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# Today's Stat Lesson

 11-12-2003, 10:57 AM #1 LALALALALALAFONTAINE Registered User   Join Date: Mar 2002 Location: Republic of Alberta Posts: 2,649 vCash: 500 Today's Stat Lesson There is a relationship between goals scored, goals given up and wins. Pretty obvious, right? Not for Buffalo. Here's the relationship between wins and losses: Create variable PYTHAG, which is GF^2/(GF^2+GA^2). This explains winning percentage like so: Regression Statistics R Square 0.95726133 Adjusted R Square 0.955734949 Standard Error 0.020875603 Observations 30 Coefficients Standard Error t Stat Intercept 0.007023497 0.020058857 0.350144452 PYTHAG 0.985790508 0.039364148 25.0428511 In other words, there is a tremendous relationship between goals for and against and winning percentage. The winning percentage the NHL is screwed up by OTL. Here's the same regression with the NHL's winning percentage as the dependent variable: Regression Statistics R Square 0.965618034 Adjusted R Square 0.964390106 Standard Error 0.017635392 Observations 30 Coefficients Standard Error t Stat Intercept 0.064969412 0.016945417 3.83404021 PYTHAG 0.932531046 0.033254235 28.04247514 Basically, the same thing. Nothing too overwhelmingly interesting. What is interesting is the Sabres GF and GA in 2 of the past 3 seasons. 2001-2 GF: 213 GA: 200 PYTHAG: 213^2/(213^2+200^2)=.531446 Predicted: .0649+.932531*.531446 = .561 = 92 pts Actual: .500, 3.43 standard deviations less than expected 2002-3 GF: 190 GA: 219 PYTHAG: 190^2/(190^2+219^2)=.42945 Predicted: .0649+.932531*.42945= .465 = 76 pts Actual: .439, 1.5 standard deviations less than expected In other words, the Sabres won less games than they should have on average. This year? 34 GF and 43 GA, meaning we should be at .432. Granted it is too early to conclude anything, but it is a good sign. What does it mean? I dunno. The idea of this is used in baseball stats, and has been speculated to indicate a good manager or coach - meaning that a coach gets more out of goals his club scores than expected. Here are the Sabres throughout history: Season Pct GF GA Coach PYTHAG EST Error 1970-71 0.404 217 291 George "Punch" Imlach 0.357357517 0.359302824 0.044697176 1971-72 0.327 203 289 Multiple coaches 0.330385633 0.332714184 -0.005714184 1972-73 0.564 257 219 Joe Crozier 0.579326375 0.578117726 -0.014117726 1973-74 0.487 242 250 Joe Crozier 0.483744135 0.483893615 0.003106385 1974-75 0.706 354 240 Floyd Smith 0.685101358 0.682389753 0.023610247 1975-76 0.656 339 240 Floyd Smith 0.666127602 0.663685595 -0.007685595 1976-77 0.65 301 220 Floyd Smith 0.651801066 0.649562625 0.000437375 1977-78 0.656 288 215 Marcel Pronovost 0.642135497 0.640034394 0.015965606 1978-79 0.55 280 263 Multiple coaches 0.531276894 0.530750981 0.019249019 1979-80 0.688 318 201 Scotty Bowman 0.714531002 0.711401231 -0.023401231 1980-81 0.619 327 250 Roger Neilson 0.631113918 0.62916942 -0.01016942 1981-82 0.581 307 273 Multiple coaches 0.558419936 0.557508347 0.023491653 1982-83 0.556 318 285 Scotty Bowman 0.554562953 0.553706168 0.002293832 1983-84 0.644 315 257 Scotty Bowman 0.600366664 0.598859054 0.045140946 1984-85 0.562 290 237 Scotty Bowman 0.59956227 0.598066089 -0.036066089 1985-86 0.5 296 291 Multiple coaches 0.50851727 0.508314748 -0.008314748 1986-87 0.4 280 308 Multiple coaches 0.452488688 0.453082276 -0.053082276 1987-88 0.531 283 305 Ted Sator 0.462637337 0.463086723 0.067913277 1988-89 0.519 291 299 Ted Sator 0.48644317 0.486554299 0.032445701 1989-90 0.613 286 248 Rick Dudley 0.570802512 0.569714979 0.043285021 1990-91 0.506 292 278 Rick Dudley 0.524546595 0.524116313 -0.018116313 1991-92 0.463 289 299 Multiple coaches 0.482998115 0.483158195 -0.020158195 1992-93 0.512 335 297 John Muckler 0.559909995 0.558977234 -0.046977234 1993-94 0.565 282 218 John Muckler 0.625936654 0.62406572 -0.05906572 1994-95 0.531 130 119 John Muckler 0.54409066 0.543382676 -0.012382676 1995-96 0.445 247 262 Ted Nolan 0.470556023 0.470892892 -0.025892892 1996-97 0.561 237 208 Ted Nolan 0.564892943 0.563889379 -0.002889379 1997-98 0.543 211 187 Lindy Ruff 0.560083029 0.55914781 -0.01614781 1998-99 0.555 207 175 Lindy Ruff 0.583185889 0.581922401 -0.026922401 1999-00 0.518292683 213 204 Lindy Ruff 0.521572685 0.551351697 -0.033059015 2000-01 0.597560976 218 184 Lindy Ruff 0.583976407 0.609545103 -0.011984127 2001-02 0.5 213 200 Lindy Ruff 0.531445841 0.560558722 -0.060558722 2002-03 0.43902439 190 219 Lindy Ruff 0.429450042 0.465444477 -0.026420087 By coach, measured by points gotten inspite of goals for and against: Sator 16.05743636 Imlach 6.972759467 Dudley 4.026993247 Smith 2.617924416 Pronovost 2.554497019 Neilson -1.627107242 Crozier -1.717769248 Bowman -1.925206769 Nolan -4.720292485 Muckler -19.0039532 Ruff -28.71511432 One thing that should be pointed out is that any coach who coached thru a partial year will have incomplete stats.
 11-12-2003, 11:03 AM #2 Takeo Registered User     Join Date: Jul 2003 Country: Posts: 18,868 vCash: 500 So the original hypothesis between goals scored as the independent variable and victories as the dependent variable is rendered spurious when controlling for the Buffalo Sabres as an intervening variable?? What am I to make of this?
 11-12-2003, 12:12 PM #3 LALALALALALAFONTAINE Registered User   Join Date: Mar 2002 Location: Republic of Alberta Posts: 2,649 vCash: 500 Basically, there is a very strong relationship between goals for, goals against and a team's record. That relationship has not been there the last 2 years for the Sabres. Remember that 95% confidence means 1 out of 20 times it should not work. I'm interested in why it doesn't work. Was it due to a young team losing its best player? Was it due to ownership? Was it due to something else? I don't know. Maybe there is another variable to consider. This year, I would expect one of two things to happen: 1. Either we start losing close games or 2. Start blowing out teams Either way, it will balance out the GF/GA ratio and our record.

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