Ok, but is that a BAD thing?
(continued from Part 2)
Now we delve into more philosophical territory. Should the team that plays ‘better’ always win? If not, then why not?
Perhaps I’m being too narrow-minded in my assessment of what defines performance in a game of Kubb. Maybe it needs to be expressed as some function of “Performance = Efficiency + Opening Toss Result”? To be fair, thus far in this series I have been implicitly treating the king toss as a sort of necessary evil, something completely separate and distinct from the game itself. The king toss definitely involves a fair amount of skill, so perhaps winning it SHOULD confer some advantage throughout the rest of the match. How much is enough? How much is too much? How much is it now?
(Well, we have to go back to game-level data here, so we’re dipping back into a smaller sample set than I’d like, but in this respect the observed data almost perfectly matches the simulated data, so I don’t despair too much.)
By current rules, using observed performances in competition-level games over the past few years, the advantage conferred by throwing first is:
Meaning, if Team B plays 12 percentage points more efficiently than Team A (relative to the baseline performance), then each team has an equal chance of winning the game. If Team B plays LESS than 12 points better Team A becomes more likely to win, and if they play MORE than 12 points better they become more likely to win. (Remember that the distribution curve isn’t symmetrical though – chances might be 50/50 with B playing 12 percentage points better, but as in the first example above Team B can play more than 100 points better and might still lose, whereas A will always win as long as they play at least equally.)
Is that OK? To me, it feels like running a 100m dash, but the other runner only has to run 88m. Does making it best-of-three races and alternating who gets the head start make it fair? Makes it MORE fair I guess, but if I were a track athlete I think I would prefer to attend meets where everybody ran the same distance.
But does a game really have to be ‘fair’? Not all games offer exactly equitable chances to each side. Chess is widely accepted to have a small but real bias toward white. Tennis highly favors the serving player. In Curling there is a large advantage to throwing last and having the ‘Hammer’, or last stone. But these games mitigate those advantages with numbers – there are 8 ends (opportunities for the advantage) in Curling and dozens of games in a Tennis match. Curling (like Shuffleboard) goes a step further by withholding the advantage from the last team to score. Perhaps Kubb could benefit from the same thinking, and rather than alternating the opening, let the team that lost the previous game have the honor?
Does ‘fair’ mean that the team that plays better wins, or does it mean everyone has an equal chance of winning? I think it has to be the former for a game to be taken seriously at a competitive level. A lottery is fair, but you don’t see a lot of people signing up for lotto tournaments.
But what if we limited the number of batons Team A could throw on the first turn? What does the advantage look like then?
Well, we have almost no data on this, so everything in this next section is based on analysis of simulated games. I think the theory is sound, but keep some grains of salt on hand. That disclaimer out of the way, here are the impacts to the best of my estimation:
If we reduce the open to 5 batons, Team B will need to outperform Team A by about 8 percentage points to stand an equal chance at winning, and if they perform equally well (+/- 1%) then Team A wins 99% of the time.
With a 4 baton open, Team B needs to outperform A by 4.75%, and equal performances favor Team A 94% of the time.
In the “Basel-3” Team A is STILL slightly favored, forcing Team B to outperform by 1.5%, and equal play translates to a Team A win 62% of the time.
The T1 Advantage is the only factor built into the design of the game that favors one team over the other, but as I said part 1 of this article, there are a number of other issues that can impact the game. Wind, sun, psychological & physiological factors, pitch conditions, etc. The main difference between these and T1 is that these other factors affect performance – the wind caught the baton, the sun blinded you, the pressure got to you. T1 is different because it doesn't affect your performance; it simply makes demands upon it. Being a little better isn't enough, you have to be demonstrably better.
So how much DO these other factors actually impact the game? Impossible to say. Professional sports are a multi-billion dollar a year business, and people a whole lot smarter than me, with better educations, better equipment, and better data wrestle with these kinds of questions all the time. I won’t pretend to have an answer.
But I certainly have an opinion. J
My gut tells me that choosing the side is usually worth more than a percent and a half of efficiency performance, even if it’s just placebo effect (current stats actually have B outperforming A by about 4.5% - I think part of that is the variance due to a small sample, but I wouldn't be surprised at all if a fair portion of that is the environment – remember that Team B has likely chosen the favorable side.)
My gut also tells me that opening with only three batons is a pretty heavy psychological burden, and the hit rates with those three are likely to be somewhat lower than the overall average. Adding even one could mitigate that quite a bit.
With these extra factors in mind, unless you are on an ideal pitch and are very confident in your 8m game then it will almost always make sense, in a Basel-3 opening, to choose side and throw 2nd if possible.
With a 4-Baton opening, the opposite becomes true. Unless the conditions heavily favor one side over the other, you will want to start the game with 4 batons in hand. If we assume that the conditions impact relative performance of the teams by 2%-3%, then Team A still has a net advantage of around 2%-3%, which is, to my mind, a far cry better than the current 10% or so net advantage they currently enjoy.
So, back to the question of “How much advantage should a
team ‘earn’ by winning the king toss?” Well, an average of 2%-3% feels about
right to me. Think of it in terms of overall throw volume. In the average
match, most teams can expect to throw around 60 batons and 45-50 kubbs. There
will be only one opening throw. (Unless you’re playing in Chaska!) Weighting it
at about a 2.5% efficiency boost feels like it brings into line with the other
throws in the game, making it only slightly more important than any other single
throw in the match (aside from any other shot involving the king).
After a thorough discussion of the theory and conclusions discussed above, the Des Moines Kubb club has elected to move to a Four Baton Start for the Iowa Summer Games in 2014. We will be watching the matches very closely, and if all goes well (which we have every reason to suspect it will), then we plan to move our Fall Kubb Klassic to this rule set as well. Our biggest concerns are adding length to games in a format where timing can be very important, and the required updates to rules for adjudication due to time, but we think these are issues we can be prepared for.
It’s worth noting that when the Des Moines Kubb club first discovered the game, the rules we found indicated a 4-baton start. It intuitively made sense to us, and in all but the rarest cases the winner of the opening toss would still choose to throw first. When we ‘graduated’ to competing regionally we adopted the rules used at other tournaments, including the 6-baton opening. In some ways, this rule change is a return to our roots.
In 2009 a 4-baton start was worth getting excited about
We hope to see you on the pitches, and look forward to your feedback on the new rule.
Well, if you’re still with me here I’d like to thank you for investing the time to read this series. It represents the culmination of a lot of discussion, a lot of thought, and a lot of work on a topic that is important to me because I care deeply about the future of this game. If anyone would like to discuss these ideas (or anything related) in more detail I would be more than happy to, just drop us a line at firstname.lastname@example.org.
Good Kubbing, and have a great season!
In : Theory
Tags: t1 advantage
blog comments powered by Disqus