overpass
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- Jun 7, 2007
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Here's a statistical method for identifying which defencemen played together at even strength, using historical game log plus-minus data which goes back to 1959-60. It's most useful for historical seasons for which we don't have any ice-time data on which players played together.
It's relatively easy to identify which forwards played together by looking at the scoring logs and seeing which forwards combined for goals. But it's relatively rare for two defencemen to combine on a goal, especially at even strength, so we have to look for another solution for defencemen. It's possible to look at the seasonal plus-minus totals and take a guess, but these guesses aren't always accurate for various reasons. Maybe the defencemen didn't play together all season, or maybe there are several defencemen all in the same range for seasonal plus-minus.
It's possible to identify which defencemen played together the most by lining up their game by game plus-minus for the season and finding the correlation between each of their game by game plus-minus results, using the correlation function in Excel. Correlations range from -1 to 1. For this method, a correlation approaching 1, e.g. 0.8 or 0.9, would mean that the players usually played together.
Here's an example, using the 1962-63 Leafs.
Tim Horton and Allan Stanley's game by game plus-minus had a very high correlation of 0.86, indicating that they were regular partners. Same with Carl Brewer and Bob Baun (0.84). Kent Douglas doesn't appear to have had a regular partner, and his highest correlation is 0.40 with Carl Brewer, possibly because Douglas played with Brewer during the 22 games that Baun missed.
Stanley-Horton
Brewer-Baun
Douglas
The same method should work for the forwards as well, although it adds less information because we can already look to see which forwards combined on points together.
Frank Mahovlich: Red Kelly 0.89, Bob Nevin 0.53, Eddie Shack 0.32, Dave Keon 0.28
Red Kelly: Frank Mahovlich 0.89, Bob Nevin 0.53, Eddie Shack 0.32, Ron Stewart 0.30,
Bob Nevin: Frank Mahovlich 0.53, Red Kelly 0.53, Bob Pulford 0.36, Billy Harris 0.28
Red Kelly and Frank Mahovlich appear to have been linemates all season. Bob Nevin was their most frequent RW, with Eddie Shack and others also playing some RW, and Nevin also played some time with Pulford and Harris.
Dave Keon: George Armstrong 0.85, Dick Duff 0.72, Frank Mahovlich 0.28
George Armstrong: Dave Keon 0.85, Dick Duff 0.79, Billy Harris 0.26, Red Kelly 0.24
Dick Duff: George Armstrong 0.79, Dave Keon 0.72, Red Kelly 0.21
Duff-Keon-Armstrong appears to have been a regular line.
Bob Pulford: Ron Stewart 0.66, Billy Harris 0.55, Eddie Shack 0.43, Bob Nevin 0.36
Billy Harris: Bob Pulford 0.55, Ron Stewart 0.50, Bob Nevin 0.28, George Armstrong 0.26
Ron Stewart: Bob Pulford 0.66, Billy Harris 0.50, Red Kelly 0.30, Eddie Shack 0.25
Pulford-Harris-Stewart was the most common third line, but wasn't as regular as the Keon line or the Mahovlich-Kelly duo. Eddie Shack, Bob Nevin, and others also got some time here.
Eddie Shack: Bob Pulford 0.43, Frank Mahovlich 0.32, Red Kelly 0.32, Ron Stewart 0.25, Billy Harris 0.21
Ed Litzenberger: Bob Pulford 0.26, Ron Stewart 0.20, Bob Nevin 0.16
Neither of the two spare forwards had regular linemates, as you would expect. It looks like Shack spent some time with Mahovlich-Kelly and some time on the third line, but very little with Keon's line. Litzenberger has very little correlation with anyone and was probably more of a true spare forward.
Mahovlich-Kelly-Nevin
Duff-Keon-Armstrong
Pulford-Harris-Stewart
Shack, Litzenberger
We can also use the plus-minus correlations to see if any forwards and defence spent more time together, or if it was pretty evenly distributed. Starting with the first line.
Douglas has lower correlations most likely because he was the 5th defenceman at EV for most of the season and played less ice time. The Mahovlich-Kelly-Nevin line appears to have played more or less evenly with the Horton-Stanley pairing and the Brewer-Baun pairing.
There may have been something going on at the RW position, where Armstrong was more likely to play with Brewer-Baun or Brewer-Douglas and Stewart more likely to play with Stanley-Horton. There's less of a pattern, if any, with the LWs and Cs on these lines.
It's relatively easy to identify which forwards played together by looking at the scoring logs and seeing which forwards combined for goals. But it's relatively rare for two defencemen to combine on a goal, especially at even strength, so we have to look for another solution for defencemen. It's possible to look at the seasonal plus-minus totals and take a guess, but these guesses aren't always accurate for various reasons. Maybe the defencemen didn't play together all season, or maybe there are several defencemen all in the same range for seasonal plus-minus.
It's possible to identify which defencemen played together the most by lining up their game by game plus-minus for the season and finding the correlation between each of their game by game plus-minus results, using the correlation function in Excel. Correlations range from -1 to 1. For this method, a correlation approaching 1, e.g. 0.8 or 0.9, would mean that the players usually played together.
Here's an example, using the 1962-63 Leafs.
Player | Position | GP | +/- | Horton | Stanley | Brewer | Baun | Douglas |
Tim Horton | D | 70 | 1 | 1.00 | 0.86 | 0.05 | 0.09 | 0.20 |
Allan Stanley | D | 61 | 2 | 0.86 | 1.00 | 0.01 | -0.07 | -0.02 |
Carl Brewer | D | 70 | 32 | 0.05 | 0.01 | 1.00 | 0.84 | 0.40 |
Bob Baun | D | 48 | 14 | 0.09 | -0.07 | 0.84 | 1.00 | 0.15 |
Kent Douglas | D | 70 | 18 | 0.20 | -0.02 | 0.40 | 0.15 | 1.00 |
Tim Horton and Allan Stanley's game by game plus-minus had a very high correlation of 0.86, indicating that they were regular partners. Same with Carl Brewer and Bob Baun (0.84). Kent Douglas doesn't appear to have had a regular partner, and his highest correlation is 0.40 with Carl Brewer, possibly because Douglas played with Brewer during the 22 games that Baun missed.
Stanley-Horton
Brewer-Baun
Douglas
The same method should work for the forwards as well, although it adds less information because we can already look to see which forwards combined on points together.
Frank Mahovlich: Red Kelly 0.89, Bob Nevin 0.53, Eddie Shack 0.32, Dave Keon 0.28
Red Kelly: Frank Mahovlich 0.89, Bob Nevin 0.53, Eddie Shack 0.32, Ron Stewart 0.30,
Bob Nevin: Frank Mahovlich 0.53, Red Kelly 0.53, Bob Pulford 0.36, Billy Harris 0.28
Red Kelly and Frank Mahovlich appear to have been linemates all season. Bob Nevin was their most frequent RW, with Eddie Shack and others also playing some RW, and Nevin also played some time with Pulford and Harris.
Dave Keon: George Armstrong 0.85, Dick Duff 0.72, Frank Mahovlich 0.28
George Armstrong: Dave Keon 0.85, Dick Duff 0.79, Billy Harris 0.26, Red Kelly 0.24
Dick Duff: George Armstrong 0.79, Dave Keon 0.72, Red Kelly 0.21
Duff-Keon-Armstrong appears to have been a regular line.
Bob Pulford: Ron Stewart 0.66, Billy Harris 0.55, Eddie Shack 0.43, Bob Nevin 0.36
Billy Harris: Bob Pulford 0.55, Ron Stewart 0.50, Bob Nevin 0.28, George Armstrong 0.26
Ron Stewart: Bob Pulford 0.66, Billy Harris 0.50, Red Kelly 0.30, Eddie Shack 0.25
Pulford-Harris-Stewart was the most common third line, but wasn't as regular as the Keon line or the Mahovlich-Kelly duo. Eddie Shack, Bob Nevin, and others also got some time here.
Eddie Shack: Bob Pulford 0.43, Frank Mahovlich 0.32, Red Kelly 0.32, Ron Stewart 0.25, Billy Harris 0.21
Ed Litzenberger: Bob Pulford 0.26, Ron Stewart 0.20, Bob Nevin 0.16
Neither of the two spare forwards had regular linemates, as you would expect. It looks like Shack spent some time with Mahovlich-Kelly and some time on the third line, but very little with Keon's line. Litzenberger has very little correlation with anyone and was probably more of a true spare forward.
Mahovlich-Kelly-Nevin
Duff-Keon-Armstrong
Pulford-Harris-Stewart
Shack, Litzenberger
We can also use the plus-minus correlations to see if any forwards and defence spent more time together, or if it was pretty evenly distributed. Starting with the first line.
Player | Position | Horton | Stanley | Brewer | Baun | Douglas |
Frank Mahovlich | LW | 0.50 | 0.37 | 0.32 | 0.54 | 0.28 |
Red Kelly | C | 0.52 | 0.43 | 0.31 | 0.48 | 0.26 |
Bob Nevin | RW | 0.35 | 0.43 | 0.50 | 0.47 | 0.23 |
Douglas has lower correlations most likely because he was the 5th defenceman at EV for most of the season and played less ice time. The Mahovlich-Kelly-Nevin line appears to have played more or less evenly with the Horton-Stanley pairing and the Brewer-Baun pairing.
Player | Position | Horton | Stanley | Brewer | Baun | Douglas |
Dick Duff | LW | 0.35 | 0.25 | 0.36 | 0.40 | 0.19 |
Dave Keon | C | 0.39 | 0.25 | 0.36 | 0.37 | 0.33 |
George Armstrong | RW | 0.31 | 0.12 | 0.49 | 0.52 | 0.32 |
Player | Position | Horton | Stanley | Brewer | Baun | Douglas |
Bob Pulford | LW | 0.40 | 0.33 | 0.54 | 0.35 | 0.45 |
Billy Harris | C | 0.34 | 0.31 | 0.40 | 0.48 | 0.25 |
Ron Stewart | RW | 0.51 | 0.52 | 0.22 | 0.29 | 0.10 |
There may have been something going on at the RW position, where Armstrong was more likely to play with Brewer-Baun or Brewer-Douglas and Stewart more likely to play with Stanley-Horton. There's less of a pattern, if any, with the LWs and Cs on these lines.