# Qualifying Math

In another thread there was a brief discussion of qualifying math, and the idea was that having 5/10 machines count makes it harder to qualify. While this line of thinking is true, it gets skewed in another direction if the tourney uses 1st place and 2nd place bonuses. I don’t really understand the 1st and 2nd place bonuses, though I have both benefited from them and been punished by them. This is because the priority becomes getting first or second on a machine. Take this example:

2 machines, 4 players qualify, 8 competing, both machines count. scoring is 100, 90, 85, 84. Getting a 1st place score means a player will qualify and unless the same player gets both firsts, that is 2 people qualified right there. (1st / 8th split = 4.5 average, yet is automatically in.) 4th / 4th = 4 average, yet is almost always out (a couple tiebreakers and only if top 3 qualifiers take up top 3 spots on both machines does the 4/4 make it in without a tiebreaker). 3rd / 3rd nets the same points as 2nd / 8th, so making it in with 3rd / 3rd is not a given and if firsts and seconds don’t have duplicates the only way in is a tie breaker (not impossible).

Now take the same examples finishing positions with an 8/7/6/5/4/3/2/1 distrubution. 3rd/3rd would be 12 points and in one scenario in a tiebreaker all others straight into finals. 4th / 4th would be 10 points and there are scenarios where you are out with 10, and scenarios where you are in a tiebreaker, but you are better off with 4th / 4th than 1st / 8th which is only 9 points.

Now if you take the 8 players across 3 machines and only 2 count, the need for a 1st place gets higher. 3rd/3rd/3rd only gets in rarely

I’m not sure I’ve ever understood the 1st/2nd place bonuses, but the smaller an event gets, the more it messes with the math.

Can someone explain why 1st and 2nd place bonuses are better/worse than reverse engineering the scoring based on the # of competitors? (X competitors = X points for 1st, X-1 for 2nd, 1 point for Xth place)

Your example works assuming every player has to play every machine, but once players are given the ability to choose their machines the logic breaks down. Games that are less desirable/play longer/have tech issues end up with a higher expected value than games that are more popular/play shorter. As an example at Pintastic, the aforementioned “long ticket” of BKSOR (100 entries), Breakshot (100), Full Throttle (107), Atlantis (111), and X-Files (93) would be much more desirable compared to a “short ticket” of Dragonfist (173), Fire (155), Flip Flop (169), Frontier (179), and Meteor (195). Even if I took 1s on all games, I would score better on the first ticket than the second.

Edit - to add a non ticket HERB example, NYCPC game participation ranged from 106 (Transformers, Whirlwind) to 144 (Flash Gordon). Still a solid scoring swing.

If you retroactively awarded the points based on the # of players that played a game, you would end up with extreme queue hassles and bad player experiences as all games are no longer equal.

I think the expanded 200-point system (bonus points down to ~15th or so, only a 5 point bump at the top end as used at Pinfest) does a great job of rewarding consistent play without being severely spiked towards #1/#2 scores.

I wasn’t suggesting that games are scored differently and yes, in my example everyone plays all games. PAPA scoring is 100, 90, 85, 84, …, 1, 0. Only the top 87 scores count. Fine. Why is 100/90/85 preferred to 87, 86, 85, …, 1, 0? That is my question. Because any time there is a bonus the math favors worse averages with outliers.

Bonus points should in theory encourage more play near the end of qualifying. You can both cover and lose more ground based on a single game result, so there’s more incentive to chase or protect.

I also don’t like the 100-90-85 scoring though.

I think putting an incentive on high scoring is perfectly fine - having an incentive to perform extremely well adds some strategic dynamics to a lot of games (should I play this well-played-so-far entry greedy and swing for the fences or take a guaranteed top 5/10 score?), although the arbitrary 100-90-85 structure is a bit crowded for this. Since I got a chance to look it up, I do like the 97.5% decay structure in general. You still have the “play well” incentive, and it’s stretched out to 12 players with a max dropoff of 5 points out of 200 (spots 1 through 4).

Why 100-90-85-84…? It is emotion-driven. It doesn’t stand up to mathematical analysis, and that is so obvious a mathematically inclined person wouldn’t even bother with it.
The bonuses are just bad.

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Why the transposition at all? Why not first on a game gets a 1, second gets a 2, etc. Lowest 24 scores or whatever advance. Is there a reason there should be a degradation to 0?

It might work better and push the inconsistency in machines played to the bottom (finishing last on the machine with the most plays versus finishing last on the machine with the least plays) and impact the top less. There is no inherent reason to have more points be better than fewer points. I like your idea

Adam covered this well in a previous thread.

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I read through the thread. I’ve been thinking all day about the inverted scoring system with the highest machine score being awarded 1 point and lower total being better, and it wasn’t mentioned in the above thread. I’d like to try it out sometime, maybe in a local game. Has anyone else tried it?

Other than the mental adjustment of getting used to looking at the golf scoring table of “lower is better” there is no difference between the system N, N-1, N-2…,1 and 1, 2, 3,…,N-1, N

The issue seems to be scoring systems that utilize a bonus or decay that takes away from the linear sequence, and what should be that bonus/decay.

A similar topic that has been discussed is finals scoring 4,2,1,0 versus wins system 3,2,1,0. Bonus versus linear.

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There is a huge difference.

Let’s say you allow N, N-1, N-2, …, 3,2,1 then you run into the problem Lewis found which is that the top score of the most popular game is valued higher than the top score of the least popular game.

Whereas, if you flip it - the bottom score of the most popular game is worse than the bottom score of the least popular game. For most large tournies, this won’t be a problem because you only use some of the scores, not all of the scores. For instance: If I run a herb format, 5/10 scores count, 1,2,3,…N-1, N it will turn out very differently from the N,N-1,…, 3,2,1 system.

And, I don’t have to worry much about making sure they all get the same plays.

I missed the part where N is the number of people playing a particular game. Usually in the large events there are many more people than 16 or 24, so either way (using a decreasing or increasing linear system) a top 16 or 24 score works out the same.

Specifically addressing Lewis’s above comment - there was a game that got 195 plays and another got 93. In 1,2,3 system, 10th place is 10 points on both machines. In N, N-1, N-2 system, 10th is 186 points on the first and 84 on the second. Obviously that difference is huge and breaks the system. Counting up maintains completely linear scoring and maintains a difference between the scores. Starting at 1000 and counting down by 1 would do the same, but for ease of use I think inverting the scoring to make a lower score the goal, 1 point for each place is also easy to think about.

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Understood. Once N is defined as the number of players on a particular game, the math for a decreasing point system does change.

For most tourneys using a decreasing system, N is fixed at something like 100 or 200 for each game.

Nonetheless, the global argument still seems to revolve around linear systems versus bonus systems