Herb style qualifying = Funny math?

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I’m revisiting this thread because I ran the numbers on the Intergalactic Championship and my predictions were way off. As it turns out the cut line was 259 points. The 40th position was tied with a player who averaged 23rd per game, and another who averaged 26th per game(with a #1 score). The player just above in 38th spot averaged 24th per game(with a #2 score).

In my hypothetical example above where someone was 4th, 12th, 19th, 20th, they would have earned 297 points - good enough for 16th position!

So this proves to me that I’m pretty bad at predicting where the cut line will be and the funny math continues!

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PERCENTAGE SCORING.PNG1238×397 39.3 KB

The major problem I have had with the scoring systems used is that they don’t reward the individual game score, just how well you compare to other people - and even then not necessarily fairly.
I have seen competition games with 3 consecutive scores being similar to this:
100,000,000, 51,000,100 & 51,000,000.
Obviously the first score is significantly better than the 2nd score but only receives a single pt more, exactly the same as the difference between 2nd & 3rd scores, where the difference could be as little as a single bumper hit.

To try and reward each individual game, I used a different scoring system. The average score across a machine would score 100pts, all other scores were then scaled to that.
It rewarded a good score, without penalising too much a very bad score.

I’ve used this ranking system twice in comps and the results are very similar each time. 7 out of 8 qualifiers remain the same and the top 2 also remained the same each time.

However, this was used in a single attempt comp, so it would be interesting to see how this would apply to an unlimited entry style qualification

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Not all games have linear scoring. If the average score is 100, then what I want to do is play the games with exponential scoring well, and I win.

The ‘ranking scores’ technique does have flaws, but it works for all machines from all eras in a predictable way.

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as opposed to wanting to play them badly? :smiley: If you play all of the machines well you win. It would be nice to be able to choose which machines you had bad games on.

Seriously, the same would go for everyone though, thus driving up the average scores, and reducing the effect of a great score.

In the example above the highest earned pts on each machine was in the 300-385 range. This comp has a range of players from children right through to top 50 players (in eff%).

The other time it was used machines included HS2, WH2O, DrWho, Flintstones and still had the same range of max pts awarded per machine

I just like a system that rewards individual scores per machine.
We did play around with various other ways of allocating the pts including:
from 0-100 for all scores
0-100 for scores below average & 100-200 for scores above average
and other non-linear scales

They ALL produced very similar results, as did all of the traditional scoring systems.

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No, the implication is that doing well on some of the games doesn’t matter.

Consider two games: one with bonus, and one with bonus and bonus X, and both with no other scoring. The latter will have a quadratic score increase with time played (approximately), while the former will have linear score over time. A simple average of the players’ scores won’t capture this difference, so ‘blowing up’ the former is a much bigger impact than blowing up the latter. You therefore bias the results (at the top of the standings) towards the players that did well on the first game rather than the second.

Now, my example isn’t entirely silly. Compare BSD to, well, a lot of games: if you do The Thing, you get like 10x ‘normal game’ points. That’s not true on lots of other games with flatter scoring curves.

(I think @bkerins has strong words to say on this topic, if he wants to chime in)

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I’ll chime in on behalf of us math geeks. Point systems with large bonuses for only 1st and 2nd are poor because they fail to capture the achievement level properly. In games with “The Thing,” the “gap” in points, IF ANY, should be between those who achieved it and those who did not. The points should NOT be proportional to score in either that or a normal situation to reflect the fact that no two machines have equally shaped scoring curves.

Example: BSD, 100 plays, top ten scores are 3.0B, 2.9B, 2.1B, 2.0B, 1.9B, 800M, 700M, 600M, 575M, 550M. Going 100-90-85-84-83, etc. gives #1 10 extra points over #2 for a 100M margin, but #5 gets only 1 point more than #6 for a 1.1B margin … smells bad. Percent-of-total scoring would be really flat beyond the top 10 or so and give a [too-] big edge to the top 5.

What’s better than either [I won’t say ideal because, well, you know how that sparks fire here] is something that uses linear points as a base, i.e. 100-99-98, etc., with perhaps a small 1st and 2nd bonus [5 points or less for first, 3 points or less for 2nd], and then has a fixed number of “game bonus points” for each machine which are distributed based on percentages of total points scored with a maximum number of bonus points per player. If that number was 15, then in the above case, I’d give players one and two four bonus points each, players 3,4 and 5 two bonus points each and player 6 one bonus point [best “non-Thing” score]. The obvious problem is this can get complicated to apply and is harder to understand. Also, when you have a machine with a really flat scoring curve and no “thing,” the game bonus points make less sense.

If percentage-like points are used, then player A who does “the thing” on a game and beats player B by just one position but a lot of points could outrank them overall even if player B beat player A by multiple positions on every other machine present. That smells bad, too.

The fundamental problem is that the “level of achievement curve” varies by machine, but we’re trying to combine results from multiple machines into a single aggregate value.

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One problem with the 100-99-98 scoring is that it weighs the scoring towards the people who come close to last if there are fewer than 100 players. For example, I get 71 points for coming last in a 30-person comp. If all people play all machines, this doesn’t matter. But if the number of players on each machine isn’t the same, and there are arbitrary sets of players on each machine (some with overlap, some without), it can create scoring anomalies.

I’m wondering whether the following would be an improvement:

Say we have eight machines in the comp. Record the maximum number of players for each machine. For example, assume the most popular machine had 41 players, and the others had fewer players. Now set the winning score to 41 for ALL machines. If the least popular machine had, say 29 players, the player who comes last on that machine would receive 13 points, but the player who comes last on the most popular machine would receive 1 point.

The idea here is two-fold: create an incentive for players to play a less popular machine (“hey, there are cheap points up for grabs here”), and to minimise the number of free points someone can get but just plunging off on a machine and walking away.

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The result is the same. The only thing that matters is the margin between the scores. You are just subtracting the same number from each score.

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“The major problem I have had with the scoring systems used is that they don’t reward the individual game score, just how well you compare to other people”

This is how every game of tournament pinball is decided everywhere.

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“Bonus Points!”

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It’s the same until we add up all the scores from different machines to make a single final ranking list. Unless I’m missing something, the scoring I suggested is less biased towards the players near the bottom of the list, and it gives more weight to a win on a machine with many players than to a win on a machine with few players.

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Followup to any scoring system edge, percentage or otherwise, for doing “the thing” … in Golf, there’s no distinction between an eagle that’s a tap-in and one that’s holed out from the fairway. A hole in one is no better than two generic birdies. “The Thing,” if there is one, is given no special treatment. In poker, if you win with a straight flush vs. ace high, it’s the same as if you had won with a pair of deuces, of if the other player had folded. So you can make a pretty good case for not having any extra reward for players who do “the thing.” They won that game, or had the high score, or whatever. Fine. On to the next game.

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It’s the same if everyone plays the number of games required to qualify. Each player would just have following subtracted from their score:

(# of game counting towards qualifying)*(100 - # of players on most popular qualifying game)

The numbers will just look different, but the results will be the same.

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Ah, yes, thank you.