 1.912 0.711 0.715 95% Wald Confidence Limits 1.003 1.007 1.03 1.047 0.932 1.014 1 1 1 1 0.994 0.998 0.048 0.14 0.986 1.072 0.363 0.775 20.63 >999.999 2.149 5.273 1.269 2.882 0.491 1.031 0.586 0.873 Model 2: Institutional factors & history Other considered variables Other variables to consider in the future: Model 3: Recruiting Effect Odds Ratio Estimates Point Estimate Cum_Losses_School_H MA5_Wins_School_H TOTAL_EXPENSE_ALL_Fo EFMaleCount_H EFFemaleCount_H Cum_Losses_School_A MA5_Win_PCT_School_A TOTAL_EXPENSE_ALL_Fo school_seasons_ldf cum_winpct_adf total_expense_all_fo school_seasons_31t75 school_seasons_31t75 school_seasons_m101_ 1.005 1.039 0.972 1 1 0.996 0.082 1.028 0.53 185.1 3.366 1.912 0.711 0.715 95% Wald Confidence Limits 1.003 1.007 1.03 1.047 0.932 1.014 1 1 1 1 0.994 0.998 0.048 0.14 0.986 1.072 0.363 0.775 20.63 >999.999 2.149 5.273 1.269 2.882 0.491 1.031 0.586 0.873