## Advantage, Efficiency, and Game Theory (Part 2 of 3)

# Kubb Economics 101

*(continued from Part 1)*

Say what now? Where’s this 40% number coming from? Well,
this gets to another project I’ve been working on, which is to express Kubb performance
in a slightly different way, and it’s based on this premise:

Kubb is not a game of accuracy - Kubb is a game of economy.

Accuracy certainly helps, but it’s only related to the goal of the game – not the goal itself. Say one player throws a perfect group of 5 field kubbs and drops them with a single baton, then goes 1-of-5 at the base kubbs. Another player throws 5 kubbs, all penalties which are then scattered all over the pitch, but she never misses with her batons, clearing them with 5 then gaining a base kubb with baton #6. Who had the better round? One player went 100% but the other only hit with 2 out of 6 batons. None of that really matters though, because the bottom line is that they each toppled five field kubbs and a base kubb with their six batons. These two rounds were equally efficient, and therefore the players were performing equally.

Think of it like a market. Each team has an ‘income’ of 6 batons per round, and they need to ‘buy’ as much material as possible with that limited resource. The first team to collect 5 base kubbs and the king wins the game. The inkastare attempts to group the field kubbs together to make them ‘cheap’, and the defender tries to raise them so that they cost as many batons as possible. (I think of an advantage line as a ‘fire sale’, where Everything Must Go and No Reasonable Offers Refused…)

So if we take the position that in Kubb performance equals efficiency, how can we measure it? Well, there are a few different methods we could use, but here is the one I chose:

Those 100+ games we have recorded throw by throw contain about 900 total turns. We have dozens and dozens of examples of teams throwing any numbers of kubbs, and we can take the average number of batons required to clear them and calculate a baseline ‘Baton Value’ (BV) for any given situation on the field. Full disclosure here – we don’t have a lot of data for rounds of 10 kubbs in play, and I’d really like to have more 1’s and 9’s, but we have quite a bit of data on 2-8, and regression/prediction modelling on the current data matches pretty well to what we’ve measured on 1, 9, & 10. Additionally, with these instances occurring so rarely in the data, being slightly off on them shouldn’t have more than a very minor impact.

So how many batons does it generally take to clear four field kubbs? Right about 3.6. Seven fields with an advantage line? Just shy of 4 batons. Base kubbs? 2.85 batons from 8 meters and 1.65 from an advantage line. Kings are worth about 1.2.

*Reference the number of field kubbs &
base kubbs to find the Baton Value of the position*

* *

With this, we can generate an estimated BV of the field at the start of a turn, then again at the end of the turn, and the difference is the value of material gained. Divide that by the count of batons thrown and you have an efficiency score – essentially, how much better or worse was the round than the average ‘expected’ performance for that situation. The same can be done for the entire game; what was the total BV of gained material, and how many total batons were thrown? With this toolset we can evaluate team performance relative to the average, and as a result relative to each other, irrespective of the final outcome – essentially applying a ‘score’ to a game without points.

This can be tracked by team over time as well. For instance, the reigning world champions Kubb’Ings have 13 games recorded, and they average at about 125% efficiency. That means, for every 4 batons they throw they are gaining 5 batons worth of material. “Buy-4-Get-1-Free” is a pretty sweet deal no matter what business you’re in.

# All of which has exactly WHAT to do with the Turn One Advantage…?

Let’s circle back briefly to the questions posed above
regarding the difference between the simulated and observed winning percentages
and the fact that we don’t see as many matches going to a 3^{rd} game
as we would expect. Let’s say we’ve got two hypothetical teams, one is a super
team that will ALWAYS play at 150% of the average, and the other is an
only-plays-once-a-year rec team that ALWAYS plays at 50%. These teams could
play 1,000 best-of-three matches and they would all end 2-0, with Team A
winning half of the time and Team B wining half of the time, because the super
team and the rec team rotate, each spending half the time as A and half the
time as B. Theoretically, you could give the opening team 8 batons per round,
every round, and the rec team would still never win a game. It might be
tempting, in that hypothetical world, to look at the data and say “There is no advantage
to throwing 8 batons instead of 6, because it has no discernible impact on the
outcome of the game.”

Now here is where you get into trouble with averages, because if you averaged the overall efficiency for all of the games it would come to 100%. Team A’s overall efficiency? 100%. Team B’s overall efficiency? 100%. So A and B are playing equally well, right? Nope, not by a long shot. If you instead looked at the averages of the winner versus the loser you would see the 150% vs 50% that tells the real story of the games.

In our current data, the winning team averages at about 114%, the losing team at about 84%, and the average difference is about 38 percentage points. The teams face off, play their hardest, and the team that performs better, wins, right?

Well, not always.

We have several occurrences of what I believe (and what the data shows) to be games where Team B actually played better than team A, but they weren’t better ENOUGH to overcome the tempo and baton advantage conferred by throwing first. Care for a concrete example or two? (presented here in abbreviated Planet Kubb Notation)

T1: 0I , - , - , B , - , B , B

T2: 3I , 3F , B , B , B , B , B

T3: 8I , 3F , 3F , 2F , B , B , K

I am not going to try to make the case that Team A doesn’t play a great game here. A three base kubb opening is really good, and then 8-with-3, base, base, king to close is great, but look at what B did; a triple to clear the entire field, then 5-for-5 at 8 meters. An absolutely PHENOMENAL game at 286% efficiency, but it’s not enough to overcome Team A’s 173% plus the T1 advantage in this high level game.

Another:

T1: 0I , B , - , B , B , B , -

T2: 4I , 2F , 2F , - , B , B , -

T3: 6I , 3F , - , F , F , - , F

T4: 6I , 3F , 2F , F , - , B , -

T5: 7I , 3F , 2F , - , F , - , F

T6: 7I , 3F , 2F , F , F , B , B

T7: 9I , 4F , 3F , F , F , B , K

Again, not a bad game here overall for Team A. Very nice 4 base kubb opening and a strong finish in turn 7, but turns 3 and 5 were only mediocre at only 76% and 83% respectively. Meanwhile, B is putting in solid performances round after round for a final comparison of 152% to 128%. Better, but not better enough.

There are no examples of team A outperforming B and losing. Zero. Not in the observed data and not in the hundreds of thousands of simulations I’ve run – it’s just not possible unless A loses by killing the king early.

*Check back
tomorrow for ‘OK, but is that a BAD thing?’ and the whole point of this
exercise…*

In : Theory

Tags: t1 advantage

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