## May 4, 2007

### Fatigue

Many people who look at hockey statistics focus on these scoring rates as a measure of performance. Alan Ryder used the difference in scoring rates of players from some marginal scoring rate to determine how much value a player added. I also focus on scoring rates to determine value. Problem is most people in hockey know that players get tired and tired players aren’t as good as fresh players.

There are a number of things to consider when looking at scoring rates, the most commonly mentioned two: who are the other 4 players on the ice with the given player and who are they playing against. However, what might be more significant than both of those issues is how much they play.

Let’s say there are two players who are identical in every way. Let’s say one gets 10 minutes of ice time and the other gets 20 minutes of ice time. Which player’s scoring rate will be higher? At this point the answer should be obvious the 10 minute player shouldn’t do worse under identical conditions as the player with 20 minutes as he’ll likely be a few seconds faster and have a little more jump. So, how does increased ice time affect scoring rates?

Short Mathematical Discussion

Determining the cost of additional ice time is not trivial. A regression on ice time and scoring rates is generally positively correlated, that is to say players with more ice time have higher scoring rates because coaches play the better players more often, but if you give the same player more ice time his scoring rate will fall. So I had to look at how individuals did with extra ice time.

Setup

I ran a regression with 4 variables: power play time [pp], penalty killing time [sh], even strength time [ev] and (power play time/1.5 + penalty killing time + even strength time) [adjusted ice time]. You can see the adjusted ice time variable lowers the value of power play time as I feel that the power play is generally easier than even strength play. This is simply my opinion. The response was how many goals the player was on the ice for in that game (for all situations), I’ll call these pluses. All ice time variables are measure in terms of hours per game.

This setup means that I will get an equation that looks like:

Regression Summary

A player will play in the neighborhood of 70-80 games a season and my model has 4 variables with very small domains, that is to say that ice time will vary by only a couple of minute per game. Due to this, some coefficients can become quite “strange” and aren’t very meaningful on the individual player level as many players do better with more ice time, which could be because they are paired with better players when they get more ice time. But, I’m not trying to discover an individual player’s fatigue pattern; instead I am looking for a trend in the NHL. So I take an average of all the coefficients to get an average coefficient.

Results

I separated forwards and defenseman:

Forwards:
Pluses/game = 4.0 * ev + 7.0 * pp + 3.0 * sh– 4.5 * adjusted ice time2
Defense:
Pluses/game = 3.6 * ev + 6.6 * pp + 3.4 * sh– 2.8 * adjusted ice time2
Time measured in hours.

There is significantly less cost for a defenseman in terms of extra ice time and this makes sense.

How does this effect even strength scoring?
The math part.

Pluses/hour = Pluses/game*games/hour =

Taking the derivative of the above expression:

And for defenseman:

The reason the equations are as complicated as they are is because there are two types of effects: fatigue factor and a different scoring rate. On the power play you get the benefit of an increased scoring rate and a cost of additional ice time. For penalty killing you are hit with a lower scoring rate and the additional ice time.

One simplification I co do is to assume sh = 0 and pp = 0:

In other words the cost of an additional hour of ice time per game is 4.5 goals for per hour. So, an additional minute (one 60th of an hour) is equal to: -4.5/60 = -0.075 goals for per hour. So the difference between a 10 even strength minute player and a 15 minute even strength player is about 0.375 GF/hour. So a player who has a scoring rate of 2.1 with 15 minutes is equivalent to a player who has a scoring rate of 2.5 with 10 minutes. That’s quite a big difference when you start thinking about it.

Application

In order to make this analysis more real I calculated how the average player would do with a given player’s ice time and compared that to how they actually did. The comparison calculated a percentage better (or worse) than average (labeled ‘P’ on the table below). A score of +100 is equivalent to doing twice as well as the average player would do with the given amount of ice time. A score of -83.5 represents playing at 16.5% (= 100+(-83.5)) of expected. Doing poorly on this metric makes you a bad offensive player, but that does not make the player bad, they can easily make up the differences by providing defense. There are other things to consider including the standard line mate problem and opposition issues. And I should note injuries and luck play their part as well.

Table

 N Lastname I ev pp sh | P 1 VANEK T 12.9 3.5 0.3 | 43.6 2 ST. LOUIS M 17.6 4.8 1.7 | 41.9 3 ALFREDSSON D 14.5 4.8 2.2 | 36.6 4 PREISSING T 11.7 3.5 0.1 | 36.1 5 SPEZZA J 14.2 4.9 0.2 | 35.9 6 LECAVALIER V 16.3 4.7 1.5 | 33.3 7 HEATLEY D 15.3 5.0 0.8 | 32.9 8 SELANNE T 12.9 4.6 0.1 | 32.7 9 CROSBY S 14.7 5.8 0.2 | 32.4 10 POMINVILLE J 12.5 2.5 2.4 | 32.1 11 THORNTON J 14.8 5.0 0.4 | 31.6 12 SAKIC J 14.5 5.1 0.6 | 31.3 13 ROY D 12.9 3.0 2.5 | 31.1 14 DATSYUK P 14.0 4.0 1.9 | 30.7 15 AFINOGENOV M 13.2 3.8 0.1 | 30.1 16 IGINLA J 15.7 5.1 1.3 | 29.9 17 BRUNETTE A 13.3 4.1 0.1 | 29.4 18 ZETTERBERG H 13.9 4.1 2.9 | 28.8 19 KUNITZ C 12.7 4.0 0.3 | 27.6 20 SULLIVAN S 12.0 4.4 2.9 | 26.8 21 MALKIN E 12.9 5.8 0.5 | 25.7 22 MCDONALD A 13.2 4.3 0.1 | 25.5 23 BRIERE D 14.1 4.7 0.3 | 25.0 24 HEJDUK M 12.6 3.7 1.6 | 24.9 25 STASTNY P 12.3 3.6 2.3 | 24.7 26 RADULOV A 9.8 1.8 0.0 | 24.5 27 JOKINEN O 15.2 3.9 1.4 | 24.4 28 PHANEUF D 18.1 5.6 2.0 | 23.9 29 JAGR J 15.9 5.7 0.2 | 23.8 30 CHEECHOO J 13.0 4.4 0.2 | 23.0 31 HOSSA M 14.3 5.3 2.1 | 22.4 32 STAFFORD D 11.8 1.3 0.0 | 22.3 33 MARLEAU P 14.1 4.3 0.2 | 22.2 34 ARNOTT J 13.4 4.5 0.2 | 22.1 35 SMYTH R 13.5 4.7 1.9 | 21.9 36 VISNOVSKY L 17.5 6.0 1.0 | 21.9 37 HECHT J 13.3 2.8 2.7 | 21.3 38 NYLANDER M 14.8 5.5 0.1 | 21.3 39 GABORIK M 14.7 3.7 1.1 | 21.0 40 CAMPBELL B 16.9 3.5 1.4 | 20.5 41 LANGKOW D 13.8 4.5 1.8 | 19.8 42 PRONGER C 17.5 5.8 3.8 | 19.7 43 BOYLE D 19.9 6.4 0.7 | 19.2 44 KOIVU S 12.3 4.0 1.8 | 18.5 45 MURRAY G 13.4 4.8 0.6 | 17.5 46 YASHIN A 13.2 3.5 0.4 | 17.2 47 HOLMSTROM T 11.1 4.1 0.0 | 17.0 48 RECCHI M 14.0 5.2 0.5 | 16.9 49 LILES J 12.5 5.0 0.3 | 16.2 50 GONCHAR S 16.1 7.4 3.1 | 16.2 51 LIDSTROM N 17.3 5.7 4.5 | 15.9 52 HIGGINS C 12.6 3.2 2.1 | 15.6 53 RYDER M 11.6 3.9 0.8 | 15.4 54 KOZLOV V 13.9 5.1 1.5 | 15.4 55 DUMONT J 12.5 3.4 0.2 | 15.3 56 OVECHKIN A 15.7 5.5 0.2 | 15.3 57 SCHUBERT C 9.4 0.7 1.1 | 15.3 58 CAMMALLERI M 13.2 4.6 0.2 | 14.5 59 WOLSKI W 12.7 2.6 0.2 | 13.4 60 NUMMINEN T 14.8 2.5 3.5 | 13.1 61 REDDEN W 15.9 4.6 2.5 | 13.0 62 HUSELIUS K 12.7 4.0 0.8 | 12.9 63 BOUWMEESTER J 18.2 3.4 4.6 | 12.9 64 KNUBLE M 13.8 4.1 1.7 | 12.3 65 NIEDERMAYER S 17.7 5.8 4.0 | 12.1 66 WHITNEY R 15.7 6.0 2.3 | 12.1 67 TIMONEN K 13.8 4.8 3.2 | 12.1 68 HAMRLIK R 17.2 4.8 2.8 | 12.0 69 BRIND'AMOUR R 14.7 5.0 3.6 | 11.9 70 MICHALEK M 12.9 3.4 0.4 | 11.7 71 SEMIN A 12.6 5.6 0.1 | 11.5 72 TALLINDER H 16.9 0.2 4.0 | 11.2 73 SCHNEIDER M 16.6 5.3 1.7 | 10.4 74 ZUBRUS D 14.5 5.1 0.2 | 10.1 75 TANGUAY A 13.5 4.1 0.0 | 9.9 76 CORVO J 13.6 3.6 0.9 | 9.8 77 HORTON N 13.8 2.8 1.5 | 9.6 78 REINPRECHT S 12.1 3.2 0.4 | 9.3 79 SEDIN D 13.5 4.4 0.1 | 9.2 80 STRAKA M 14.1 5.2 0.7 | 8.9 81 LEGWAND D 13.8 2.0 2.6 | 8.8 82 WELLWOOD K 12.3 4.3 0.0 | 8.7 83 GETZLAF R 10.1 3.4 1.5 | 8.4 84 SAVARD M 14.5 5.4 0.3 | 8.4 85 SEDIN H 13.8 4.4 0.3 | 8.4 86 KOZLOV V 12.9 2.1 1.4 | 8.3 87 GAGNE S 14.3 4.5 2.2 | 7.2 88 PAETSCH N 13.2 1.8 0.2 | 6.9 89 GOMEZ S 14.4 4.5 0.0 | 6.0 90 CARLE M 13.2 4.6 0.3 | 5.9 91 HEMSKY A 12.6 4.3 0.1 | 5.8 92 EHRHOFF C 13.5 4.1 1.0 | 5.7 93 HEWARD J 12.6 2.5 1.3 | 5.7 94 FROLOV A 13.9 4.5 1.5 | 5.6 95 KUBA F 14.9 3.0 2.3 | 5.2 96 MALIK M 15.7 0.4 3.1 | 5.1 97 STUMPEL J 12.9 3.2 3.1 | 5.0 98 COMRIE M 11.5 2.9 0.0 | 4.9 99 WHITNEY R 13.5 5.0 0.2 | 4.6 100 SUNDIN M 13.8 5.0 1.7 | 4.5 101 WEISS S 12.1 2.5 2.5 | 4.0 102 STAAL E 14.5 5.4 0.3 | 4.0 103 KARIYA P 15.0 5.0 0.4 | 4.0 104 CLARK C 12.2 3.5 2.7 | 4.0 105 SHANAHAN B 12.2 5.1 2.5 | 3.8 106 KABERLE T 16.5 5.8 3.6 | 3.7 107 BLAKE J 14.0 3.8 0.3 | 3.6 108 VLASIC M 16.6 2.3 3.3 | 3.4 109 RAFALSKI B 19.5 4.7 1.2 | 3.4 110 DEMITRA P 14.5 4.4 1.8 | 3.2 111 WEBER S 15.9 2.6 0.9 | 3.1 112 KALININ D 15.2 1.0 3.3 | 3.0 113 KLEE K 16.4 1.3 3.0 | 3.0 114 ALLEN B 16.6 1.1 3.9 | 2.7 115 MOSS D 9.3 1.9 0.0 | 2.6 116 ANTROPOV N 13.7 2.4 0.5 | 2.5 117 SOURAY S 15.3 4.9 3.0 | 2.3 118 MARTINEK R 16.1 1.7 2.1 | 2.3 119 GELINAS M 11.4 2.0 0.1 | 2.1 120 KELLY C 12.0 0.2 3.1 | 1.9 121 PONIKAROVSKY A 13.6 2.6 1.0 | 1.7 122 RICHARDS B 16.7 5.2 2.2 | 1.6 123 KOPITAR A 13.8 4.6 2.1 | 1.5 124 STOLL J 10.7 4.8 2.7 | 1.2 125 MCCABE B 17.1 5.9 3.8 | 1.0 126 ERAT M 13.7 4.3 1.0 | 1.0 127 MARKOV A 16.5 4.4 3.6 | 0.7 128 HARTNELL S 10.9 3.4 1.4 | 0.6 129 SPACEK J 14.2 3.0 2.0 | 0.6 130 BERGERON P 12.7 5.1 2.9 | 0.6 131 BOUCHER P 15.8 4.1 3.0 | 0.4 132 ROCHE T 13.0 3.3 0.7 | 0.3 133 KOVALCHUK I 14.8 6.6 0.1 | 0.2 134 VOLCHENKOV A 16.6 0.2 4.5 | 0.1 135 ARMSTRONG D 12.2 2.7 0.2 | -0.1 136 PARISE Z 14.3 3.0 0.2 | -0.1 137 ROBERTS G 13.3 3.7 0.1 | -0.6 138 CLARK B 16.6 3.3 3.7 | -0.6 139 TUCKER D 12.2 5.0 0.6 | -1.0 140 SOPEL B 15.1 3.4 2.5 | -1.3 141 PAVELSKI J 12.1 2.8 0.1 | -1.4 142 COLE E 12.9 4.3 0.8 | -1.6 143 RIBEIRO M 10.9 4.0 0.0 | -1.6 144 PERRY C 9.7 2.7 0.1 | -2.1 145 RANGER P 16.8 1.8 1.8 | -2.3 146 STREIT M 10.4 2.8 0.8 | -2.6 147 SIMON C 9.1 1.8 0.1 | -2.6 148 GAUSTAD P 9.7 1.7 1.9 | -2.7 149 PENNER D 11.0 2.9 0.0 | -2.8 150 ZIDLICKY M 15.1 4.4 0.3 | -2.9 151 WHITE I 15.2 1.8 1.6 | -3.1 152 ELIAS P 14.0 4.4 0.2 | -3.1 153 O'BRIEN S 12.2 1.4 0.4 | -3.2 154 ROZSIVAL M 15.9 4.6 3.3 | -3.2 155 WILLIAMS J 13.6 4.5 2.7 | -3.4 156 FISHER M 13.1 2.8 2.5 | -3.9 157 HAVLAT M 15.2 4.7 1.5 | -3.9 158 PROSPAL V 16.3 2.8 0.0 | -4.3 159 DOAN S 14.3 4.4 1.7 | -4.5 160 LANG R 13.1 3.6 0.1 | -4.7 161 JACKMAN B 17.0 1.2 3.3 | -4.8 162 METROPOLIT G 9.5 2.2 0.0 | -4.9 163 KOTALIK A 11.8 2.7 0.1 | -5.0 164 PELTONEN V 12.2 0.9 3.3 | -5.2 165 BURNS B 13.8 1.3 0.7 | -5.4 166 LYDMAN T 16.1 0.9 3.6 | -5.5 167 ZUBOV S 16.9 5.7 3.3 | -5.5 168 MCCARTHY S 10.4 4.8 0.0 | -5.6 169 DRURY C 11.4 4.4 2.9 | -5.6 170 SAPRYKIN O 11.6 1.7 0.2 | -5.8 171 ARNASON T 11.9 2.3 0.1 | -5.9 172 O'NEILL J 10.7 3.0 0.0 | -5.9 173 SALO S 14.6 3.6 3.2 | -6.0 174 LANGENBRUNNER J 13.7 4.2 0.6 | -6.4 175 GIONTA B 13.9 4.4 0.5 | -6.6 176 BERGERON M 12.9 4.0 0.5 | -6.7 177 WEIGHT D 13.5 4.5 0.3 | -6.7 178 PLEKANEC T 12.0 2.0 2.0 | -6.9 179 KUBINA P 16.1 2.1 3.1 | -7.1 180 CLOWE R 11.5 1.6 0.0 | -7.1 181 STEMPNIAK L 11.3 3.2 0.2 | -7.1 182 SUTTON A 15.6 0.4 3.5 | -7.3 183 OUELLET M 10.2 3.2 0.0 | -7.4 184 ARMSTRONG C 11.6 1.4 3.9 | -7.5 185 KOVALEV A 13.1 4.1 1.1 | -7.6 186 BACKMAN C 15.9 3.6 2.7 | -7.6 187 PITKANEN J 17.6 4.7 2.2 | -7.9 188 EAVES P 10.8 1.0 0.4 | -7.9 189 LOMBARDI M 11.4 2.5 2.5 | -8.0 190 BIEKSA K 16.9 3.7 3.6 | -8.0 191 WESLEY G 11.9 0.3 3.4 | -8.0 192 MARKOV D 15.8 0.2 2.9 | -8.1 193 JOVANOVSKI E 15.7 5.1 2.3 | -8.2 194 VYBORNY D 13.0 4.6 2.8 | -8.3 195 NAGY L 13.2 4.0 0.7 | -8.3 196 SMOLINSKI B 12.8 3.2 2.6 | -8.3 197 POTI T 16.5 4.6 4.6 | -8.4 198 FRITSCHE D 11.6 1.3 1.2 | -8.7 199 PHILLIPS C 17.5 0.2 4.7 | -8.9 200 SKRASTINS K 16.7 0.2 4.3 | -9.1 201 CHRISTENSEN E 9.1 2.5 0.0 | -9.1 202 STAAL J 10.7 1.2 3.0 | -9.1 203 GILL H 14.9 0.1 4.0 | -9.3 204 WHITE T 12.2 2.5 2.6 | -9.6 205 CHARA Z 17.8 5.2 4.9 | -9.7 206 SVATOS M 9.9 2.6 0.0 | -9.9 207 SUTER R 14.3 2.5 3.3 | -10.0 208 PARRISH M 10.5 3.8 0.0 | -10.1 209 SCHAEFER P 12.4 2.3 2.1 | -10.1 210 LARAQUE G 9.6 0.7 0.0 | -10.1 211 BERNIER S 11.2 2.4 0.0 | -10.2 212 ROBITAILLE R 12.5 0.9 0.4 | -10.3 213 GIORDANO M 10.3 2.7 0.4 | -10.4 214 BEAUCHEMIN F 18.5 3.0 4.0 | -10.4 215 ZAJAC T 13.3 2.7 0.0 | -10.5 216 HILL S 16.1 2.8 3.5 | -10.8 217 BOUCHARD P 12.5 3.5 0.0 | -11.0 218 CULLEN M 12.1 2.3 2.7 | -11.0 219 COMMODORE M 15.8 0.4 3.7 | -11.0 220 NASLUND M 13.7 4.0 0.0 | -11.0 221 SILLINGER M 12.5 3.3 3.4 | -11.1 222 VERMETTE A 11.9 0.9 2.9 | -11.2 223 ROLSTON B 13.4 5.2 2.6 | -11.3 224 SATAN M 13.6 3.7 1.2 | -11.3 225 BROWN D 12.7 3.7 2.4 | -11.5 226 CAJANEK P 11.9 3.1 1.2 | -11.8 227 HORCOFF S 13.9 3.5 3.4 | -11.9 228 MCAMMOND D 8.9 0.4 1.7 | -11.9 229 MALONE R 12.0 1.6 2.7 | -12.1 230 BATTAGLIA B 11.1 0.3 1.0 | -12.3 231 HUDLER J 8.5 1.5 0.0 | -12.4 232 HAVELID N 17.2 3.5 4.6 | -12.5 233 MODANO M 13.2 3.7 1.5 | -12.6 234 RICHARDS M 13.0 1.5 3.4 | -12.8 235 SAMUELSSON M 12.0 3.0 0.1 | -12.8 236 KOIVU M 12.6 3.3 1.6 | -12.9 237 MESZAROS A 15.4 3.7 2.5 | -13.1 238 HAMILTON J 9.5 3.4 0.0 | -13.1 239 COLAIACOVO C 15.3 1.6 1.1 | -13.2 240 LEBDA B 13.7 1.1 0.1 | -13.4 241 WILLIAMS J 11.5 2.8 0.1 | -13.4 242 LEHTINEN J 12.9 3.5 3.0 | -13.6 243 REGEHR R 16.6 1.1 4.2 | -13.6 244 SYKORA P 12.0 4.6 0.1 | -13.7 245 HAMHUIS D 16.7 0.3 4.3 | -13.9 246 HUNTER T 11.7 1.3 2.9 | -14.0 247 MELICHAR J 15.0 0.1 3.7 | -14.0 248 FEDOROV S 13.2 4.4 2.4 | -14.2 249 GUERIN B 13.2 4.0 0.2 | -14.2 250 STAJAN M 12.2 2.1 1.9 | -14.3 251 POTHIER B 16.5 4.2 3.1 | -14.4 252 WITT B 16.7 0.1 4.7 | -14.4 253 RACHUNEK K 14.0 2.8 2.5 | -14.5 254 SALEI R 16.9 3.3 3.1 | -14.8 255 BALLARD K 16.0 2.0 3.7 | -14.9 256 HNIDY S 13.7 0.5 1.5 | -15.1 257 BLAKE R 15.5 5.1 3.8 | -15.2 258 AVERY S 12.6 2.5 1.8 | -15.4 259 CARNEY K 13.3 0.0 2.2 | -15.4 260 KRONVALL N 16.5 2.5 1.6 | -15.5 261 NASH R 13.0 4.5 1.7 | -15.6 262 VAN RYN M 15.4 2.4 3.4 | -15.6 263 KOLNIK J 10.7 0.9 0.4 | -15.7 264 STUART B 16.7 2.2 4.0 | -15.7 265 VAANANEN O 13.8 0.1 0.4 | -15.7 266 KEITH D 18.4 1.7 3.5 | -15.8 267 CARTER J 13.6 3.0 2.3 | -16.0 268 CLEARY D 10.8 2.1 2.5 | -16.1 269 PRUCHA P 10.1 2.9 0.0 | -16.1 270 NOLAN O 10.9 2.6 1.9 | -16.1 271 MORRISON B 12.3 3.4 2.3 | -16.2 272 RUCINSKY M 12.2 3.4 1.1 | -16.4 273 MORRIS D 14.7 2.6 3.1 | -16.5 274 MCCLEMENT J 10.8 0.6 2.5 | -16.7 275 WIDEMAN D 14.5 4.3 1.4 | -17.1 276 MCLAREN K 17.4 1.2 2.8 | -17.1 277 HUTCHINSON A 8.2 3.8 0.2 | -17.2 278 STEEN A 12.2 1.5 2.0 | -17.5 279 HANNAN S 17.9 1.5 3.4 | -17.5 280 STURM M 11.9 4.3 2.4 | -17.7 281 PYATT T 11.0 3.0 0.0 | -17.7 282 VISHNEVSKI V 16.1 0.1 3.0 | -17.7 283 EMINGER S 15.5 0.2 3.3 | -17.8 284 ERIKSSON A 14.5 2.8 2.9 | -18.1 285 NASREDDINE A 12.8 0.1 2.8 | -18.3 286 NUMMELIN P 15.0 3.9 1.3 | -18.4 287 DE VRIES G 17.1 2.1 3.1 | -18.6 288 ORPIK B 15.2 1.1 0.3 | -18.7 289 MICHALEK Z 16.8 3.4 3.5 | -18.8 290 WALKER S 12.6 3.3 0.2 | -18.8 291 JOHNSSON K 17.2 2.8 3.6 | -18.9 292 LILJA A 12.3 0.1 3.0 | -19.0 293 MARCHANT T 11.7 0.1 3.3 | -19.0 294 KOMISAREK M 15.7 0.1 3.5 | -19.1 295 TKACHUK K 13.4 3.9 0.2 | -19.1 296 BACKES D 10.9 2.4 0.0 | -19.3 297 ALEXEEV N 12.1 1.1 1.1 | -19.3 298 MCLEAN B 11.7 1.1 0.8 | -19.5 299 PICARD A 15.2 2.4 0.8 | -19.5 300 FRANZEN J 11.9 1.2 2.5 | -19.7 301 JOHNSON A 11.6 0.7 0.4 | -19.8 302 PERREAULT Y 13.3 3.8 0.5 | -19.9 303 HILBERT A 10.2 0.1 1.1 | -20.3 304 PERRIN E 13.5 1.6 1.9 | -20.4 305 SANDERSON G 10.5 3.0 0.5 | -20.6 306 RUUTU T 13.8 3.4 0.1 | -20.6 307 CHIMERA J 11.9 0.8 2.6 | -20.7 308 TANABE D 13.3 3.0 1.5 | -20.7 309 ZANON G 13.0 0.2 4.2 | -20.8 310 O'DONNELL S 16.1 0.1 3.7 | -21.1 311 POHL J 9.5 1.6 0.2 | -21.5 312 KWIATKOWSKI J 8.6 0.9 0.3 | -21.7 313 JOKINEN J 10.8 3.1 0.0 | -21.8 314 OLESZ R 11.6 1.0 2.9 | -22.1 315 PISANI F 12.4 2.0 2.6 | -22.1 316 CARTER A 11.1 3.2 0.5 | -22.1 317 CRAIG R 10.2 3.7 1.5 | -22.2 318 GRATTON C 10.7 1.1 0.3 | -22.5 319 SKOULA M 17.0 0.7 2.6 | -22.8 320 FOSTER K 13.3 3.7 0.9 | -22.9 321 KLEPIS J 8.3 1.6 0.0 | -23.1 322 LADD A 9.4 1.6 0.0 | -23.1 323 JANIK D 13.3 0.5 0.7 | -23.3 324 KILGER C 10.7 0.3 3.5 | -23.5 325 BOOTH D 8.8 0.1 0.7 | -23.7 326 RUCCHIN S 13.4 2.4 2.5 | -23.7 327 KESLER R 11.6 1.1 3.7 | -23.7 328 AXELSSON P 13.0 3.0 3.2 | -23.7 329 BOUILLON F 15.2 0.6 2.5 | -23.7 330 LAPERRIERE I 11.8 0.4 1.6 | -23.8 331 MELLANBY S 9.7 4.0 0.1 | -23.8 332 SCUDERI R 14.5 0.6 3.7 | -24.0 333 FEDOTENKO R 14.3 1.9 0.1 | -24.0 334 HATCHER D 17.3 0.8 5.6 | -24.1 335 OHLUND M 17.1 4.2 3.5 | -24.1 336 WALLIN N 15.2 0.2 3.2 | -24.1 337 PETTINGER M 11.5 2.5 2.9 | -24.2 338 GORDON B 11.9 0.1 3.9 | -24.2 339 YELLE S 11.0 0.4 3.3 | -24.2 340 VRBATA R 12.7 3.4 0.8 | -24.3 341 COOKE M 12.3 0.8 2.5 | -24.3 342 SLATER J 9.5 0.2 0.5 | -24.6 343 SHARP P 12.3 1.9 2.9 | -24.6 344 GAUTHIER D 12.0 0.0 4.6 | -24.6 345 FIDDLER V 10.6 0.2 2.8 | -24.7 346 JONES R 12.0 1.2 2.9 | -24.7 347 CHISTOV S 7.7 0.9 0.0 | -24.7 348 SAMSONOV S 11.8 2.0 0.1 | -24.9 349 RIVET C 15.5 2.2 3.4 | -25.0 350 BABCHUK A 13.6 2.1 1.8 | -25.0 351 CULLIMORE J 12.4 0.1 3.8 | -25.3 352 DALEY T 16.0 0.7 2.6 | -25.3 353 BOYES B 12.4 2.8 0.8 | -25.3 354 WISNIEWSKI J 15.4 2.2 1.5 | -25.8 355 ASHAM A 9.1 0.2 0.0 | -25.9 356 FERENCE A 13.2 2.1 3.2 | -26.0 357 BOURQUE R 12.0 2.3 1.6 | -26.0 358 GRIER M 12.4 0.7 3.3 | -26.1 359 WALKER M 13.4 0.1 1.7 | -26.3 360 BEECH K 9.2 3.1 0.1 | -26.3 361 MORRISONN S 16.4 0.3 4.2 | -26.3 362 CAMPOLI C 12.3 1.9 0.6 | -26.3 363 MIETTINEN A 11.1 2.9 0.3 | -26.7 364 BOOGAARD D 4.6 0.0 0.0 | -26.8 365 HALE D 9.6 0.0 0.0 | -26.9 366 HEDICAN B 15.6 2.3 2.1 | -26.9 367 AFANASENKOV D 11.3 0.4 0.0 | -27.1 368 RADIVOJEVIC B 10.9 2.0 0.1 | -27.5 369 MODRY J 14.4 1.5 1.6 | -27.5 370 BRASHEAR D 7.5 0.4 0.0 | -27.5 371 SAUER K 15.7 0.1 2.6 | -27.5 372 HAINSEY R 15.5 3.7 3.6 | -27.9 373 SIM J 9.9 1.9 0.0 | -28.1 374 MARTIN P 19.4 3.1 2.7 | -28.1 375 MARA P 15.9 2.8 3.2 | -28.2 376 LINDROS E 11.0 3.6 0.0 | -28.2 377 WARD A 16.4 0.3 3.0 | -28.4 378 GREEN M 12.7 2.5 0.2 | -28.5 379 MODIN F 12.5 3.6 3.1 | -28.6 380 HAGMAN N 11.2 0.6 2.6 | -28.6 381 FITZPATRICK R 11.7 0.3 2.0 | -28.8 382 NEIL C 11.0 2.1 0.0 | -28.8 383 LINDEN T 8.8 1.9 1.6 | -28.8 384 BREWER E 17.2 3.4 3.9 | -28.9 385 HOLIK B 12.2 1.3 2.4 | -29.1 386 HALPERN J 13.0 1.0 2.9 | -29.1 387 MALHOTRA M 11.1 0.6 3.0 | -29.4 388 SMITH J 16.9 0.1 4.0 | -29.4 389 SALMELAINEN T 8.9 0.7 0.3 | -29.4 390 MEZEI B 13.1 0.2 2.7 | -29.9 391 THORNTON S 8.4 0.1 0.0 | -30.0 392 PARK R 8.4 0.1 3.1 | -30.6 393 KAPANEN N 10.1 0.5 0.1 | -30.7 394 LUKOWICH B 17.0 0.3 3.0 | -30.7 395 WARD J 9.1 0.2 3.0 | -30.8 396 ERIKSSON L 11.8 1.4 0.0 | -31.0 397 ALBERTS A 16.2 0.2 3.3 | -31.3 398 DVORAK R 12.4 2.2 1.1 | -31.5 399 KRAJICEK L 14.1 2.4 2.1 | -31.7 400 RICHARDSON B 10.2 0.1 2.9 | -32.1 401 TORRES R 12.4 1.8 0.0 | -32.3 402 ROBIDAS S 14.7 1.8 1.6 | -32.5 403 TALBOT M 9.7 0.1 4.1 | -32.5 404 CLYMER B 10.8 2.3 0.6 | -32.6 405 WALZ W 12.6 0.2 2.1 | -32.7 406 LAPIERRE M 9.9 0.1 1.5 | -32.7 407 GORGES J 14.6 0.7 2.5 | -32.7 408 DIPENTA J 10.9 0.0 1.3 | -33.3 409 BELANGER E 10.7 2.7 1.5 | -33.3 410 UMBERGER R 11.1 0.9 2.5 | -33.5 411 O'SULLIVAN P 10.1 3.2 0.7 | -33.6 412 BOULTON E 6.2 0.0 0.0 | -34.1 413 TOLLEFSEN O 12.0 0.1 2.1 | -34.2 414 MADDEN J 15.4 0.2 3.2 | -34.2 415 BATES S 9.1 0.2 3.2 | -34.4 416 LATENDRESSE G 10.8 1.8 0.0 | -34.5 417 FILPPULA V 9.7 0.8 0.8 | -34.5 418 GLEASON T 14.7 0.9 3.3 | -34.6 419 KOSTOPOULOS T 9.9 0.3 1.4 | -34.7 420 KUKKONEN L 12.5 1.4 2.6 | -34.8 421 CONROY C 11.8 2.1 1.6 | -34.9 422 BOYNTON N 13.7 0.5 2.6 | -34.9 423 ROENICK J 10.7 2.0 1.2 | -35.0 424 BONK R 12.4 0.5 3.0 | -35.1 425 EXELBY G 15.7 0.1 2.2 | -35.2 426 KESSEL P 11.6 2.4 0.1 | -35.2 427 YORK J 11.8 0.2 1.1 | -35.2 428 PEREZHOGIN A 11.1 0.7 0.0 | -35.3 429 VANDERMEER J 14.2 1.6 2.1 | -35.3 430 STAIOS S 16.1 2.1 3.2 | -35.4 431 STILLMAN C 13.2 4.1 0.0 | -35.4 432 DALLMAN K 10.0 2.4 0.4 | -35.5 433 ZHERDEV N 12.2 3.9 0.1 | -35.5 434 SMID L 16.0 1.2 2.0 | -35.7 435 JOHNSON M 12.2 0.5 2.6 | -36.1 436 MONTADOR S 11.6 0.8 0.7 | -36.4 437 STEFAN P 10.7 0.1 1.3 | -36.7 438 SJOSTROM F 10.8 0.6 2.7 | -36.9 439 LUPUL J 12.6 3.0 0.0 | -37.0 440 ODUYA J 15.5 1.5 1.5 | -37.3 441 SEABROOK B 15.1 2.1 3.5 | -37.3 442 SYDOR D 14.9 2.3 3.0 | -37.5 443 KAPANEN S 11.9 1.8 3.3 | -37.7 444 BELL M 11.2 1.7 0.0 | -37.8 445 DRAPER K 12.8 0.3 3.6 | -37.8 446 THORESEN P 10.0 0.5 0.9 | -38.0 447 RITCHIE B 8.4 0.3 1.1 | -38.1 448 SHANNON R 10.4 0.2 0.0 | -38.2 449 BULIS J 11.8 1.3 1.3 | -38.4 450 WARRENER R 13.7 0.1 3.3 | -38.6 451 GREENE M 14.7 0.1 2.8 | -38.6 452 BRYLIN S 13.6 2.5 1.6 | -39.0 453 NOVOTNY J 10.1 0.3 1.9 | -39.1 454 MITCHELL W 16.9 0.3 5.0 | -39.1 455 COWAN J 7.9 0.2 0.2 | -39.6 456 TYUTIN F 16.0 1.3 2.8 | -39.7 457 RISSMILLER P 9.6 0.3 2.3 | -39.7 458 WHITE C 18.5 0.7 3.3 | -39.9 459 KLESLA R 16.2 2.8 4.0 | -40.0 460 ARKHIPOV D 11.7 1.2 2.8 | -40.0 461 AMONTE T 11.8 1.4 1.0 | -40.1 462 BARNES S 12.5 0.5 3.1 | -40.2 463 HOSSA M 9.9 0.7 1.8 | -40.3 464 FOOTE A 16.6 3.2 5.0 | -40.5 465 ZIGOMANIS M 11.0 0.8 3.1 | -40.8 466 ORTMEYER J 10.3 0.2 2.1 | -40.9 467 SCHULTZ N 16.6 0.1 3.5 | -41.0 468 LAICH B 10.0 1.5 2.1 | -41.1 469 SALVADOR B 15.5 0.2 4.0 | -41.3 470 Aucoin A 14.0 2.7 4.2 | -41.7 471 PRATT N 12.8 0.0 3.0 | -42.1 472 FEDORUK T 8.9 0.1 0.0 | -42.1 473 BROWN C 9.7 0.1 3.3 | -42.2 474 HAMEL D 5.0 0.5 0.0 | -42.2 475 RYCROFT M 7.9 0.1 1.4 | -42.4 476 CALDER K 11.2 2.1 1.7 | -42.7 477 SMITH M 8.9 0.9 0.7 | -42.9 478 POCK T 13.7 1.3 1.2 | -43.3 479 NILSON M 10.3 0.4 2.4 | -43.8 480 SCATCHARD D 9.7 1.1 2.7 | -44.2 481 MILLER A 15.0 0.2 4.4 | -44.2 482 CHELIOS C 13.0 0.3 4.8 | -44.3 483 DANDENAULT M 14.0 0.2 2.0 | -44.4 484 MOEN T 11.9 0.2 2.7 | -44.6 485 LETOWSKI T 7.7 0.5 1.4 | -45.0 486 TARNASKY N 6.5 0.0 0.0 | -45.5 487 SARICH C 14.8 0.2 3.1 | -45.8 488 SVITOV A 10.9 1.8 1.1 | -45.9 489 MOORE D 10.3 0.6 2.2 | -46.0 490 GERVAIS B 13.3 1.2 0.9 | -46.2 491 SUTHERBY B 10.4 0.2 3.0 | -46.2 492 MAYERS J 11.4 0.2 2.9 | -46.5 493 ZYUZIN A 11.0 0.9 1.9 | -46.5 494 PETERSEN T 10.4 1.4 2.0 | -46.6 495 WILLSIE B 10.5 0.7 2.1 | -46.8 496 BEGIN S 9.3 0.0 2.6 | -47.0 497 TENKRAT P 10.2 1.5 0.9 | -47.4 498 DONOVAN S 11.5 0.2 2.2 | -47.5 499 FRIESEN J 9.1 0.5 2.5 | -47.6 500 LAROSE C 7.7 0.2 2.4 | -47.7 501 PAHLSSON S 12.7 0.2 4.5 | -47.8 502 SMITHSON J 7.5 0.2 3.4 | -48.1 503 POULIOT M 11.1 1.2 0.8 | -48.5 504 MOWERS M 9.7 0.2 2.1 | -48.7 505 HINOTE D 9.5 0.2 3.3 | -48.9 506 HORDICHUK D 4.7 0.1 0.0 | -49.0 507 KARLSSON A 7.9 0.2 0.3 | -49.0 508 NORSTROM M 16.4 0.4 4.2 | -49.3 509 RUPP M 5.5 0.9 0.0 | -49.6 510 LAPOINTE M 10.4 2.1 1.4 | -49.6 511 THORNTON S 10.1 0.2 2.0 | -49.8 512 BRADLEY M 10.4 0.1 1.4 | -50.4 513 NIINIMAA J 12.7 0.6 1.5 | -51.0 514 ROY A 4.5 0.0 0.0 | -51.2 515 RASMUSSEN E 9.3 0.1 0.0 | -51.7 516 JOHNSON R 9.6 0.1 2.7 | -51.8 517 PRIMEAU W 11.0 1.1 2.9 | -51.9 518 NICHOL S 9.1 0.1 3.2 | -51.9 519 MAIR A 7.4 0.1 0.0 | -52.4 520 EAGER B 8.2 0.1 0.0 | -52.5 521 PANDOLFO J 15.3 0.2 3.1 | -52.9 522 BRULE G 8.9 1.7 0.0 | -53.2 523 VEILLEUX S 10.7 0.4 1.2 | -53.7 524 LAAKSONEN A 7.8 0.0 2.8 | -53.9 525 RUUTU J 8.6 0.1 0.6 | -54.1 526 NIEDERMAYER R 12.7 0.2 3.7 | -54.2 527 DUPUIS P 11.7 0.8 2.7 | -54.4 528 TOOTOO J 8.2 0.1 0.0 | -55.0 529 HALL A 8.5 1.7 2.2 | -55.5 530 GOC M 9.3 0.3 2.3 | -55.6 531 REASONER M 10.3 0.8 2.7 | -55.9 532 VIGIER J 8.0 0.1 2.9 | -56.5 533 BELAK W 5.0 0.0 0.0 | -56.6 534 SMITH W 9.3 0.2 0.0 | -56.9 535 WINCHESTER B 7.7 0.4 0.0 | -57.3 536 CHOUINARD M 6.1 0.5 2.9 | -57.3 537 LARSEN B 9.1 0.1 3.2 | -57.9 538 HOLMQVIST M 10.0 0.9 2.9 | -58.6 539 MALTBY K 10.5 0.2 2.5 | -59.7 540 TAYLOR T 6.3 0.0 1.6 | -60.3 541 GREEN J 8.6 0.3 2.5 | -60.5 542 BETTS B 10.5 0.2 3.4 | -60.6 543 ADAMS C 7.7 0.1 2.3 | -61.6 544 CAMPBELL G 7.9 0.1 2.6 | -61.7 545 DRAKE D 9.4 0.2 3.3 | -61.8 546 JONES M 14.1 0.2 2.1 | -62.8 547 IVANANS R 6.9 0.1 0.0 | -62.9 548 BURROWS A 7.9 0.2 3.3 | -64.8 549 DOWD J 6.4 0.1 1.9 | -65.8 550 GRATTON J 5.7 0.2 0.0 | -68.0 551 Orr C 5.3 0.0 0.0 | -70.6 552 SHELLEY J 4.8 0.0 0.0 | -71.9 553 MCGRATTAN B 3.7 0.0 0.0 | -72.3 554 HOLLWEG R 8.0 0.1 0.1 | -72.6 555 HOGGAN J 6.5 0.1 0.5 | -73.1 556 MURRAY G 7.5 0.0 0.8 | -74.7 557 PETERS A 3.7 0.0 0.0 | -78.0 558 JANSSEN C 4.1 0.0 0.0 | -83.5

Anonymous said...

Fatigue is an interesting theory, and I don't doubt it exists, but the way the NHL is played I am not sure you can analyze fatigue without simultaneously analyzing who the players are playing with and against and even the game situation.

First off many teams line match so players on the ice at any given time might accumulate minutes at more or less the same rate.

Second, a team that is winning by a couple of goals in the third period might ease off trying to score goals this making players on good teams look like they fatigue in the third period when in fact they just play a different style. Conversely teams that trail in the third period will play a more offensive style to score goals. If you simultaneously considering goals against might help eliminate change in style of play.

Finally, every player is going to fatigue at different rates based on their style of play, their age, and most importantly their conditioning level.

Again, I don't doubt that fatigue exists but I am just not convinced that the analysis that you are doing considers all the factors necessary. It might be interesting to do a simple test by taking a ratio of third period PF/Min vs First and Second period PF/Min and then see how that ratio correlates with total ice time. You could even take it a step further by only considering 'close' games so that style of play changes are minimal.

Plus, a more important fatigue might is probably playing in back to back games. If every team plays the same number of back to back games and plays the same number of opponents on the second night of back to back games then maybe the results if your analysis won't change much, but for any single game it does matter immensely as can be seen by teams winning percentages in back to back games. Playing on the road probably also contributes to fatigue.

JavaGeek said...

1. Matching in the regular season is not that dominant that it would have a huge effect on this analysis. Its effects wouldn't affect the results, as the players get more ice time against the same competition their scoring rates still fall with increased ice time. (I don't see a problem here).

2. The question to ask here is how is the coach adjusting his lines when he goes into his defensive shell. If he increases the top line minutes in the last period that will mean he has to decrease the minutes of his lower guys. This would imply his lower guys should start scoring more often. In other words the one will cancel out the other.

3. Due to this, some coefficients can become quite “strange” and aren’t very meaningful on the individual player level as many players do better with more ice time, which could be because they are paired with better players when they get more ice time. But, I’m not trying to discover an individual player’s fatigue pattern; instead I am looking for a trend in the NHL. So I take an average of all the coefficients to get an average coefficient.

The question I'm not asking: "Does player performance degrade in the third period, due to fatigue". That would be quite different. Fatigue occurs as soon as you skate down the ice to chase a puck and if you're double shifted you have a lot less time to recover: you wont chase the puck as much and you probably wont score as often. That's all this is trying to do. Players are built to play for 60 minutes so their performance should be reasonably constant under ideal conditions, but if they play outside their conditioning or experience their performance should fall...

If this wasn't the case why then does Radulov and others with similar stats get such little ice time?

I did the defensive regression and it does appear that as players get tired they substitute offense with defense.