The [ppm] eyrie

November 6, 2009

Advanced PPM-o-metrics

Filed under: powerplay manager hockey, PPM.statistics — glanvalleyeaglets @ 3:43 pm

Howdy everyone,

I haven’t posted for a while, you should appreciate the reasons – the daily job, the autumn blues, Dinamo Riga underperforming in the second KHL season and, most importantly, the lack of fresh ideas and results to present.

There are many discussions out there about the use and futility of counter-tactics, inconsistency of the game engines, about theories how to build player attributes to suit the demands of certain tactics. I don’t “know” the answers, all I can provide is evidence based on evaluation of over 200 000 games played in the second season of powerplay manager hockey. My opinions and interpretations may be wrong, cruical aspects of the game might be missing in my analysis and you can always believe your intutition outperforms any analysis, or you might just not believe the existence of a “game matrix” when facing the evident and omnipresent random factor making you win a game with 10:0 and losing the next one by 0:10 all settings being equal. Nevertheless I think I have a point to make and this blog is the perfect vehicle for doing so.

Let me keep this stupid and simple – apart from the aesthetics, ice hockey is all about scoring goals and preventing goals. In order to score goals, you have to shoot on the net and shoot with a certain quality. Everybody knows, what the average number of shots per game means. The quality of the shots is measured by the shot efficiency, which I’ll define as the inverse of “shots per goal” (the number of shots needed to score 1 goal). 5 goals with 40 shots gives an efficiency of 5/40 = .125 = 12.5%.

Take the number of shots per game and multiply it by the shot efficiency and you’ll recover the number of goals scored. Learn how to control the two factors and you’ll understand the game. What are the important factors and variables? How big or small is the random factor and what does it depend on?

The best variables available for analysing team strength are the “stars” shown in the profile page of a team. Let us suppose our team has a goaltending at 29 (notation: G+=29), defence at 26 (D+=26), offence at 25 (O+=25) and shooting at 23 (S+=23), and our opponent has goalkeeping G-=28, defence D-=19, offence O-=24 and shooting S-=17. In order to compare our offence to opponent’s defence, we introduce the offence-defence quotient O+/D-, which in this case would be 25/19=1.32. A good measure of comparison between our shooting quality and opponent’s goaltending quality is the shooting-goaltending quotient S+/G- given by 23/28=0.82. It turns out that these along with the corresponding quotients from opponent’s point of view (O-/D+ and S-/G+) are very important indicators for the chances of the teams.

Let us look at the graph in Figure 1. It shows the average number of shots per game versus the offence-defence quotient O+/D-. The blue line is computed from the data of all teams, the green line – from teams playing the right countertactics and the red line – from teams playing against the countertactics.

Avg shots per game vs O+/D-

Fig. 1. Average shots per game versus the O+/D- quotient for all teams (blue), teams playing countertactics (green) and teams playing against countertactics (red)

Evidently this is a “master curve” of the game. We see how the counter-tactics work (improving the shot differential), we see that teams with a weak offence perform few shots against a team with a strong defence, and we see that there is a saturation effect – the average number of shots per game stays below 35.

The lines show an almost cosmic order, but there is the back-side – the mighty random. To estimate its influence, let me introduce the variance \sigma=\sqrt{N^{-1}\sum_{i=1}^N (x_i-\bar{x})^2}. It is a moment of probability distribution function, but very roughly saying, in most games the deviation will be considerably smaller than \sigma.

O+/D- Shots p G Variance \sigma
30-40 16.5 3.28
50-60 20.8 7.17
80-90 27.4 12.8
120-130 31.0 15.8
150-160 32.3 17.1
170-180 32.9 17.4
200+ 33.2 17.5

What this shows is that a weak offensive line will not likely create many shots against a much stronger defence (low variance at low O+/D- levels), but the stronger team may have a good or bad shooting day 🙂 (By the way, the rule of three sigmas doesn’t apply here as the number of shots is not a normal random variable.) (Should provide a graph to illustrate this in the future.)

So we have learned that the number of shots on the net depends on the offence-defence quotient. If one keeps the O+/D- quotient constant and increases the strength of the own defence, the number of shots slightly increases. This probably has to do with the fact that the better defence creates more offensive situations and the defenders themselves are more likely to take a shot or two. We also have seen the huge variance, so don’t come to me and complain that your team managed only 20 shots whereas it was suppose to generate at least 30. It will all even out in the long run 🙂

Do different tactics have different number of shots versus O+/D- quotient curves? If this was true, then there might be a tactic suited for stopping better offensive lines, or a tactic that generates more shots on average, but is it so? Is there a secret key to success hidden in the sea of data?

Alas, see Figure 2.

ShotsTac

Figure 2. Shots per game vs O+/D- for various tactics (excluding counter-tactics situations). (Sorry, there are three 'extra' zeroes on the y axis, cross them out when reading the graph)

This study suggests that the answer is negative. Within the margin of errors the lines coincide. (It has to be remarked that towards the extreme ends of the graph the error margin increases considerably due to significanltly smaller amount of available data.) Once more, for underlining and pinning on the walls: no tactics is better suited to a certain team, every one will perform the same way in the long run. Or, more modestly, I could not confirm the opposite to be true although the Universe knows I tried 🙂

Let us now move to the second parameter – shot efficiency alias scoring percentage. Figure 3 below shows the mastercurve “shot efficiency vs the shooting-goaltending quotient S+/G-” for all teams (blue line), teams playing counter-tactics (red line) and teams playing against countertactics (red line).

EfF_CT

Fig. 3. Shot efficiency vs S+/G- for all teams (blue), teams playing countertactics (green) and teams playing against countertactics (red)

This chart is worth a thousand words. Not only does it confirm that the relation between shooting skill and opponent’s goaltending skill is the most important factor determining the scoring percentage, but it also shows an almost linear dependence of shot percentage on S+/G-. One more thing we can read off the curves is that counter-tactics do not influence the shot percentage.

To estimate the magnitude of random in scoring efficiency (including the famous goalie’s good/bad night effect), let us look at the variances.

S+/G- Shot effic. % Variance \sigma
30-40 5.9 5.84
50-60 10.2 6.09
80-90 13.7 7.03
120-130 18.4 7.91
150-160 21.9 8.92
170-180 24.2 9.42
200+ 29.1 10.6

As we see, the variance grows slower than the scoring efficiency, hence the bigger your S+/G- advantage, the less likely gets the chance for the great upset. It is difficult enough for an average goalie to stop a much stronger offence. However, and I want to emphesize this, the stronger the goalie, the larger the relative fluctuations in his game!

However, S+/G- is not the only one parameter that influences the scoring percentage. You don’t have to train the shooting skill exclusively to improve your shot efficiency. This curve happens to shift considerably with changing offence-defence O+/D- quotient.

EfF_OD

Fig. 4. Shot efficiency versus shooting-goaltending ratio (S+/G-) for various offence-defence ratios (O+/D-)

This is illustrated in Figure 4.

Again, no words are required to explain the results – except that I’ve found out that the shot efficiency is more sensitive with respect to shooting-goaltending ratio S+/G- than it is to offence-defence ratio O+/D-. The bottom line is – you gotta train both offence and shooting for the best performance 🙂

The final picture for today studies the curves for different tactics played.

GKTac

Fig. 5. Goaltending efficiency versus goaltending-shooting ratio (G+/S-) for the different tactics.

Figure 5 shows the opposite quantities to Figure 4, namely, goalkeeping efficiency versus goalkeeping-shooting ratio G+/S-. However, it is basically the same thing as goalkeeping efficiency is just 100% minus shot efficiency and G+/S- is just reversed S-/G+, so basically it is the same thing (but the tactics are chosen by the defensive team). The thing to take home from here is the fact that the curves coincide within the margin of error. No optimal tactics for a great goalie or for a team with great shooting, it is all the same 🙂

I’d like to conclude that the following passage in the Guide is henceforth a busted myth:

“Every team has a different composition of player attributes and therefore a different style of play is suitable for each team. Therefore you need to find the right style of play that suits your team. A different style of play is suitable for a team with a weak goalie and brilliant forwards and vice versa for a team with a goalie star. “

Hopefully they’ll implement it some day 🙂

Right, folks, that’s it for today. Good luck for the upcoming playoffs everyone! (And thanks for your interest, I never expected to get tens of thousands of hits in the first half-year of this blog!)

September 17, 2009

The key factor

Filed under: powerplay manager hockey, PPM.statistics — glanvalleyeaglets @ 12:08 pm

Let us put the tactics and game importance aside for a while and ask: what is the most important factor that decides the outcome of a game? Today we’ll talk team strength. Whether we like it or not, as much as we sometimes wish an underdog to win, the stronger teams usually do better and prevail in the long run. The ice-hockey simulation in powerplay manager is no exception.

One could write monographs about what makes a great team great. Luckily, it is easier in PPM. Each team has a profile page where you can find the estimate of team strength based on the lineup used in the previous official game. These are the ominous “stars”, the four integers indicating the levels of Goaltending, Defence, Offence and Shooting. There is a fifth one that shows the total team strength, but it is just the arithmetic mean of the former four. So let us look at the four numbers as a measure of team strength.

There is a long ongoing discussion about “what do you mean by saying that your team was much stronger”. With the scale going up to 200, it doesn’t sound like a big difference between 15 and 20, it is a basic beginners level. In the same time the difference between 15 and 20 is 25% down or 33% up, and this is no peanuts anymore. We can see whether our team is better or worse in terms of the stars, but how does it affect the chances of winning the bloody game? Be the first to know and keep reading this great feature article in the [ppm] eyrie. We bring to you the whole story as it unfolds! Blah, blah, blah!

A typical ppm ice hockey team in the middle of second season might have Goaltending GT rated at 16, Defence DF=16, Offence OF=15 and Shooting SH=14. My Eaglets have (23, 23, 22, 19); Radowan’s Enterprise is currently rated at (30,25,28,17), the best Latvian team Pardaugavas Lauvas impresses with (31,29,23,22).

We’ll do the simplest thing out there and just sum the four indicators (GT + DF + OF + SH) of both teams and compute the difference, and see how the teams perform against each other in dependence on this difference.

The results can be summarized in a table. The first column shows the difference, then the percentage of wins (in regular time), overtimes and losses of the stronger team and finally the number of games used to calculate the “odds”.

Diff W % OT % L % N
1-2 47.3 15.0 37.5 7588
3-4 51.8 14.5 33.5 7176
5-6 56.8 14.2 28.9 6153
7-8 62.0 13.4 24.4 5363
9-10 68.0 11.9 20.0 4609
11-12 72.3 11.0 16.6 3906
13-14 77.5 10.1 12.3 3412
15-16 81.7 8.0 10.2 2865
17-18 84.4 8.0 7.4 2298
19-20 88.6 6.9 4.4 1859
21-22 90.2 5.7 3.9 1512
23-24 92.9 4.2 2.7 1199
25-26 94.6 2.4 2.9 892
27-28 95.8 1.6 2.5 718
29-30 96.8 2.2 0.9 540
31+ 99.8 0.1 0.0 5199

The trend is visible, isn’t it? The advantage of some 6-7 team strength points weighs approximately as much as the correct counter-tactics. I hope to get to the corresponding effect of game importance in a future article.

How does this info add to the understanding of the game? Let’s speculate and assume that I am to throw my 87 points against Liepinsh’s 105. Under normal conditions I’m at -18 meaning that my chances of winning the game are somewhere around 7.4%. Can I influence my odds? Sure, I can choose the game importance and tactics. With the right counter-tactics, the odds would shift in my favor, perhaps the shift is worth as much as 6 points making the gap approx. -12 points wide. Why, according to this arithmetics, the chance of winning just sky-rocketed to 16%! If I am lucky and my team actually plays that tactics well and if I use higher game importance, my chances might improve even further. (Of course, the life is never as simple as that) 🙂

Just want to make a final remark. Perhaps I am looking at the wrong thing. The quotient of team strength indicators might be more important than the difference. Say, is the difference between 110 and 100 points “ten points” or “ten percent” wide? Is it as good as 20 vs 10 (difference) or as good as 11 vs 10 (quotient)? Or is it something in between? I don’t know the answer, but some day…

September 16, 2009

Tactics and home ice advantage

Filed under: powerplay manager hockey, PPM.statistics — glanvalleyeaglets @ 10:41 am

In the first season I was first and foremost interested in finding out the basic relations of the tactics and countertactics, so I only recorded the tactics and the score of the match. As the spread in the teams’ strength increases, the grand total tables make less sense, so I decided to create a more serious databasis for the second season. So for each game under consideration I store the tactics, game importance, team strength estimates (the “stars” for goaltending, defensive, offensive and shooting), shots, penalties and the final score. I find this is a much better tool for studying how this game works!

I hope this is the first post in a series of articles. Today I want to address a simple question: is there a home ice advantage in regular season games and what does it have to do with the tactics?

Let us start with the grand total table using all the games I’ve gone through. All are from the regular tournament of the second season, match days 1-16 (games with participation of inactive teams were excluded, but it was done with care in order not to lose games like this one 🙂 ). In total 48,770 games of powerplay manager ice-hockey. For those interested: the most popular pairing of tactics is Normal vs Normal with 5083 games; the most exotic is Defensive (home team) vs Breaking up (road team) with 416 games. Here the rows represent tactics of the home team, the columns – the tactics of the road team. The numbers are percentage of home wins, games with overtime and away wins.

Normal Offensive Defensive Counteratt Breaking Forecheck
Normal 48.1-11.4-40.3 42.3-11.8-45.8 63.1-10.4-26.4 47.1-13.5-39.2 37.8-10.1-52.0 45.8-10.8-43.2
Offensive 54.4-11.5-34.0 48.9-12.1-38.8 37.5-13.0-49.3 48.0-13.3-38.5 52.8-10.3-36.8 62.7-12.0-25.1
Defensive 37.8-12.5-49.6 59.6-12.4-27.9 48.0-12.3-39.6 51.0-11.6-37.2 47.8-11.7-40.3 43.6-13.2-43.0
Counteratt 49.3-12.0-38.6 48.1-12.6-39.2 47.6-11.3-40.9 48.0-13.2-38.6 58.1-11.8-30.0 37.0-9.0-53.8
Breaking 61.9-8.9-29.0 46.7-12.5-40.6 42.3-12.6-44.9 34.5-12.5-52.8 45.0-11.8-43.1 45.3-9.8-44.8
Forecheck 51.4-11.6-36.8 35.0-12.1-52.7 44.5-11.2-44.2 61.1-12.8-26.0 51.1-12.2-36.6 47.8-13.0-39.1

The home teams win approximately 48% of the games and lose some 40%, so there is a measurable home ice advantage in this game.

The average team in this study has goaltending rated at 16.1 stars, defense 16.0, offense 15.4 and shooting 14.1. No wonder that, for instance, offensive tactics overall does slightly better than defensive tactics (it is worth paying more attention to the weakest part of the team). For offensive teams, the opposite is the case!

On the top of this we clearly see the famous ring of countertactics in action!

Of course, games of equally rated teams are more interesting to us. Taking the sum of goaltending, defense, offense and shooting “stars” as a measure of team strength and filtering out all games where the difference exceeds 5, I was left with mere 18,508 games. Here is the resulting table:

Normal Offensive Defensive Counteratt Breaking Forecheck
Normal 49.5-14.5-35.9 46.8-15.7-37.4 65.9-12.0-22.0 50.4-15.4-34.1 38.7-12.0-49.1 47.5-12.9-39.5
Offensive 48.8-15.2-35.8 46.7-16.2-37.0 36.1-17.6-46.2 48.6-16.2-35.1 51.9-13.7-34.2 60.6-15.1-24.1
Defensive 34.5-16.5-48.8 63.3-14.3-22.2 45.9-14.2-39.8 45.8-16.2-37.9 49.4-11.7-38.8 43.4-17.3-39.1
Counteratt 51.4-13.7-34.8 52.0-15.2-32.7 48.2-14.5-37.1 47.7-16.5-35.7 60.0-12.8-27.2 36.3-12.1-51.5
Breaking 62.0-11.5-26.4 50.1-13.5-36.2 45.9-13.1-40.9 31.5-16.3-52.1 45.6-12.8-41.5 49.5-11.6-38.8
Forecheck 52.0-15.0-32.8 37.4-16.7-45.7 43.4-15.6-40.9 63.2-15.8-20.8 49.3-13.8-36.7 50.7-16.2-32.9

We see that in this case the draw margin is way bigger and that it is harder for the visiting team to win the game; home wins ~ 48%, away wins ~37% of the “equal” games.

I must stress that these tables are not there to suggest that “some tactics are better than others”. It is true that the tactics should suit your team and tactics that one team uses with great success may miserably fail for another team with different skill distribution.

So we have seen the importance of home ice in games of the regular season. It is claimed that there is no such thing in cup games or friendlies. In the next article I plan to go deeper into the overall team strength – performance relation. It will turn out that the team strength may be more important than the tactics 🙂

July 16, 2009

Tactics Check XL

Filed under: PPM.statistics — glanvalleyeaglets @ 8:31 am

Recently we have witnessed quite a few controversal discussions about the use and abuse of tactical tables. In the course of the discussions, the focus has shifted from “how do I use tactics to beat my opponent” to “how do I do my best to outshoot him”?

The shot differential is influenced by many factors. First there are the offensive and defensive skills of the guys on the virtual ice – all other factors being equal, the better team should outshoot the opponents. (Just for the record, in many cases it is far from being clear, which team is better.) Further important factors are game importance and seasonal energy – this has been documented in another article. The chemistry of the lines is a big deal too, and as the experience of the best players increases it might also play a major role in the coming seasons. There are more factors like home ice advantage etc. Now the tactics are supposed to act on this complex background.

Believe me, I would like to make scientifically correct statements about the tactics-countertactics relations, but I’m not in position of doing so. Technically speaking, we are dealing with multidimensional data with in part large uncertainties. We are about to ignore all the various “dimensions” – save the tactics 🙂 – and try to extract information on distribution of victories, goals, shots and penalty minutes. In theory, such model reduction requires a careful preparation and pre-conditioning of the incoming data. The main point is that if we want to ignore a variable, we ought make sure that the data are not biased by that variable…

The sociologists are dealing with similar problems when conducting some polls – the point is to choose the sample pool so that one can extrapolate the data from 1000 people to many millions and obtain realistic results (contrary to my intuition, this is indeed possible). In PPM we would require a range of teams with parameter distributions characteristic of the whole PPM, and getting this is hardly possible without breaking the rules (e.g., creating a thousand of teams for tests).

In the present study we go another way and sample the huge number of games by… a very large number of games! There is a certain doubt whether the skill distributions of teams preferring a given tactics is close enough to the skill distributions of all teams of PPM. All I can say is – nevermind.

To be sure we are after something that is real, let me cite one of the leading guys in PPM from the English forum.


vlady 10.07.2009 15:59:10
THE OFFICIAL STATEMENT OF THE DEVELOPMENT TEAM

You have been waiting for this for a long time and here it is. The number of shots is determined by the overall strength of the team compared to opponent and by the the tactic that you use. We will not disclose the details but these are the two main components that determine the number of shots on goal. It means that if you have a better team and if you have chosen the right tactic, you will most likely outshoot your opponent.

This part of the game engine is planned to be improved in the future though. We plan to take into account several other factors for you to ponder about.

Enjoy the game and don’t stress too much! Chill out people!

Ok, enough of text, let us turn to the results. Again, the data are given in the format Row vs Column. First line shows the percentage of wins, OTs and losses, S shows average shots per game, P penalty in minutes and N is the number of samples (i.e., games).

Normal Defensive Offensive Counteratt Breaking Forecheck
Normal 58.5-10.2-31.2
G: 4.41 – 3.17
S: 30.1 – 22.9
P: 2.98 – 4.00
N: 1855
42.6-11.7-45.5
G: 3.83 – 3.87
S: 27.1 – 27.2
P: 3.46 – 3.55
N: 3866
48.1-11.8-39.9
G: 4.04 – 3.61
S: 27.8 – 26.5
P: 3.31 – 3.68
N: 2548
36.1-11.0-52.7
G: 3.47 – 3.99
S: 23.9 – 29.3
P: 3.79 – 3.20
N: 1902
47.9-11.3-40.6
G: 4.12 – 3.63
S: 28.0 – 26.7
P: 3.29 – 3.73
N: 2816
Defensive 31.2-10.2-58.5
G: 3.17 – 4.41
S: 22.9 – 30.1
P: 4.00 – 2.98
N: 1855
53.7-11.2-35.0
G: 4.13 – 3.39
S: 29.7 – 23.8
P: 3.08 – 3.88
N: 1335
42.0-12.9-45.0
G: 3.77 – 3.88
S: 27.4 – 27.1
P: 3.39 – 3.75
N: 844
44.8-9.9-45.1
G: 3.80 – 3.83
S: 27.5 – 26.9
P: 3.40 – 3.59
N: 591
45.1-11.6-43.1
G: 3.93 – 3.80
S: 27.3 – 27.1
P: 3.54 – 3.51
N: 915
Offensive 45.5-11.7-42.6
G: 3.87 – 3.83
S: 27.2 – 27.1
P: 3.55 – 3.46
N: 3866
35.0-11.2-53.7
G: 3.39 – 4.13
S: 23.8 – 29.7
P: 3.88 – 3.08
N: 1335
47.0-10.9-42.0
G: 3.92 – 3.74
S: 27.4 – 26.8
P: 3.47 – 3.55
N: 1722
45.7-9.8-44.3
G: 3.90 – 3.69
S: 27.4 – 26.2
P: 3.25 – 3.63
N: 1116
60.7-11.3-27.8
G: 4.62 – 3.06
S: 30.4 – 22.1
P: 2.89 – 4.11
N: 1801
Counteratt 39.9-11.8-48.1
G: 3.61 – 4.04
S: 26.5 – 27.8
P: 3.68 – 3.31
N: 2548
45.0-12.9-42.0
G: 3.88 – 3.77
S: 27.1 – 27.4
P: 3.75 – 3.39
N: 844
42.0-10.9-47.0
G: 3.74 – 3.92
S: 26.8 – 27.4
P: 3.55 – 3.47
N: 1722
56.6-13.0-30.3
G: 4.27 – 3.14
S: 29.9 – 23.0
P: 2.98 – 3.94
N: 738
35.5-9.2-55.2
G: 3.32 – 4.24
S: 23.4 – 29.8
P: 3.77 – 3.23
N: 1343
Breaking 52.7-11.0-36.1
G: 3.99 – 3.47
S: 29.3 – 23.9
P: 3.20 – 3.79
N: 1902
45.1-9.9-44.8
G: 3.83 – 3.80
S: 26.9 – 27.5
P: 3.59 – 3.40
N: 591
44.3-9.8-45.7
G: 3.69 – 3.90
S: 26.2 – 27.4
P: 3.63 – 3.25
N: 1116
30.3-13.0-56.6
G: 3.14 – 4.27
S: 23.0 – 29.9
P: 3.94 – 2.98
N: 738
45.8-12.2-41.8
G: 4.00 – 3.84
S: 27.3 – 26.9
P: 3.48 – 3.51
N: 716
Forecheck 40.6-11.3-47.9
G: 3.63 – 4.12
S: 26.7 – 28.0
P: 3.73 – 3.29
N: 2816
43.1-11.6-45.1
G: 3.80 – 3.93
S: 27.1 – 27.3
P: 3.51 – 3.54
N: 915
27.8-11.3-60.7
G: 3.06 – 4.62
S: 22.1 – 30.4
P: 4.11 – 2.89
N: 1801
55.2-9.2-35.5
G: 4.24 – 3.32
S: 29.8 – 23.4
P: 3.23 – 3.77
N: 1343
41.8-12.2-45.8
G: 3.84 – 4.00
S: 26.9 – 27.3
P: 3.51 – 3.48
N: 716

The results have been compiled from games played in some German, Slovak, Czech and Latvian leagues in game days 22 through 38 (the games with participation of noname teams have been excluded), so all from the second round. Hence, this summary does not include any games used in this previous study.

We see that even though the teams have developed, the tactics still work in a very similar way, in particular, the ring of countertactics Normal > Defensive > Offensive > Forechecking > Counterattacks > Breaking up > Normal remains valid.

My last words for today: I am looking for new ideas. If you want a certain aspect of this game being dissected in a similar manner, please contact me or drop a line in the comments and I’ll see what I can do.

Good luck in the upcoming play-offs, folks!

Legal disclaimer: Dear guest who might have stumbled at this site and wonder what it is all about, please be aware that you are reading and using this ressource at your own risk. I won’t be liable for any kind of damage, whether direct or indirect, resulting from use of the information provided in this site, including but not limited to screwing up vitally important games and getting a round-house kick from Mr. Chuck Norris after having advised him to use this site. I am just a regular user of PPM and have no connections to the development team, however, I do assume that the game engine will change with time and this information will eventually be out of date. In such cases I am under no obligation to update this information. Ich habe fertig.

July 9, 2009

Game importance revisited

Filed under: PPM.statistics — glanvalleyeaglets @ 8:02 am

In a previous posting I had published some data that suggest a very minor impact of game importance on the final result. There was this feeling that playing with higher importance was as “D&G” – expensive and stupid (Dorogo & Glupo as they say). Now this is not the whole truth. Taking a bigger sample of match reports from League match days 1 through 4, this is what came out.

Low vs Normal
Sample size: 700 games
Result in percents: 41.1 – 11.2 – 47.5
Average result (goals): 3.71 – 3.96
Average shots per game: 25.4 – 28.9
Average penalties in minutes: 2.54 – 4.44

Low vs High
Sample size: 88 games
Result in percents: 35.2 – 10.2 – 54.5
Average result (goals): 3.15 – 4.07
Average shots: 22.4 – 30.0
Average penalties in minutes: 2.65 – 4.36

Normal vs High
Sample size: 1978 games
Result in percents: 41.9 – 14.0 – 44.0
Average result (goals): 3.88 – 3.89
Average shots: 26.2 – 28.5
Average penalties in minutes: 2.67 – 4.35

So we see that the team playing the higher importance has a slight but firm advantage in the games in spite of more time spent in the cooler. In a sharp contrast to this, the following are results from the second round (match days 22 thru 35).

Low vs Normal
Sample size: 2649 games
Result in percents: 51.0 – 12.1 – 36.7
Average result (goals): 4.00 – 3.42
Average shots per game: 26.6 – 27.4
Average penalties in minutes: 2.43 – 4.61

Low vs High
Sample size: 582 games
Result in percents: 74.3 – 7.2 – 18.3
Average result (goals): 5.42 – 2.56
Average shots per game: 28.9 – 24.1
Average penalties in minutes: 1.85 – 5.12

Normal vs High
Sample size: 5188 games
Result in percents: 71.4 – 8.4 – 20.0
Average result (goals): 5.27 – 2.69
Average shots per game: 29.7 – 23.2
Average penalties in minutes: 2.14 – 4.84

Actually that’s it for today. The figures here seem to say more than thousand words. Ok, I’ll write the essence of this all anyway: High importance should be used only a few times in a season. Misuse shall be punished by the game engine.

June 3, 2009

What the hell are these numbers!?

Filed under: PPM.statistics, Uncategorized — glanvalleyeaglets @ 10:30 am

Honestly, would you say you believe in statistics? I was taught to distrust any statistics that I didn’t make up myself. (98.3% of all statistics are actually made up.)

When I was younger, I was forced to have some lessons in the noble subject of mathematical statistics after my epic fail at the oral exam in probability theory, so I can hardly be accused of being in love with the matter which Laplace has called “common sense reduced to calculus”.

So, do you believe in statistics? Does the old sailor believe in the drag of the wind? Break the wind down to the molecules and you’ll see miriads of them releasing their kinetic energy to the wrong side of the sails. Break the great laws of Powerplay Manager down to single games and you’ll see nothing but Random. I bet I’ll deny the cosmic order when the mighty Random hits me in midair at the least appropriate time and that will surely happen provided that this is a part of the cosmic ppm order.

The topic is – how do we measure the weight of the wind given the molecules?

Let us start with an assumption. The game results are computed by some sophisticated, possibly probabilistic algorithm. (No malevolent demon or creature making fun of our feeble attempts to understand the natural laws.)

Consequently, given the values of all the visible and hidden variables that can influence the game, including but not limited to the skill attributes and seasonal energy of all the players engaged in the game and the tactical options chosen by the managers, there exists a well-defined probability for each event expressed in terms of result of the game, e.g., the probability of the event “team A wins” or of the event “the total number of shorthand goals scored by both teams in the game lies between 1 and 3”. The probability exists but remains unknown to us.

Let us first consider the idealized case that all teams are equal. This is certainly not true now and will be even less true in the future as the difference in rates of team development plays a more and more prominent role. Suppose that we observe n games, where team with tactics A plays vs a team with tactics B. Let us choose an event, e.g., that team A wins or that the game ends in overtime. Let us define the random variable X_k, which takes the value X_k=1 if the event happens in the k-th game and X_k=0 if it does not.

How would you estimate the probability of the event from the data (X_k)_{k=1}^{n}? Of course, you would count the cases when the event happened and divide by the total number of the games, i.e., you’d take the sample mean M:=\frac{\sum_{k=1}^nX_k} {n}. Let us ask the obvious question: how good is this estimate?

Evidently, the random variable nM is the sum of n Bernoulli random variables and hence has a binomial distribution. Let the true and unknown expectation of X_k for any k be p, then M has the expectation \mathbb{E}(M)=p and variance \sigma^2=p(1-p).

By the Central Limit Theorem we know that the random variable
Z:=\frac{M-p}{\left[M(1-M)/n\right]^{1/2}} \to N(0,1), n\to \infty
asymptotically (for large n) tends to the standard Gaussian distribution. From here we can express
p=M-Z\sqrt{\frac{M(1-M)}{n}},
but we know that Z \sim N(0,1) that gives us a weapon to compute the confidence intervals for our estimates!

For example, there is a 95 \% chance that Z\in (-1.96,+1.96), see here for other values (in this table you should look up the value of half of the probability, e.g., \frac{0.95}{2}=0.475 since the integration starts from zero.)

Let us assume that M=0.4 (a typical value in our statistics study), then for n=200 we get a \pm error of 0.0679, i.e., less than 7\%. For n=1000 this 95\% confidence interval halfwidth is 0.030 so that I dare say that a result of 50/30 in our data is a statistically significant difference while 44/41 is not!

So you still do not believe in statistics? Well, all of the above was true, had our random variables X_k had equal distributions. Alas, in the real virtual PPM life the outcome of a game with Tactics A vs Tactics B depends on so many additional factors, that we may fairly assume that for each k the expectation \mathbb{E}X_k=p_k is different. A generalization of the central limit theorem still holds, but what we are estimating is the value of n^{-1}\sum_{k} p_k. This value depends on the everchanging distribution of player skills, energies, injuries, teams that play this tactics – countertactics pair. In short, it depends on the available sample pool.

As long as the parameter distribution in this sample pool is neat enough, our data will give a faithful estimate of the performance of Tactics A vs Tactics B for “average” teams. I hope I have convinced you and thus can spare more detailed formulations and mathematical proofs of the corresponding results and conclude that there is a very good chance that our tactics-countertactics tables actually “work” for an “average” team, quod erat demonstrandum by this article.

June 2, 2009

Update on tactics

Filed under: PPM.statistics — glanvalleyeaglets @ 11:56 am

Half of the first regular PPM season is over, the games of the last 19-th round were played yesterday, so this seems to be a good time to update the tactical tables. I have added data from a few Slovak and Czech leagues; of course, the 21 top German leagues are still in the data pool. The total number of games included in these statistics is close to 3 countries times 21 leagues times 10 games times 19 rounds, which amounts to 11970 games. It is over ten thousand, mind you! The reader is encouraged to check the results as I am not a machine and as this would give him an idea about how it is to click through 10k game reports!

The reward is more data and more insight in the performance of less frequently applied tactics, such as Defensive versus Breaking (which is the smallest sample with 183 played games).

So, here we go:

D/SK/CZ Normal Defensive Offensive Counteratt Breaking Forecheck
Normal XX-XX-XX 315-69-167 481-151-545 418-129-404 233-80-430 519-154-446
Defensive 167-69-315 XX-XX-XX 178-48-109 122-43-95 82-25-76 132-51-119
Offensive 545-151-481 109-48-178 XX-XX-XX 238-66-215 141-59-153 398-87-140
Counteratt 404-129-418 95-43-122 215-66-238 XX-XX-XX 163-28-66 133-54-251
Breaking 430-80-233 76-25-82 153-59-141 66-28-163 XX-XX-XX 121-39-133
Forecheck 446-154-519 119-51-132 140-87-398 251-54-133 133-39-121 XX-XX-XX

The same table showing percentage of wins, overtimes and losses (row vs column):

D/SK/CZ Normal Defensive Offensive Counteratt Breaking Forecheck
Normal XX-XX-XX 57-13-30 41-13-46 44-14-43 31-11-58 46-14-40
Defensive 30-13-57 XX-XX-XX 53-14-33 47-17-37 45-14-42 44-17-39
Offensive 46-13-41 33-14-53 XX-XX-XX 46-13-41 40-17-43 64-14-22
Counteratt 42-14-44 37-17-47 41-13-46 XX-XX-XX 63-11-26 30-12-57
Breaking 58-11-31 42-14-45 43-17-40 26-11-63 XX-XX-XX 41-13-45
Forecheck 40-14-46 39-17-44 22-14-64 57-12-30 45-13-41 XX-XX-XX

It seams that the primary ring of tactics-countertactics looks as follows.

* Normal beats Defensive
* Defensive beats Offensive
* Offensive beats Forechecking
* Forechecking beats Counterattacks
* Counterattacks beats Breaking
* Breaking beats normal

Beautiful ring of countertactics, isn’t it? Reminds me of Ouroboros, the famous serpent that bites into its own tail 🙂

Let me quote the PPM Guide once more. It says,

“Finding the right style of play helps you achieve better results. Try finding the right style for your players. You can select from mutliple options. It is up to you, whether you choose to play offensively, defensively, counterattacks or you choose other option on this page. There are two things to remember. First: For every style of play there is an effective counter-play, which can give an advantage to the team that uses it. Second: Every team has a different composition of player attributes and therefore a different style of play is suitable for each team. Therefore you need to find the right style of play that suits your team. A different style of play is suitable for a team with a weak goalie and brilliant forwards and vice versa for a team with a goalie star.”

I firmly believe that the ring of counter-tactics, at least the dominant ring of first 19 rounds, has been identified in the current research project and related efforts. There is no guarantee that this ring won`t change with time (it only takes a small tweak in the game engine), and, of course, the tactics is just one facet of this complex game – still in some cases, choosing the right tactics can make the difference between three points and zero.

Concerning identification of the best-suited tactics for a team with given player skills distribution, this seems to be more difficult issue to investigate. One reason is that currently most teams are still pretty equal in skills. Furthermore, brute-force approaches involving gathering a huge mass of data and extracting some more or less valuable information are effectively prohibited by the makers of PPM, for the skills of players from other teams are only visible after scouting. What can I say, keep investigating this by yourself and stay tuned!

May 14, 2009

The russian science

Filed under: PPM.statistics — glanvalleyeaglets @ 8:14 am

The West has always lagged behind the Russians in the scientific arena.” The certain irony lying behind this citation which I took from the homepage of David Wilcock lies in the fact that both I and Wilcock use some real scientific data from Russia to feed wild speculations about a universe 🙂

A group of scientists from the data mining field under the supervision of the leader of Black Pilots have ( here and here ) published the last and ultimate volume of data about the performance of tactics and countertactics in PPM hockey game.

This time I will play Prometheus and not the Eagle and bring these secret data to you dear reader who have stumbled across this weblog. The data are stored as follows. #{Games with regular victory for row tactics} – #{Games with Overtime} – #{Games with regular victory for column tactics}

RU/UKR Nor Def Off Cat Brk Fch
Normal XX-XX-XX 57-8-46 111-43-148 96-30-83 37-24-86 65-11-74
Defensive 46-8-57 XX-XX-XX 40-11-30 17-4-18 23-5-14 19-6-21
Offensive 148-43-111 30-11-40 XX-XX-XX 71-21-44 47-13-41 52-7-26
Ctrattack 83-30-96 18-4-17 44-21-71 XX-XX-XX 39-6-15 17-7-46
Break up 86-24-37 14-5-23 41-13-47 15-6-39 XX-XX-XX 15-2-28
Forechcng 74-11-65 21-6-19 26-7-52 46-7-17 28-8-15 XX-XX-XX

These data are from the Russian leagues I.1-III.16 and Ukrainian leagues I.1-II.4, including all Russian games of Days 1-8 and some incomplete input from later days 9 and 10. These data may be regarded as independent from mine and hence interesting.

May 10, 2009

How important is game importance?

Filed under: PPM.statistics — glanvalleyeaglets @ 6:54 pm

“I am hunting high and low…” or should I rather take the golden mean and go with normal? This is supposed to be a high-wire act, a matter of balance – to save the seasonal energy while not losing too many points due to low importance.The cost in terms of energy has been revealed. A league game with low (L) importance costs 0.08 points of seasonal energy, for normal (N) importance it is 0.4 and 2.0 for high (H). The cost in terms of performance is far less known. So let us let the statistics speak. German leagues I.1 thru III.16 again, games of TeamNonames excluded.

Day H-N H-L N-L
1 12-1-12 2-1-1 5-1-9
7 7-5-16 0-0-2 6-2-9
8 17-4-15 1-2-0 8-1-8
9 8-6-18 0-0-2 5-7-9
10 13-6-17 1-0-1 10-2-7
NC2 21-8-32 0-2-2 8-1-11
11 13-3-10 2-0-1 11-0-11
12 10-7-14 1-0-2 11-0-5
13 8-5-19 1-0-3 4-3-14
Total 109-45-153 8-5-14 68-17-83

Please take these stats with a grain of salt. I can think of many reasons why these data might be biased, such as:

– frequent usage of high importance leads to rapid energy decrease, which in turn leads to bad performance of High in this very study.
– good managers will seldomly use high importance in a league game.
– managers of teams performing above average in their league might go down to low importance for some games. If there is a bias towards stronger teams in the pool of teams playing Low importance, this will surely influence the stats in favour of Low importance.

This has a personal flavour, too 🙂 In the first 7 rounds my team played with Normal importance and did not lose a single game. When I switched to Low importance, we lost 2 league games out of 3! All low counterattacks vs normal breakup…

May 8, 2009

Raw data from the maze of tactics

Filed under: PPM.statistics — glanvalleyeaglets @ 8:04 am

Please don’t ask me about the purpose of this posting, it is just what it is. A small-scale study of the relative performance of different ppm hockey tactics.
Let me credit the manager Gibeor who inspired this study by his own project Тактика-контртактика.

The data were collected manually using the match protocols of games played in the first three German leagues I.1 III.16. The games with participation of TeamNoname were excluded from the statistics.

Notation: Day: match day of the league game (NC – National Cup), Nor: Normal tactics, Def: Defensive, Off: Offensive, Cat: Counterattacks, Break: Breaking up of play, Fch: Active forechecking. Since not all the names of tactics have been translated consistently (the meaning of Pressing is different from German to Russian version), here is a small dictionary.

English Normal Defensive Offensive Counterattacks Breaking up of play Active forechecking
Deutsch Normal Defensive Offensive Konter Pressing Aktives Forechecking
Latviešu Normāli No aizsardzības Uzbrūkošs Pretuzbrukumi Pretinieka spēles izjaukšana Aktīva atbloķēšana
Русский Средне Оборонительный Атакующий Контратаки Разрушение игры Активный прессинг

The data are stored in a self-explanatory way. For example, if you seek the performance statistics of Defensive tactics against Offensive tactics, you find the third table (against Offensive) and the third column (for Defensive). The entries are total number of wins – overtimes – losses; these are further sorted by the league game days (in separate rows). The bottom row is the sum over all games of the season.

Performance against opponents playing Normal

Day Def Off Cat Break Fch
1 3-0-3 15-2-10 4-3-4 12-1-5 11-6-16
2 0-3-3 9-1-9 6-2-6 15-3-8 12-2-11
3 4-2-7 14-0-5 4-5-6 21-2-10 8-3-10
4 2-1-5 14-3-10 10-0-5 17-2-7 11-7-10
5 3-1-4 8-1-14 10-0-5 12-3-7 7-3-14
6 2-1-4 4-2-11 5-0-2 7-4-7 5-4-6
7 1-0-1 4-4-12 6-1-3 10-3-9 6-2-12
8 2-2-5 5-3-12 3-1-8 9-3-4 10-5-4
9 2-0-5 5-2-5 5-2-7 15-4-5 5-2-8
10 3-2-7 6-5-5 7-0-3 12-4-3 12-3-10
NC2 3-0-5 12-1-9 7-3-5 13-7-10 12-4-15
11 0-3-2 9-2-5 3-3-4 14-1-6 3-1-5
12 2-0-3 13-1-4 6-0-5 9-2-6 12-2-9
Total 27-15-54 118-27-111 76-20-63 166-39-87 114-44-130

Performance against opponents playing Defensive

Day Nor Off Cat Break Fch
1 3-0-3 0-0-2 1-0-0 2-0-1
2 3-3-0 0-0-3 1-1-1 2-0-2 2-0-3
3 7-2-4 1-0-0 2-0-2 2-1-0 0-0-1
4 5-1-2 1-2-2 2-0-1 1-0-0 2-0-2
5 4-1-3 0-0-1 1-1-1 1-0-0
6 4-1-2 1-0-2 0-0-1 1-0-3 1-0-1
7 1-0-1 1-1-2 0-0-2 1-0-2
8 5-2-2 0-1-2 0-1-1 2-0-0 0-1-1
9 5-0-2 0-0-2 0-1-1 3-0-1
10 7-2-3 1-1-2 1-0-0 1-1-1
NC2 5-0-3 2-0-0 0-0-1 2-1-0 1-1-0
11 2-3-0 0-0-2 1-0-2 1-0-3 1-0-2
12 3-0-2 1-0-2 3-1-1 0-0-2
Total 54-15-27 8-5-21 7-3-13 16-4-10 15-3-17

Performance against opponents playing Offensive

Day Nor Def Cat Break Fch
1 10-2-15 2-0-0 0-0-4 4-3-0 0-2-3
2 9-1-9 3-0-0 2-1-1 2-1-0 1-1-5
3 5-0-14 0-0-1 1-1-3 4-0-2 2-2-2
4 10-3-14 2-2-1 0-0-2 3-0-3 2-1-0
5 14-1-8 1-0-1 5-1-6 1-1-2
6 11-2-4 2-0-1 0-1-1 1-2-2 4-0-4
7 12-4-4 2-1-1 2-1-3 5-0-2 1-0-2
8 12-3-5 2-1-0 1-1-0 2-2-3 2-0-1
9 5-2-5 2-0-0 1-1-1 5-0-3 3-1-2
10 5-5-6 2-1-1 3-0-1 2-1-2 1-0-3
NC2 9-1-12 0-0-2 4-3-0 1-1-2 2-0-1
11 5-2-9 2-0-0 2-0-1 2-1-5 1-1-3
12 4-1-13 2-0-1 4-2-2 1-2-3 0-1-7
Total 111-27-118 21-5-8 21-11-20 37-14-33 20-9-37

Performance against opponents playing Counterattacks

Day Nor Def Off Break Fch
1 4-3-4 4-0-0 0-0-2 3-1-1
2 6-2-6 1-1-1 1-1-2 0-0-6 1-0-0
3 6-5-4 2-0-2 3-1-1 1-0-1 1-1-1
4 5-0-10 1-0-2 2-0-0 0-0-2 2-0-2
5 5-0-10 1-0-0 1-0-1 1-0-0 2-1-1
6 2-0-5 1-0-0 1-1-0 3-0-4 2-0-1
7 3-1-6 2-0-0 3-1-2 1-0-3 2-0-1
8 8-1-3 1-1-0 0-1-1 2-1-2 4-1-0
9 7-2-5 1-1-0 1-1-1 1-1-2 2-1-1
10 3-0-7 0-0-1 1-0-3 2-0-1 1-0-0
NC2 5-3-7 1-0-0 0-3-4 0-0-1 2-0-2
11 4-3-3 2-0-1 1-0-2 1-0-3 2-0-1
12 5-0-6 2-2-4 0-0-1 2-0-1
Total 63-20-76 13-3-7 20-11-21 12-2-28 26-5-12

Performance against opponents playing Breaking up of play

Day Nor Def Off Cat Fch
1 5-1-12 0-0-1 0-3-4 2-0-0 1-0-2
2 8-3-15 2-0-2 0-1-2 6-0-0 1-0-0
3 10-2-21 0-1-2 2-0-4 1-0-1 2-1-1
4 7-2-17 0-0-1 3-0-3 2-0-0 3-2-1
5 7-3-12 1-1-1 6-1-5 0-0-1 4-0-1
6 7-4-7 3-0-1 2-2-1 4-0-3 4-1-0
7 9-3-10 2-0-5 3-0-1 4-0-3
8 4-3-9 0-0-2 3-2-2 2-1-2 3-0-2
9 5-4-15 3-0-5 2-1-1 2-0-4
10 3-4-12 2-1-2 1-0-2 1-1-3
NC2 10-7-13 0-1-2 2-1-1 1-0-0 1-0-3
11 6-1-14 3-0-1 5-1-2 3-0-1 2-0-4
12 6-2-9 1-3-3 3-2-1 1-0-0 2-0-3
Total 87-39-166 10-6-16 33-14-37 28-2-12 30-5-27

Performance against opponents playing Active Forechecking

Day Nor Def Off Cat Break
1 16-6-11 1-0-2 3-2-0 1-1-3 2-0-1
2 11-2-12 3-0-2 5-1-1 0-0-1 0-0-1
3 10-3-8 1-0-0 2-2-2 1-1-1 1-1-2
4 10-7-11 2-0-2 0-1-2 2-0-2 1-2-3
5 14-3-7 0-0-1 2-1-1 1-1-2 1-0-4
6 6-4-5 1-0-1 4-0-4 1-0-2 0-1-4
7 12-2-6 2-0-1 2-0-1 1-0-2 3-0-4
8 4-5-10 1-1-0 1-0-2 0-1-4 2-0-3
9 8-2-5 1-0-3 2-1-3 1-1-2 4-0-2
10 10-3-12 1-1-1 3-0-1 0-0-1 3-1-1
NC2 15-4-12 0-1-1 1-0-2 2-0-2 3-0-1
11 5-1-3 2-0-1 3-1-1 1-0-2 4-0-2
12 9-1-12 2-0-0 7-1-0 1-0-2 3-0-2
Total 130-44-114 17-3-15 35-10-20 12-5-26 27-5-30

Last update 17/5/9

The tables and this page might be updated or not updated on more or less regular basis depending on my mood, time schedule or any other objective or subjective reasons left to my own discretion.

Caution: If you stumble upon this entry and plan to apply this for your next match in PPM, be careful! The match result will depend not only on the tactics but also on the players’ skills, energy, lines, special lines, game importance and other tactical aspects. A team may be better suited to play one tactics than another. Finally, there is an allmighty god or goddess that we know by the name HOLY RANDOM.

There are situations where average data just don’t help. The average temperature of two sick persons may be 36.6 degrees centigrade even when one has 42 and the other 31.2, right?

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