# 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) $(130-80-30) < (100-80-50) \implies \frac{1}{\gamma} < \frac{10}{3}$

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!)

1. 1 compliment, 1 question, 1 challenge…

1. First, I have been reading for a while now and I love this stuff! Especially this article… it really hit a lot of the things myself and a buddy were working on. It feels good to have a lot of your theories independently supported by someone else, especially someone as concise as yourself.

2. As far as the guide goes, since it is news to me that the developers did not write it, what do you think of the table that describes the primary and secondary attributes? It’s hard not to notice that the secondary attributes for a goaltender are reversed from that of an offensive center. Do you think this implies any meaning? You have shown you believe the 2 secondaries to have equal impact on their EPA. Maybe you could comment on this.

3. I have never formally talked about or used this average of important qualities. I was going to challenge you, and say that if training increase/decrease was linear that time saved with the first two attributes would equal time lost with the last one.
But this is only true assuming you train each attribute for an equal length of time. Doing that gives the unwated side effect that your attributes approach the same ratio your qualities have relative to each other.

In short I am glad you also pointed that out, it was not readily intuitive that it is true a 60-60-60 is better.

Thanks,

Comment by Nathan — January 19, 2010 @ 6:08 pm

• Hi Nathan,

re “2.”: there is a way to answer the question. Collect the data – I mean, the exact player builds and the corresponding team strength ratings – and then try reverse engineering the links between the attributes, EPA and the team strength rating. Maybe I should ask some volunteers to send their data so I can try my luck…

There might be a world beyond the EPA. The Guide provides a detailed explanation of the different skills. So, for example, a team with lower strength rating might have a better passing and aggressiveness and thus dominate the game and eventually beat a seemingly “stronger” team.

Different attributes may be important in various game situations. For example, for the most of the time a center might be recognized by his EPA (2:1:1), but in the face-offs one could consider only the technique. The same goes for technique + aggressiveness for body-check situations and passing when in control of the puck.

Should the game engine be sufficiently complicated, players of different builds can be “incomparable” in general – only the game situation, the opponent and the tactical settings determine, who is better. The formula for computing the EPA can still be correct – but the game would be more than that.

As far as I know, large parts of the Guide were written up when the implementation of the game was still in progress. This is why some things described in the Guide are not really implemented. Have you noticed the lack of correlation between puck control, face-offs and shots on the net? The puck control does “distinguish” powerplay situations, but is there much beyond that?

This is why I believe in simple theories and simple ratios and cling on everything that shows in a clear direction. The future may prove me wrong.

On 3: you can check that if you train a 60-60-60 player for the 2:1:1 ratio, his effective quality is 60. For the 85-85-10 player the effective quality is BELOW 30, so he will take twice so long to raise his OR effectively – even though his PRIMARY quality is 85!

The key point is to look at the TIME needed to improve by one point. The training ratio is roughly proportional to the quality (plus a random factor). Q99 2 days, Q50 4 days, Q25 8 days, Q12 16 days, you catch the drift – one very low quality spoils the whole soup 🙂

Comment by glanvalleyeaglets — January 20, 2010 @ 10:42 am

• 3 topics to touch on again, numbered for easy reference

1. If it is true that there is a much larger world beyond the EPA, and that many of these situations break the mold beyond a players ability to execute the basic tasks of their position like “Offensive effectiveness”, that would make it harder to figure out the most effective team build strategy.

I know we are hoping this is the case when facing that much better team according to the Overall Team Stength hahaha

2. One of your previous articles on team Strength (cumulative stars) and the correlation to winning suggests to me that shooting, offense, defense and goaltending are the biggest factors for winning a game. However, I guess it wouldn’t show up as statistically significant if very few people are pursuing alternate player builds like “the hitman”, “the play maker” and “the face off pro” etc. etc. Those that do pursue those builds and win more often than it seems they should for a team with their team strength would look like outliers (if too few people are pursuing these builds).

3. About your very first comment, where you suggested reverse engineering the links between attributes and the team strength… I think a great many people would be interested!

Comment by Nathan — January 22, 2010 @ 4:47 pm

2. In regards to the 60-60-60 is better than 85-85-10. That point I have been trying to make for a while, but I like people don’t believe it as I get cheaper players to train on the market because of it.

I see it much like you do.

If you train in a 2-1-1 fashion, and for your facilities and staff are at a level that the quality (Q) = the training percentage (T) per day then to build a player to

40-20-20 from scratch would take (in full days)

@ 85-85-10 Qualities
((40/.85)+(20/.85)+20/.1)
= 48 + 24 + 200 or 272 days

@ 60-60-60 Qualities
((40/.6)+(20/.6)+(20/.6))
= 67 + 34 + 34 or 135 days

So in actual fact 60-60-60 is nit just better but is actually twice as good as 85-85-10, although I am not sure if there is a drop off in training efficiency to quality level. is the training improvement from a quality of 60-70 the same as the training improvement from from a quality of 80-90?

Comment by Sean — January 28, 2010 @ 6:40 pm

• Hi mate,

Thanks for all your great bogs!
I have read them with great interest.
If you ever want to research something more in PPM, I would be very interested how across the board, teams with 3 lines set perform against teams with 4 lines set. And how the 4-4-3 teams compare to both.
Is it true that 3-3-3 teams tend to have a weaker third period against 4-4-4 teams?

Cheers,

Schorpie

Comment by Schorpie — February 10, 2010 @ 7:11 am

3. Great post(s), I’ve been using your analysis to great advantage having just ended my 1st regular season in 3rd place! So first off thanks for the great work, it’s helped enrich the game for me a lot!

The point I’d like to make – as someone who knows very little about math – is how well PPM simulates real hockey. I’ve built my team around basic (Canadian) hockey commonsense.

‘You don’t score if you don’t shoot’ is certainly true in this game. I focus on player’s who can shoot the puck – especially defencemen and centres. Of course your wingers should be snipers, but if you can pepper the net from all sides you will win more than you lose.

‘Go with the hot hand’ is also totally true. Through blind luck, I bought a young goalie for \$30,000 in one of my first trades. He was better than my original goalie, so I figured that I’d use him until I could afford a better one. He played well, so I kept using him and he kept winning. At the season midpoint, I had enough money, so I bought an expensive older goalie with MUCH better skills than my first guy, but guess who’s my starter? The young, cheap one who I believed in. He probably would have be awarded Rookie of the year if they awarded such a thing on PPM, LOL. He finish his first season as the leagues’ #1 goalie at the tender age of 17 and was also awarded a first full ‘star’. (Ambróz Studený /Canada/Hogtown Habs/20/1160/374/24/93.58/5/4)

Statistics are important (after all, this game is fundamentally math) but don’t forget the emotion and passion of the game either. I think that might be the game’s X-factor.

p.s. If you are looking for areas to research, why not do a complete analysis of tactics vs. chemistry/energy in the playoffs. I’ve been playing under the very Canadian assumption that every playoff game is by its very nature ‘Important’ and it’s brought me to the brink of the league championship (with 2 overtime and 1 shootout win so far). Very Canadian, eh?

Comment by BadHabits — March 9, 2010 @ 11:32 pm

• The 3rd paragraph should read ‘You CAN’T score if you don’t shoot.’

Comment by BadHabits — March 9, 2010 @ 11:36 pm