# The [ppm] eyrie

## June 15, 2009

### The next moon

Filed under: GVE chronicles — glanvalleyeaglets @ 9:29 am

The river of time keeps flowing and the time has come for the second monthly progress report of my team. Moon is my unit of time that lasts four calender weeks, thus a PPM season can be conveniently divided into 4 Moons and four reports. The pain of writing the report gives a new meaning to the word Moonsorrow 🙂

I have slightly extended the range of data I’m collecting for statistics, including shot efficiency, penalty minutes and some rudimentary statistics on the team strength “stars” (the numbers estimating the overall goaltending, defence, offence and shooting abilities). Measuring the effects of these stars is a very elusive stuff, I must say. It will take some time to collect enough of data worth of publishing, but some day you can hope to find an executive summary in this blog.

Let us turn to the performance of my own team.

The second moon has seen 12 rounds of regular season league games. This time my Eaglets had to face all three Noname teams that currently reside in our German league III.7. I will focus on the remaining 9 games, which ended with 4 victories after regular time, 3 overtimes (1 won, 1 lost, 1 draw) and 2 losses. Perhaps we have lost some points due to the low game importance, but I have to admit that most of the points were lost after a tactical defeat. Sure, it is nice to win, but the game wins in substance when the other side uses unexpected tactical variants 🙂

Having started with two victories 6:2 and 8:1, the Eaglets faced the leading team of the league in terms of facility development, ESV Kaiserslautern Koi’s. With an aggressive transfer policy they have erected the 6th level of TF and 5th level of RF and HRED. I think we’ll see this team go really far indeed. The derby in front of 429 we played defensively against breaking tactics. An exchange of many goals ended with zero points for the Eaglets, 6:7. Our next guest was the 17th number of the league who reached the round of last 64 in the National Cup – Briesnitzer Eisballerinas. Although Eaglets had the clear tactical edge defensive vs offensive, the only reward was one point – 4:4. There followed another victory 7:3 and an unexpected loss against Crusaders’ top goalie Kannast with 1:3. The game aganist Darmstadt improved the situation – 4:1, however, the last two games ended in overtime. First the Eaglets managed to take 2 points against Iron Wolves with 5:4 in OT, but on Friday we lost against Berlin Capitals 6:7 OT (reminding of the match in the first round). The strange thing is that Eaglets keep flying on Position 1 in the table, 3 points ahead of Koi’s and 11 points ahead of the 9th placed Capitals. The margins are still extremely narrow and the competition on the verge of play-offs is extremely tough. With 14 rounds remaining, the 11 point margin lets us feel everything but safe.

The hunting grounds of the National Cup are considered to be even more rough and dangerous as the first slip is usually the last. It took both skill and fortune for the Eaglets to reach the round of last 32. The National Cup, probably the highest peak a team can reach in the first season, is only five games away. So close at hand, yet as unreachable as the Moon 🙂 The first serious opponent was Red Devils Berlin. Eaglets played offensive against forechecking and marked an impressive 8:2 victory. The next in line was PreussenSpiders with an inactive manager. Scoring 2 goals in the last seconds, Eaglets saved the day with a tough 4:1 victory. HC Growl fought furiously using the forechecking tactics against offensive finding a response to every goal scored by the Eaglets. As the evening dusk fell, we saw a deserved yet lucky 6:5. The next draw revealed SRBIJA as the next opponent, but they went anonymous right before the match. Although they, having been overtaken by a new manager in the last minutes before 18.00, did show a serious resistance, Eaglets still managed to convert this chance – 6:2 and here we are.

Ruhrpott Icetigers from IV.1 will be the next team that comes to Angelo d’Arrigo Ice Forum with the firm resolution to kick the hosts out of the tournament. In terms of stars the Eaglets have a slight but firm advantage, yet the manager of the Icetigers cares well for his team, so the tactical schemes are adapted on a regular basis. I’m flirting with the idea to send my Eaglets in the fight with high importance for the very first time. Unfortunately, I have some good arguments both pro and contra, so it is going to be a tough last minute decision for me.

Sometimes I wish I could transfer the success streak in friendlies to the league. In the last 5 weeks Eaglets have won 15 of 15 friendlies, thus winning the Group D in Libertadores Cup with a considerable margin. Now we can prepare for the play-off rounds in series of best of 3. Hoping for more than just one round.

Players. Still waiting for the first blue wonder from our Sports Academy. We already have 5th level for a while, and still waiting for the first youth player to come with an OR over 160. The only serious addition to the roster was the defender Rainer Buhs. The french goalie Gary Florin was the second addition to the team. There have been no big transfers to report.

Facilities: HR 4, REG 4, TF 5, SA: 5 (6). Team strength (a.k.a. Stars): GT 15, DF 16, OF 16, SH 15 (16). Overall team rating 69.49. Place 90 in a out-of-date world ranking table (there are over 25 000 active teams around) thanks to the lucky streak in the National Cup, and place 2 in German ratings (out of date as well).

## 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

### Wir sind Herbstmeister!

Filed under: GVE chronicles — glanvalleyeaglets @ 1:14 pm

Press release.

Glan Valley Eaglets have finished the first round of the first season on the top spot in the German division III.7, scoring 44 points in 19 games (total record 14-2[0-1-1]-3, goals 130:53). Five players can be found in the top 6 scorer list of the league. Captain Jonathan Schirmer leads the list with 29 (11+18) points, Gunar Ihle has 26 (12+14), Mark Umbeck – 24 (13+11), followed by the top defenders Arno Karsten (11+11) and Timon Schürrle (6+16) with 22 points each.

With overall team rating of 53.24 points the team has reached its highest spot ever in the World rankings of PPM. At the moment Glan Valley Eaglets are ranked number 175 in the PPM World! (The total number of PPM hockey teams is 26922 currently.)

The manager speaks: “Yes, it is nice to be a Herbstmeister, it is an important moment in the young history of our team. I want to congratulate the players, they have done a great amount of hard work during the last months and the team play has improved enormously. Yet I would be more happy if we played like this in the last rounds of the season to reach the play-offs and spare our best hockey for the last games of the season.”

### 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!