# The [ppm] eyrie

## January 19, 2010

### Players

Filed under: powerplay manager hockey, PPM.miscellaneuous, Uncategorized — glanvalleyeaglets @ 3:21 pm

This is an article I always wanted to do – about the named bundle of attributes, qualities and statistics, about the silent knight of Powerplay Manager, about the goat, ass, horse or hypogrif that carries or brings down the hopes of the manager, the entity that gets nominated for the national team and without hesitation goes through fire and water, checks and fights, not afraid of any kind of fractures, inflammations, abdominal stretches and anginas when serving his Manager, who are you, my dear reader. Let me introduce Mr. Ice Hockey Player. Treat him well and he will thank you on the ice.

Your goal must be to train the player correctly, preferably so that he is the best possible player he could ever be at any time. I’ll leave the definition of the phrase “best player” as an exercise for the interested reader 🙂

The best service you can do to a Player is give him the right training for a certain position. The player will become your vision, so take care to have the right visions. It is perfectly all right if you want to turn a young center into a winger, if he has the quality-wise disposition for this. Scout your players, this will show you the way.

Read the Guide if you haven’t done so yet. Re-read it every now and then. The Guide was never written by the actual developers, so it is no wonder that it contains lots of bugs and omissions. Follow the Guide, but don’t trust it. Don’t trust me either, I’m much further from the developers than the authors of the Guide.

One of the most quoted and mysterious passages in the Guide is the following:

“Player with attributes 180 – 25 – 25 or 70 – 90 – 90 /where the first one is the primary main attribute and the last two are secondary main attributes/ is not as good for the given position as a player with attributes 120 – 30 – 50. Similarly a player with attributes 130 – 80 – 30 or 80 – 80 – 80 is not as good as a player with attributes 100 – 80 – 50.”

What in the world is it supposed to mean? Here are two of the most common misinterpretations of this verse:

* Guide states that 100-80-50 is the best distribution
* There is a built-in penalty for excessive secondary attributes, so 70-90-90 might be strictly worse than 70-70-70.

The Guide doesn’t state any of this. Instead, the Guide
* identifies a player with its primary and secondary attributes (three numbers) and
* states that a player P can be strictly better or worse than player Q for a given position.

Hold your horses, what does it mean “better”? My best guess is that the Guide compares players according to their contribution to the team and line strength rating (a.k.a. the pucks and the stars). In this sense one can introduce a number that measures the effectivity of a player for a certain position. I sometimes call it the “effective primary attribute” (EPA).

The guide confirms that EPA depends only on the primary and both secondary attributes. The possible dependence of this relation on the position remains obscure.

I will try to interpret what the Guide tells about the EPA, and will use some maths. If you want to skip this section, you are welcome to do so.

Let me denote the primary and secondary skills by A, B and C. We are looking for a non-negative function of three non-negative arguments with following properties:

1) Monotonicity (better attributes = better player): if $A_1>A_2, B_1>B_2, C_1>C_2$, then $EPA(A_1,B_1,C_1)>EPA(A_2,B_2,C_2)$
2) the A-skill monster punisher: as any one or two of $A, B, C$ tend to infinity and the third remains fixed, $EPA(A,B,C)$ remains bounded.

The simplest functions with the desired properties (punishing the weakest link) are involving the minimum operator:
$EPA(A,B,C)= \mathrm{min} \{A, B/\beta, C/\gamma\},$
where $\beta, \gamma>0$ are constants. Such function has a clear interpretation: the optimal ratio of skills is $1:\beta:\gamma.$

The constants can be estimated by using the examples from the Guide. The strictest inequalities are:

1) $(70-90-90) < (120-30-50) \implies \frac{1}{\beta} > \frac{7}{3}$
2) $(130-80-30) < (100-80-50) \implies \frac{1}{\gamma} < \frac{10}{3}$

I will add another one:
3) Since the first secondary skill cannot be less worth than the second secondary skill, we have $\frac{1}{\beta}\leq \frac{1}{\gamma}.$

(1-3) together imply: $\frac{7}{3} < \frac{1}{\beta} \leq \frac{1}{\gamma} < \frac{10}{3}$,

So according to the Guide, the optimal distribution should be in the range (7-10):3:3.

At the beginning of the third season a group of Latvian managers carried out an experiment to find out the optimal primary-to-secondary skill ratio for goalkeepers. They nominated only one goalie for the first game of the league, and then collected the attributes, chemistry and experience in a table together with the rating for goaltending. The data were surprisingly consistent and clearly demonstrated that the ratio 1:0.5:0.5 = 2:1:1 gives the best results.

It also supported the old rumors about the influence of Chemistry and Experience. This law of thumb states that “100 points of chemistry give +20% to the attributes and each 100 points of experience give additional +20% to the attributes.”

So this might be the key to high rating of team strength. Have we come closer to answers to the question – what is the best training for my Mr. Player?

Not necessarily.

* The best Defender will not help his team much if he spends his life in the cooler. A good way to reduce his time on the penalty bench is – train up his technique to match the aggressiveness. Open question: should the Tec:Agg ratio be 1:1, 9:10, or perhaps even 2:1?

* The shooting attribute is independent from the primary/secondary bundle. Open question: which ratio to the primary and secondary skills is the best for the different positions?

* Passing, Technique and Aggressiveness: is there a use for higher values of these attributes than half of the primary skill?

* The “alien primary skills”: does the center need defense and if so, how much?

* Special players: perhaps it is wise to build several types of players – the offensive specialists for PP, defensive masters for PK, mix up good passers and good shooters to increase the productivity of a line? If so, then different attribute ratios should be followed for different players.

It is up to the manager.

Now back to the quality of a player. Yes, I mean it, THE quality.

Suppose you want to train your Player in $k$ skills with the ratio $R_1:R_2: \dots :R_k$. Let the corresponding qualities of the attributes be $Q_1, Q_2, \dots, Q_k$ and the daily progress of the attributes at the current stage of development is correspondingly $P_1,P_2, \dots, P_k.$

Then the effective quality of the player for that ratio is given by the weighted harmonic mean

$\frac{R_1 + R_2 + \dots + R_k}{\frac{R_1}{Q_1} + \frac{R_2}{Q_2} + \dots + \frac{R_k}{Q_k}},$

and the average time in days for the player to increase his overall rating by one point with the current facilities and staff is the weighted mean

$\frac{\frac{R_1}{P_1} + \frac{R_2}{P_2} + \dots + \frac{R_k}{P_k}}{R_1 + R_2 + \dots + R_k}.$

Along with the age and career longevity, the effective quality is the only parameter that determines the future of the player and should be the only number to look at when evaluating a future prospect!

(A side note. There is a weird misconception traveling around, which is called the average of important qualities. This has no “physical” interpretation and anybody using it should be sued for crimes against maths. Qualities 60-60-60 are MUCH better than 85-85-10!)