(c) by colourbox.com

Regelreform Basel 3 eliminiert Startvorteil

English Version:
At Sure Shot 10 (September 7, Schützenmattpark) the rule change Basel 3 is introduced: The new rule states that the team that starts a game has only three instead of six throwing sticks available. In particular, because the 16th and 8th finals will be played on only one game, the rule change contributes to a fairer, more balanced tournament. Roger Züst on behalf of Baselcitykubb calculated the effects of the starting sequence. The calculations have shown that the starting advantage in playing at a high level is 50 percent – the starting team wins against an equally strong opponent on three of four occasions. If the starting team has just three sticks available, the initial advantage is only 2 percent.

Abroad there were already some tournaments that have experimented with the so-called 2-4-6 rule to reduce the advantage of the starting team. There, the first team has only two sticks and the opposing team must throw four sticks in the first round. The simulation shows that Basel 3 works better and also eliminates the disparity of the 2-4-6 rule (No player is left out and no one is allowed to throw twice in the case of four sticks).

The rule Basel 3 in details: Whoever wins the opening can choose which team starts, and this team then just throws three sticks in the first round. Since the statistical advantage of the starting team is minimal with this rule change, the team that won the opening can also pick the side and leave the opponent with the choice of the starting team.

The simulation

Roger Züst: “The simulation is relatively simple and can be controlled by the input of only two numbers for each team, the hit rate on base kubbs and the hit rate on field kubbs. Setting the kubbs randomly creates a certain number of groups of kubbs. Each group of kubbs is eliminated by a single hit, the hit rate on such a group is identical to that on a single field kubb. Generating these groups is the same for both teams and it tries to simulate a relatively good thrower. For example in the setting of three kubbs to 30% there will be one group, to 40% two groups and to 30% three groups. Clearly, these numbers are heuristic and could be optimized. Playing around with it, however, has shown that the win/lose statistics are quite robust to changes in these probabilities.”

The effects

Christian Horisberger: “I was especially interested what the effect of different hit rates in the new system Basel 3 is and how the chances of winning is influenced compared to other systems (as before, beginning with 6 sticks but also the 2-4-6 system). As expected, the winning probability in the previous 6-6-6-system strongly depends on the hit ratio of the starting team: Does it hit base kubbs good or very good (ratio above 45 percent), the initial advantage is very clear. At a lower hit rate of 17 percent for example (which corresponds to one hit with six sticks) also games in the old 6-6-6 system are very balanced. In this case the opponent needs only a slightly better hit rate of 20% (one hit with five sticks) to have the same chance to win. In the Basel 3 system, the influence of the starting advantage in all combinations of hit probabilities is minimal. My conclusion: The new 3-6-6 system for average skilled teams makes little difference, but with good teams it eliminates the big starting advantage.”

Still in doubts?

Christian Horisberger made a java applet out of a Kubb simulation programmed by Roger Züst and therefore all have the opportunity to experiment for themselves. The settings allow multiple systems (2-4-6, 6-6-6, 3-6-6, etc …) to test with different hit rates of the two teams. For questions, praise and criticism, the comment form is open and the Sure Shot 10 will show whether Basel 3 leads to balanced and thus more exciting games in practice.

Am Sure Shot 10 (7. September, Schützenmattpark) wird die Regeländerung Basel 3 eingeführt: Die neue Regel besagt, dass das Team, das den Satz beginnt, nur drei statt bisher sechs Wurfhölzer zur Verfügung hat. Insbesondere weil die 16tel- und 8tel-Finals auf nur einen Satz gespielt werden, trägt die Regeländerung zu einem faireren, ausgeglicheneren Turnierverlauf bei. Roger Züst hat im Auftrag von Baselcitykubb die Auswirkungen des Anspiels berechnet. Die Berechnungen haben ergeben, dass der Startvorteil bei Spielen auf hohem Niveau 50 Prozent beträgt – das Team mit Anspiel also gegen einen gleich starken Gegnern drei von vier Spiele gewinnt. Stehen dem startenden Team nur drei Stöcke zur Verfügung, beträgt der Startvorteil lediglich 2 Prozent.

Im Ausland gab es bereits einige Turniere, die zur Abschwächung des Startvorteils mit der sogenannten 2-4-6 Regel experimentiert haben, bei der das Team mit Anspielrecht zunächst nur zwei Stöcke und das gegnerische Team in der ersten Runde vier Stöcke werfen darf. Die Simulation zeigt, dass Basel 3 besser funktioniert und erst noch die Ungleichheit der 2-4-6-Regel eliminiert (Kein Spieler wird ausgelassen und niemand darf bei vier Stöcken zweimal werfen).

Die Regel Basel 3 lautet im Detail: Wer das Anspiel gewinnt, kann wählen, welches Team beginnt, wobei dieses Team in der ersten Runde nur drei Stöcke werfen darf. Da der statistische Vorteil des beginnenden Teams mit dieser Regeländerung minimal ist, kann sich das Team, das das “Anspiel” gewonnen hat, auch entscheiden, die Platzseite zu wählen und dem Gegner die Wahl der startenden Mannschaft zu überlassen.

Die Simulation

Roger Züst: “Die Simulation ist relativ simpel und lässt sich durch die Eingabe von lediglich zwei Zahlen für jedes Team steuern, der Trefferquote auf Basiskubbs und der Trefferquote auf Feldkubbs. Durch das Setzen der Kubbs entsteht zufällig eine gewisse Anzahl Gruppen von Kubbs. Eine Kubbgruppe wird jeweils mit einem Treffer umgeworfen, wobei die Trefferquote die selbe ist wie die auf einzelne Feldkubbs. Das Generieren von Kubbgruppen ist bei beiden Teams gleich und versucht einen relativ guten Einwerfer zu simulieren. So entsteht zum Beispiel beim Setzen von drei Kubbs zu 30% eine Gruppe, zu 40% zwei Gruppen und zu 30% drei Gruppen. Klar, diese Zahlen sind heuristisch und könnten optimiert werden. Herumspielen damit hat jedoch gezeigt, dass die Gewinnstatistiken ziemlich robust sind unter Veränderungen dieser Wahrscheinlichkeiten.”

Die Auswirkungen

Christian Horisberger: “Mich hat speziell interessiert, was das neue System Basel 3 für Auswirkungen bei unterschiedlichen Trefferquoten der Teams hat und wie es die Siegchancen im Vergleich zu anderen Systemen (wie bisher, Beginn mit 6 Stöcken aber auch das 2-4-6-System) beeinflusst. Wie zu erwarten, hängt die Siegwahrscheinlichkeit beim bisherigen 6-6-6-System stark von der Trefferquote des startenden Teams ab: Trifft dieses die Basis-Kubbs gut oder sehr gut (Quote über 45 Prozent), ist der Startvorteil sehr deutlich. Bei einer tieferen Trefferquote von beispielsweise 17 Prozent (was einem Treffer pro sechs Würfen entspricht), sind auch Spiele im alten 6-6-6-System sehr ausgeglichen. Der Gegner braucht nur eine minimal bessere Trefferquote von 20% (jeder fünfte Wurf trifft), um die exakt gleichen Siegchancen zu haben. Beim System Basel 3 ist der Einfluss des Startvorteils bei allen Kombinationen von Trefferwahrscheinlichkeiten minimal. Mein Fazit: Das neue 3-6-6-System macht bei mittelguten Teams keinen grossen Unterschied, eliminiert aber bei guten Teams den grossen Startvorteil.

Noch Zweifel?

Christian Horisberger hat die von Roger Züst programmierte Kubb-Simulation in ein Java-Applet verpackt und somit allen die Möglichkeit gegeben, selber zu experimentieren. Die Einstellungen erlauben es, mehrere Systeme (2-4-6, 6-6-6, 3-6-6, etc…) mit jeweils unterschiedlichen Trefferquoten der beiden Teams zu testen. Bei Fragen, Lob und Kritik steht die Kommentarfunktion offen und der Sure Shot 10 wird zeigen, ob Basel 3 auch in der Praxis zu ausgeglicheneren und damit spannenderen Spielen führt.

*”Basel 3” bezeichnet (gemäss Wikipedia) ein Reformpaket des Basler Ausschusses der Bank für Internationalen Zahlungsausgleich (BIZ) für die bereits bestehende Bankenregulierung Basel II. Es stellt die ab 2013 gültige Reaktion auf die von der weltweiten Finanz- bzw. Wirtschaftskrise ab 2007 offengelegten Schwächen der bisherigen Bankenregulierung dar.

* “Basel 3” means (according to Wikipedia) a package of reforms by the Basel Committee of the Bank for International Settlements (BIS) for the existing banking regulations of Basel II, it is the valid from 2013 onwards in response to the weaknesses of the existing banking regulation revealed by the worldwide financial and economic crisis starting in 2007.

Bild: Colourbox

Kommentare

  1. Princip question: Why eliminate a certain advantage (if there is one?) of the game?

    I don’t see the point, the world is unequal, as is the world of sports, why eliminate the underdog perspective?

    /S

  2. Ich finde nach wie vor keine Freude an diesem System wenn ich ehrlich bin!

    Trotz irgendwelchen mathematischen Berechnungen und vielem drumherum, sollte man sich eher auf andere Sachen konzentrieren im Regelwerk als den Vorteil des Anspiels wegzunehemen.

    Wenn das Ziel sein soll Kubb in der Schweiz soweit zu verbreiten dass es sich auch etabliert und viele Teams spielen werden, dann wäre es eher gut wenn man nicht allzu viele Regeln ändert, sondern schaut das sich die Grunderegeln etablieren, da mir bei vielen Diskussionen mit “Laien” aufgefallen ist, dass grundsätzliche Regeln gar nicht bekannt sind.

  3. @Sören
    Just because the game isn’t, at least the way I see it, about who can throw a stick closer to the king. And this one shot has become too important, especially if you play only one game. Underdogs, as before, can win. Now, even more so those who lose the opening 😉

    @Jan
    Dänk do gohts meh ums turnier als um grundsätzlichi regeländerig. und würklich kompliziert isch si abgseh devo au ned…

  4. Well, beats me. I thought skills are to be promoted, not punished, thats why I don’t understand the rule. In my statistical universe, who is the idiot who want’s to start with such a rule attached to the game? I will every time I can choose the 6 sticks in the same round as my opponent only will be aloud of throwing 3. All the time.

    Beeing grumpy (I don’t mistrust your intensions, I just don’t understand) what says all (3) players have to be involved in the 3 sticks of the starting team? Am I not aloud to throw my two sticks if I’m the best 8-meter hitter?

  5. @Sören: Well if you win the opening you are free to choose the opponent to start with 3 sticks if you feel that this is an advantage for you (so, no skill is wasted there). I’m not the organizer of this tournament, but I think that the first 3 sticks are thrown by different members of the team.
    It was also my first impression that it should be a clear disadvantage to start with 3. The simulation, as imperfect as it may be (there are no psychological things considered, like pressure of starting with 3 or that if you have two throws in a row, the second one might have a higher chance of hitting…), tells a different story. Even more, as for the simulation; the better the hitrate on base kubbs of the two opponents, the bigger the advantage of starting with 3. It is to be seen if this holds true in practice. And I definitely would be interested to have some real statistics thereof :)

  6. Interesting solution to what I think is the 1 structural issue w/ kubb (more batons than base kubbs).

    In a match at US Nationals this year, the opening team knocked all 5 base kubbs down. In US rules when that happens – the 6th baton is forfeited. So they did. The answering fought back and won the game. That is to say – it’s not a forgone conclusion when the opening team clears the baseline.

    I’m definitely interested in the data behind the simulation. It seems to much more strongly bias the opening team than the game data within http://wiki.PlanetKubb.com Is the underlying data from tournament games as well? Thanks.

  7. Ich bi am Afang sehr drgäge gsi – vor allem, will ich au nid gärn so vill Regeländerige seh… Und nei, nid will ich das als für mi nochteilig seh!
    Abr trotz alledem – ich bi gschpanne, wie sich das entwicklet. Macht bi hochkarätige Begegnige sicher eventuell Sinn. Abr grad jetzt, woni so oft s’Aaspiel gwünn… ;o))) Jänu, wird ich halt zum Taktiker! ;-P

  8. @Garrick van Buren: With the preset numbers in the simulation above, the hitrate on base kubbs is 50% and the hitrate on field kubbs is 90% for both teams. In the simulation (with 6 starting sticks) this leads to an average of 4.83 turns per game. As I see, the average of turns on PlanetKubb is 8.8 (though this number may not have been updated lately), therefore I think that the average hitrate of the games on this site is significantly lower then those preset in the simulation. If you enter lower hitrates above, the starting advantage decreases and the games last longer as expected…
    Apart from these 4 numbers there is a 10×10 matrix (respectively half of it) with probabilities for the throwing of the kubbs (Inkastare or whatever this is called). This matrix is the same for both teams and fixed as it would be rather laborious to modify them in the app above. The probabilities in the matrix are purely heuristic based on years of playing kubb and there is no data to justify them :) But as written in the report, the win/lose statistics do not depend that strongly on it… Anyway, if you wish to see respectively modify the sourcecode (or the Inkastare matrix) I can send it to you, that’s no problem…

  9. Viel sinnvoller wär, wenn meh mehr würd luege, dass keini Helikopter gworfe werde. In dem Johr isch es anschinend wieder Mode, dass meh d’Wurfstöck “rotiere” loht (sin au e huufe Teams drmit gmeint, wo keini “Rookies” meh sin!!!).

  10. I expect environmental factors to account for at least +/- 2% (sun, wind, pitch level, corner pitch condition, etc.) In this situation, where a 2% advantage is given to the opening team, would you not ALWAYS choose side to gain the environmental advantage, and use the opening king toss as a warm-up throw for your eventual win?

  11. The key question to me are: Is the opening toss a part of the game? If yes, how strongly do you wanna weight it? If one team already is a lot stronger than the other, is it fair then, if they are rewarded with throwing 6 sticks first, because they are also stronger with their opening toss?

    Please remeber, we are mainly talking about using this rule in round robin games, where we are only playing one single set! With both things already happend to us as a team a) opponent already coming to our side to congratulate and shake hands after we’ve thrown the first round (no, we didn’t do the perfect game, but almost ;-)) b) loosing because of a perfect game, I am actually looking forward to the tournament, to see how well this rule works. And it’s just a test…

    @Josh: Depending on the “quality” of the sides or maybe disturbing factors behind one of the baselines, I think our team may go for the side as well! Thus we are rewarded for winning the opening toss and have a small advantage…

  12. @Gravi @Garrick @Josh @Bjogge
    To me, here is a mash-up between statistical scores that sums up history and the situation at hand facing the players in the actual moments. Average hits rates are always historical, as a player I will have to face the actual hits.

    My historical figures will only help me to predict the possibility of the outcome of the next throw, not the actual outcome. This is one of the problems with simulations. And those numbers will not be handed out with regularity, on the contrary. The Stove-Icebucket example is a good metaphor. With one foot on the red hot stove plate and the other one in an icebucket, my average numbers are quite comfortable. This is another problem with the simulation.

    As a player facing a game, I have look upon it from a game theory perspctive instead. How do I gain the most advantage of the situation, should I gamble or should I play it safe?

    1. The starting throw is still there for deciding, so I still have to be good at this particular skill, I still have to practice it to get in decision-position.
    2. The team that looses the throw(Team A)/the decision will face the possibility to throw just one round with three sticks, while their opponents still can make a perfect match in the same round, depending on the scenarios. Sounds like a safe bet, not even a gamble, to choose not to start?
    3. This is what the non-starting team (Team B) have to face
    – Worst case scenario (almost unlikely over a certain skill level – almost):
    Team A hits 4 (yes, four – I’ve seen it happen) kubbs with (their) three sticks.
    Team B misses 1 F-kubb despite throwing 6 sticks and let forward A. Unlikely? Probably? I will bet against, every time, every time.
    – Best case scenario:
    A misses every stick, B wins with a perfect match
    Question, why take away this possibility for one team, but not the other?
    – 2:nd best case:
    A hits just one B-kubb. B throws the kubb long, it places itself handy in front of a B-kubb, B hits the “long double” with it’s first stick (BTW, Terry Ekelöf who will play in Basel, did this twice this year when we played together in the Stockholm tournament “Kubbistan”). Team B now still have the opportunity to make a perfect match…
    – Other better case scenarios:
    It’s not so much about A hitting 1-3 B-kubbs, it’s about how many sticks B needs to clear the field. As long as B have more sticks to the B-kubbs of A (6-5-4), they have an advantage (or even 3-2-1, depending on how many A have hit/missed!). This fact is why I will choose to be Team B every time, it will take a lot of bad play for me before Team A will get even with me with both teams throwing 3 sticks at the B-kubbs. You follow me? Game theory, to me, are heavily in favors of the team throwing 6 sticks in the same round as the opponent is limited to 3. And, there is no stats here, for this actual situation, to prove me wrong.

    Then what to do?
    In Rone it all started out with the teams flipping a coin about who’s to start. That is as fair 50/50 as you can get. when we met “Elefantbajs” in 2010 and they offered us this alternative, I took it imediately, having a 50% chance to start against them… (I lost the flipping, but starting wouldn’t have matterd then, anyway)

    The arrangers of “Kubbistan” in Stockholm have the following start for their 1-set games in the consolidation “Lilla Kubbistan”:
    Both teams Line up behind each base line. Team A throws three sticks, one for each player. (let’s say)they hit 2 kubbs. Team B now does the same, they hit 1 kubb. Now the game starts with, the team who managed to hit less base line kubbs than the other (Team B) throws all the knocked base line kubbs out. Simple and clean, and just game skills. What if the teams hit even amount of kubbs? Then you call it a draw, and redo the procedure, until one team hits more kubbs than the other.

    If we have a problem with masses of perfect matches when we play 1-set, why not just take away the last stick of the first throwing team in the first round? That game can still turn around?

    Oh, and a last question within the issue:
    Why does “everyone” believe a starting advantage lasts all rounds out of the set? To me, if there is one, it ends when the second round is played out, because then another round have been played, that impacts the game in one or another way, and to me regarding ALL factors that uptil then have had impact of the game, the starting advantage have been reduced with all those actions you just can’t think away. And in the next round, it’s impact will be even less. Or, do I miss anything important here?

    Sorry for the amount of words, and if I bore you out, I just got going 😉

    /Sören

  13. @Sören
    Thanks for the little Kubb history, wasn’t aware of this…

    “My historical figures will only help me to predict the possibility of the outcome of the next throw, not the actual outcome.”
    Sure, but thats the whole point of statistical inference :) And it makes sense, because noone, at least in my worldview, can forecast the “actual future” (in a situation as complex this one). And so, also this simulation does give you only probabilities of outcomes not actual outcomes…

    Well, writing down scenarios is all good and fine but one has to indicate how likely they are. Any scenario is already included in the simulation but with the right probability of it turning up, so to speek. Just for the sake of the argument, here are also two scenarios where team A wins:

    best case scenario:
    Team A starts with 3 base Kubbs, team B takes those in front with one hit and takes all 5 base Kubbs, team A hits down the 8 field Kubbs with 3 then the 2 remaining base Kubbs and the King -> team A wins

    some average case scenario:
    Team A starts with 2 base Kubbs, Team B takes the 2 with one hit and takes 3 base Kubbs, team A takes the 5 field Kubbs with 2 and hits 2 more base Kubbs, Team B takes the 7 field Kubbs with 3 and the remaining 2 base Kubbs, team A hits the 9 field Kubbs with 4 the remaining base Kubb with 1 and the King -> team A wins

    So what is the point? there are many more scenarios to be considered…

    Here is some other heuristic argument that starting with 3 may be fair. First team A has 3 shots, so it had 3 shots more then team B, then team B answers with 6 shots, so team B had 3 more then team A. After the third turn team A had a total of 9 shots, that is 3 more then team B had before, etc… So, after any turn, this team had in total 3 more shots then the other team. There is something to this symmetry…
    And the reason why in the simulation with very high hitrates team A has an advantage (more so then with lower hitrates), is that Team A has a reasonable chance to end the game at turn 3 (as in the best case scenario above) well before team B had the chance to do so (take into consideration that with a high base hitrate of team A it will very likely hit at least 1 base Kubb and team B is unlikely to answer with a “perfect game” in this case)… This observation is easy to check: putting all hitrates to 100% (or less but just to make the point) the average number of turns is below 4, and almost all games with less then 4 turns are won by team A…

  14. Hope ya’all will have a great tournament. It’s a hell of a starting field you have managed to gather! We’ll be there another year, take care and good luck!!

    /Sören

  15. Do we have stats from Basel now we can extrapolate? Would love to see some data about how it went, how many matches where winning king toss team deferred to throw first, and overall rounds played, etc. etc.

    ____
    Soren asked:
    “Oh, and a last question within the issue:
    Why does “everyone” believe a starting advantage lasts all rounds out of the set? To me, if there is one, it ends when the second round is played out, because then another round have been played, that impacts the game in one or another way, and to me regarding ALL factors that uptil then have had impact of the game, the starting advantage have been reduced with all those actions you just can’t think away. And in the next round, it’s impact will be even less. Or, do I miss anything important here?”

    The way I like to think of Basel 3 and the continual advantage is similar to this:

    Team A: I throw six (Team A has a 6 baton advantage)
    Team B: I throw six (Team A and B are now even)
    Team A: I throw six (Team A has a 6 baton advantage)
    etc. etc. Team B never has an advantage of tosses

    So, Basel 3 goes like this:

    Team A: I throw 3 (team A has a 3 baton advantage)
    Team B: I see your 3 and throw 3 more (team B has a 3 baton advantage)
    Team A: I see your 3 and throw 3 more (team A has a 3 baton advantage)
    etc. etc. Teams A and B rotate the advantage through the turns

    Either way, @gravi got the kubb world thinking. Jolly good show!

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