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01-24-2013, 08:38 PM
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Rough ice time estimates are pretty straightforward. No need to reverse-engineer an existing method. And in fact we may not want to use a method to estimate Gretzky that was derived for use with the general population of players.

Take Gretzky in 1981-82.

Special teams ice time is really easy. Gretzky was on the ice for 75 of Edmonton's 86 PPG or 87%. The PP is probably less efficient without him so let's say he get's 80-85% of PP ice time. Gretzky was on the ice for 14 of 67 PPGA, or 21%. But he also scored 6 G and 2 A while shorthanded, so he may be killing overmatched second PP units. Let's say he's on anywhere from 20-30% of the time on the PK. I don't feel like estimating team special teams ice time so let's assume PP and PK are equal on the team level. Gretzky was on the ice for about 50-60% of special teams ice time.

At even strength Edmonton scored 310 and allowed 220.
Gretzky was on the ice for 190 ES+SH GF and 109 ES+SH GA. Remove a few goals to eliminate SH, leaving 182 ESGF and 102 ESGA for Gretzky.

Let's use a few different assumptions.

1. Goals are scored at the same rate when Gretzky is on the ice as when he is off the ice. Edmonton just scores more of them with him on the ice. So because 54% of ES goals are scored with Gretzky on the ice, he played 54% of ES ice time.

2. Gretzky's defensive effect is zero and his offensive effect is hugely positive for Edmonton. In this case his GA alone provide the best estimate. So because Gretzky was on the ice for 46% of ESGA he was on the ice for 46% of ES ice time.

3. Gretzky was an incredible defensive player but average offensively. GF alone provide the best estimate. Gretzky was on the ice for 59% of GF and 59% of ES ice time. (Yes this is a stupid assumption but Sports Illustrated wrote that Sather said Gretzky was playing 38 minutes a game in 1981-82. For that to be true the assumptions given here would have to be true.)

4. Gretzky cheated for his offence, costing his team GA. The team allowed GA at a 10% higher rate when he was on the ice. So he was on for 46% of GA but only 43% of ice time.

Which assumption is true? Well, Edmonton actually allowed fewer goals than the league average in 1981-82 (220 ESGA compared to 239 league average) so I doubt Gretzky was worse defensively than the average first line centre. But if teams tend to allow more GA with their top line on the ice, assumption 4 could still be close. I'm going to throw out assumption 3 as stupid.

Anyway, let's say that reasonable estimates for Gretzky's ES ice time range from 43% to 54%, depending on your assumptions. (The higher-end assumptions suggest Gretzky as a puck-possession-dominant player who lowers GA as much as boosting GF by denying the other team the puck, rather than a gambling attacker who liked to trade chances.) And his special teams ice time is 50+%. So it's not inconceivable that Gretzky played 30 minutes a game in 1981-82. The lower-end estimates would put him around 26 minutes a game.

One factor that may or may not be considered - bottom sixers tend to play things safe in the ice time era and the estimates are probably based on that assumption, with lower GF and GA rates for lesser players. Did this assumption hold in the 1970s and 1980s?

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