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01-30-2008, 11:45 PM
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Czech Your Math
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Quote:
Originally Posted by seventieslord View Post
This looke like it could be quite useful... but can you better explain it?
Sorry, I meant to post an explanation earlier, but although the idea is simple, it can be difficult to explain.

I am attempting to derive a number to use to calculate adjusted playoff goals per game, by using the regular season GPG and adjusting it based on actual playoff results. The point of adjusting statistics is to give them the proper contextual value. When goals are more easily scored, the value of each goal is diminished. When goals are scarcer, the value of each goal is increased.

To account for the difference in scoring level between the playoffs, I calculated expected playoff goals by team. For each team, the equation would be:

(EPG) Expected Playoff Goals = poGM * [ (rsGF + rsGA) / rsGM]

GF=Goals For; GA=Goals Against; GM=Games; po=playoffs; rs=regular season; GPG=total goals per game

The EPG for all teams would then be summed to get a total EPG for that season.

Actual Playoff Goals (APG) is then summed by team and then totalled for the season.

If a team scored at the same level as the regular season (and likewise the league did overall during the playoffs), then APG=EPG. The teams in the playoffs scored at the level you would expect based on regular season statistics.

If there was a four team league, where each plays 50 games:

team A: 200 GF, 150 GA
team B: 150 GF, 100 GA
team C: 250 GF, 250 GA
team D: 200 GF, 300 GA

The regular season scoring level is (800 GF + 800 GA)/200 GM = 8.0 GPG

Two teams play for the trophy, A and B. They play a 6 game series, during which A outscores B 24-21.

So what number should be used to adjust playoff statistics? Could use regular season GPG of 8.0 or calculate actual playoff GPG:

APG = (24+21)/6 = 45/6 = 7.5 GPG

However, I took this approach:

in regular season team A averaged (200+150)/50 = 350/50 = 7.0 GPG, while team B averaged (150+100)/50 = 250/50 = 5.0 GPG

So, in the playoffs, EPG = [(7.0*6) + (5.0*6)]/(6+6) = (42+30)/12 = 72/12 = 6.0 GPG

Since actual APG was 7.5 GPG, the ratio of actual to expected GPG is (7.5)/(6.0) = 1.25. This means the teams scored 25% more goals than expected by their regular season performance.

To get a number for adjusted playoff goals that corresponds to the regular season number, it is adjusted as follows:

Adjusted Playoff GPG = rsGPG * (APG/EPG) = 8.0 * 1.25 = 10.0

This happens in some playoff seasons, but it's more common that adjusted playoff GPG is less than regular season GPG.

I hope this helped to clarify my approach to this project.

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