Penalty Killing

[zg88]

Since the disastrous (1-for-5?) Dartmouth game knocked the Big Red P.K. from the top of the national rankings to about 12th, they have managed to claw their way back to #3!

(#2 combined special teams)

[Josh '99]

Also, they're back to #1 in the conference in both PP and PK after having behind Dartmouth in PP and SLU in PK.

How's this for statistical weirdness:

Our conference combined special teams,
17/65 PP + 47/54 PK = 64/119 combined = 53.8%

is somehow WORSE than RPI's combined special teams,
12/54 PP + 50/60 PK = 62/114 combined = 54.3%

despite the fact that they're 3rd in the conference in PP and 5th in PK.  I'm not even gonna try to figure out why that is.

[Beeeej]

Because it's bad math.  You're adding fractions by adding the numerators and denominators, which is simply wrong - you can't add 2/3 and 2/5 and expect that the result should be 4/8.

Beeeej

[ugarte]

Because it's bad math.

The math isn't wrong in one sense: RPI has a higher percentage of good outcomes per special teams opportunity than we do.  

The statistic is deceptive because they are given "credit" for the extra penalty kills that they get because they are a man down more often than we are, (though they only kill 50% of those "extra" penalties) and it outweighs (on a percentage basis) the credit we get from our additional goals from being on the power play more often (though we score on 45% of those "extra" power plays).

[zg88]

OK, so what IS the correct formula for "combined special teams"??

My somewhat-intellectually-lazy guess:  (PP% + PK%)/2

Which, if applied to Josh's admittedly-puzzling brain-teaser, gives:

ECAC combined special teams:
Cornell:  (26.2% + 87.0%)/2 = 56.6%
......RPI:  (22.2% + 83.3%)/2 = 52.8%

...And, thus, everything is right with the universe once again...

(The real formula may involve weighting the PP & PK percentages based on the relative numbers of opportunities... but that's too much math for me right now... anyone??)

[rsafploc 03]

Guess this is all the doing of good ole simpson's paradox...  ::nut::

learnt that recently in or270....:-D

[Greg Berge]

The correct formula for combined special teams (and screw anybody who says otherwise):

(Cornell successful pp chances + Cornell killed shorthands)
 / (Cornell pp + Cornell shorthands)

Example:

Say Cornell is 2x5 on pp, and Harvard is 1x4 on pp.

Cornell combined special teams =

(2 + (4-1)) / (5 + 4) = 5/9 = .556

Harvard combined special teams =

(1 + (5-2)) / (4 + 5) = 4/9 = .444

Note that if you simply combined the percentages, you would have:

Cornell combined special teams =

.400 + .250 = .650

which is wrong.

[pat]

If you combine those percentages a la zg88's formula, you get:

Cor PP = 2/5 = .400                       Har PP = 1/4 = .250
Cor PK = 3/4 = .750                       Har PK = 3/5 = .600
Cor CST = (.4+.75)/2 = .575               Har CST = (.25+.6)/2 = .425

which still adds up to 1.000, as it should. Having said that; that's not how they do it, they add the numerators and denominators. (Where "they" in this case is collegehockeystats.com.) Now, if one of those penalties was a major, that's a whole 'nother kettle o' fish.

[jeh25]

For this reason, and due to laziness, I prefer to use rank order. Plus the math is easier.

Add our PP rank to our PK rank. #1 + #1 = 2.

Add Dartmouth's PP (#2) to their PK (#7). 2 + 7 =9

SLU 6 + 2 = 8

etc.

Lowest score wins....

[Al DeFlorio]

The explanation is that you're literally adding apples with oranges in coming up with a total percentage.  Even the worst penalty-killing team will have a much higher percentage of success killing penalties than the best power-play team will have scoring on a penalty.  So, if a team has more PK opportunities than PP opportunities (e.g., RPI), it will inflate the total percentage, especially if the team being compared with (e.g., Cornell) has more PP opportunities than PK opportunities.

Take an extreme case to demonstrate the point:

Team A has a great power play and converts on 25 of 75 opportunities (33.3%).  It kills all 25 of its PK opportunities (100%).  So it winds up with a total success rate of 50% (50 of 100) (and would rank below both RPI and Cornell in the example above).

Team B has a terrible power play (0 for 25) and manages to kill only 50 of 75 penalties (66.7%), but winds up with the same 50% success rate.

[ugarte]

Al made the point I was trying to make, but better. Thanks for the pickup.

::help:: no longer needed.

[Al DeFlorio]

And apologies for not giving credit where due.