WOWY Is Worthless: Part 1

We know a lot about the Blues players without using WOWY. Looking at the Blues Corsi results for last season we see:

Player	Corsi%
TARASENKO	58.1
STEEN	57.0
SOBOTKA	56.9
SCHWARTZ	56.7
BACKES	55.5
SHATTENKIRK	55.3
PIETRANGELO	54.9
BERGLUND	54.6
OSHIE	54.5
BOUWMEESTER	53.9
OTT	53.7
PAAJARVI	53.4
ROY	53.2
LEOPOLD	53.1
JACKMAN	52.9
COLAIACOVO	52.4
JASKIN	52.3
POLAK	49.4
CRACKNELL	48.8
STEWART	48.4
MORROW	48.4
COLE	48.4
PORTER	47.2
REAVES	46.3
LAPIERRE	45.2

Tarasenko is the best Blues player, with Steen, Sobotka, and Schwartz not far behind. Lapierre is the worst Blues player, with Reaves and Porter also at the bottom of the table.

Without resorting to WOWY, we know that Tarasenko had to have a tendency to make the other Blues players better. His numbers were better than everybody else, so your shifts with Tarasenko had to be better than your shifts without him (on average). Similarly, your shifts with Lapierre had to be worse than your shifts without him. Remember that WOWY isn't really With Or Without You. It's With You or With Some Other Guy. Tarasenko is, by definition, better than SOG, whoever that may be. The only place where WOWY would be of value is if there is some unsuspected synergy between two players.

For example, if you look at David Backes With/Without Patrik Berglund, it looks like there may be something there. Backes with Berglund is 68.2%. Backes without Berglund is 55.4% Maybe Bergy has some synergy with Backes.

Card Shuffling Model

Let's use a card shuffling model for WOWY. David Backes had 1388 5v5 shifts in 2013-14. He had 1010 offensive Corsi events and 810 defensive Corsi events. Imagine that we write the results of each shift on cards, one shift to a card. We would have a ton of cards that say "Offense: 0 Defense: 0", a lot that say "Offense: 1 Defense: 0", a lot that say "Offense: 0 Defense: 1", etc., on up to 4 cards that say "Offense: 5 Defense: 0", and one card that says "Offense: 1 Defense: 7".

If Bergy has no effect of Backes, if we shuffle the cards and deal them randomly, he should get some good cards and some bad cards. If Bergy has a positive effect on Backes, he should get more good cards than we can account for simply by random shuffling. If Bergy has a negative effect on Backes, he should get more bad cards than predicted.

It looks like Backes had about 35 shifts with Berglund and therefor about 1353 without. (The numbers are a little inexact because sometimes their shifts didn't begin and end at the same time.) To simulate Backes with and without Berglund we can take the 1388 Backes cards and shuffle them up. Put 35 cards in the "With" pile and the other 1353 in the "Without" pile. Total up the Corsi events "With" and "Without". Repeat 10,000 times. What we get for Berglund is the following:

The lowest "With" we see is 24.4%. The highest "With" is 86.7% The 95% Confidence Interval is 38.1% to 72.7%. Bergy isn't magic! The 68.2% we saw could easily just be randomness.

Next up, Backes and Steen. 990 shifts/cards with Steen 398 without. Then Backes and Oshie. 880 shifts/cards "With" and 508 "Without". Repeat the process throughout the lineup. We get

Player	With/Without	Actual With	0%	2.5%	97.5%	100%
BACKES	BERGLUND	0.682	0.244	0.381	0.727	0.867
BACKES	BOUWMEESTER	0.567	0.505	0.529	0.582	0.603
BACKES	COLAIACOVO	0.558	0.326	0.440	0.671	0.794
BACKES	COLE	0.506	0.396	0.470	0.639	0.731
BACKES	CRACKNELL	0.500	0.000	0.200	0.889	1.000
BACKES	JACKMAN	0.539	0.465	0.507	0.603	0.658
BACKES	JASKIN	0.778	0.000	0.273	0.824	1.000
BACKES	LAPIERRE	0.545	0.071	0.310	0.800	1.000
BACKES	LEOPOLD	0.562	0.379	0.456	0.651	0.709
BACKES	MORROW	0.468	0.293	0.407	0.703	0.830
BACKES	OSHIE	0.562	0.512	0.534	0.576	0.598
BACKES	OTT	0.481	0.315	0.444	0.664	0.811
BACKES	PAAJARVI	0.500	0.138	0.342	0.765	0.936
BACKES	PIETRANGELO	0.572	0.503	0.530	0.580	0.613
BACKES	POLAK	0.509	0.431	0.501	0.609	0.658
BACKES	PORTER	0.615	0.118	0.321	0.786	0.950
BACKES	REAVES	0.396	0.262	0.392	0.717	0.900
BACKES	ROY	0.624	0.325	0.438	0.674	0.790
BACKES	SCHWARTZ	0.596	0.474	0.510	0.600	0.640
BACKES	SHATTENKIRK	0.548	0.466	0.508	0.601	0.639
BACKES	SOBOTKA	0.450	0.207	0.372	0.737	0.893
BACKES	STEEN	0.554	0.523	0.538	0.573	0.589
BACKES	STEWART	0.468	0.397	0.479	0.633	0.698
BACKES	TARASENKO	0.710	0.277	0.406	0.702	0.827

In this table, 0% is the lowest value seen in the Monte Carlo, 2.5% is the lower limit of the 95% Confidence Interval, 97.5% is the upper limit of the 95% Confidence Interval, and 100% is the highest value seen. So when it comes to their effect on Backes, Stewart is just below the lower limit of what you would expect to get from random shuffling and Tarasenko just above the upper limit.

If you do this for all 25 Blues players, and look at all 25x24 = 600 WOWY interactions, we get 38 pairs where the observed value is above the upper boundary of the 95% Confidence Interval and 45 pairs where the observed value is below the lower boundary of the 95% CI. (We would expect a total of about 30 pairs to fall out of the CI (5% of 600)). The players who made their teammates better:

Players	Number of Pairs
Berglund	3
Bouwmeester	1
Colaiacovo	1
Ott	1
Paajarvi	1
Pietrangelo	2
Roy	3
Schwartz	3
Sobotka	6
Steen	7
Tarasenko	7

20 of the 38, slightly more than half, come from Tarasenko, Steen, and Sobotka. The players who made their teammates worse:

Players	Number of Pairs
Backes	1
Bouwmeester	1
Cole	5
Cracknell 1	1
Jackman 2	2
Lapierre 10	10
Leopold 1	1
Morrow 3	3
Ott 1	1
Polak 5	5
Porter 3	3
Reaves 5	5
Stewart 6	6
Tarasenko 1	1

A little less than half (21 of 48) come from Lapierre, Stewart, and Reaves. Add in Polak and they explain more than half. Amusingly, Tarasenko makes Lapierre worse.

Sample size issues

Bouwmeester makes Cracknell "better" based on 72 events (41min 27sec). Paajarvi makes Roy "better" based on 132 events (75m 37s). Bouwmeester made Jackman "worse". 54 events or 28m 38s. Tarasenko and Lapierre had 50 events together in 29m 12s. Pretty much all of the "significant" effects are based on very limited samples sizes.

Talent is persistent

If Bouwmeester truly makes Cracknell better, it ought to happen year after year. Let me define WDiff as (Corsi With) – (Corsi Without). In the Backes/Berglund example above WDiff is 68.2% - 55.5% = 12.7%. or 0.127. Looking back a year at the available pairs

Player	With/Without	2013-14 WDiff	2012-13 WDiff
COLAIACOVO	BERGLUND	0.160	NA
OTT	BERGLUND	0.096	NA
SHATTENKIRK	BERGLUND	0.060	0.000
CRACKNELL	BOUWMEESTER	0.173	-0.095
BERGLUND	COLAIACOVO	0.108	NA
BERGLUND	OTT	0.078	NA
ROY	PAAJARVI	0.114	NA
BOUWMEESTER	PIETRANGELO	0.095	0.099
PORTER	PIETRANGELO	0.141	0.036
LAPIERRE	ROY	0.156	NA
PAAJARVI	ROY	0.120	NA
STEEN	ROY	0.169	NA
JACKMAN	SCHWARTZ	0.061	-0.003
MORROW	SCHWARTZ	0.172	NA
POLAK	SCHWARTZ	0.088	-0.055
BERGLUND	SHATTENKIRK	0.076	0.099
JACKMAN	SHATTENKIRK	0.056	0.030
ROY	SHATTENKIRK	0.084	NA
COLE	SOBOTKA	0.120	0.147
MORROW	SOBOTKA	0.125	NA
POLAK	SOBOTKA	0.099	0.063
SHATTENKIRK	SOBOTKA	0.067	0.007
STEWART	SOBOTKA	0.114	0.026
TARASENKO	SOBOTKA	0.070	0.081
BERGLUND	STEEN	0.135	No events
BOUWMEESTER	STEEN	0.061	0.131
OSHIE	STEEN	0.064	-0.058
PIETRANGELO	STEEN	0.061	-0.023
POLAK	STEEN	0.072	-0.215
ROY	STEEN	0.206	NA
TARASENKO	STEEN	0.141	-0.021
BACKES	TARASENKO	0.160	0.042
BERGLUND	TARASENKO	0.062	0.101
JACKMAN	TARASENKO	0.105	0.097
PIETRANGELO	TARASENKO	0.060	0.033
SHATTENKIRK	TARASENKO	0.091	0.036
SOBOTKA	TARASENKO	0.092	-0.093
STEEN	TARASENKO	0.152	0.057

So a lot of these "effects" look to be merely random fluctuations.

A problem with this model

An issue I have with this model is that I think it substantially underestimates the variability in these systems. As a result, this model suggests that some player A/player B pairs show a statistically significant effect when really there is nothing there. I will get into why this model underestimates the variability in part 4 (so you have that to look forward to!).

So let's take a different approach. Doctors like placebos. ("Placebo. So powerful, it's the standard by which medications are tested. ") In part 2, I look at WOWY using a form of placebo.