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Today's Stat Lesson

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Old
11-12-2003, 10:57 AM
  #1
LALALALALALAFONTAINE
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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.

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Old
11-12-2003, 11:03 AM
  #2
Takeo
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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?

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Old
11-12-2003, 12:12 PM
  #3
LALALALALALAFONTAINE
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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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