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(Topic ID: 69694)

Tournament Directrs: Choosing a scoring scale for round-robin


By jpolfer

6 years ago



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  • 22 posts
  • 11 Pinsiders participating
  • Latest reply 6 years ago by jpolfer
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    #1 6 years ago

    I've been running a small monthly pinball tournament in Milwaukee using a format of: round-robin (each player gets one try on each game at the location), feeding into a top-4 player playoff game. I've been running this in an Excel spreadsheet (it works pretty well - the Scott Danesi tool doesn't really add much over Excel for this).

    What I'm wondering about is: what are some guidelines around selecting a scoring scale to translate a player's individual game score into a point score? I'm talking about what's referred to as IFPA scoring (100-90-85-84-83-...-1-0-0-0-...) or linear scoring (1-2-3-4-5-6-...) in Scott Danesi's tool.

    I've been using linear scoring (top qualifier on a game gets 1pt, 2nd -> 2pts, 3rd -> 3pts, etc), and then add up the player's points to get a total. This works, except it tends to generate ties, and can create complicated matchups if you are selecting more than top 4 for a playoff of some sort. I think the scale is frustrating as player, because it doesn't really do a good job at selecting who, on average, scores better than others by only have a single point spread between each score. Because of the granularity of the scale, it creates a lot of ties.

    I talked about this with a friend who is well-versed in statistics, and he argued that I should try having the players points be computed by taking the natural logarithm [ln(x)] of the player's individual game score in Excel, and then adding up the players points at the end.

    Individual machine points, then, would be dependent on how much better / worse your score is compared to the overall average player score on the machine. The higher your individual machine score is compared to the average machine score by all players, the higher your individual machine points will be. Which makes sense to me. Also, because its less granular (decimal places / floating point offer more opportunities for discrimination), it also has fewer ties. I also learned that natural logarithm scoring is used in some poker tournament systems for scoring, so there is *some* precedent to using it in competitive gaming.

    To experiment, I used previous tournament data and tried re-running the qualifying order using ln(x) scoring, and it ended up with similar results to linear scoring when no ties were present, but clearly broke the ties when they were present in the linear scoring situations.

    Does anyone here have experience in using natural log scoring in a pinball setting? If so, are there any caveats or things to watch out for?

    I figure this is worth trying out - I've decided to use this scoring scheme for my tournament this upcoming Monday and get some feedback from players on it. I will report back results on Tuesday after its done.

    #2 6 years ago

    I think it could work okay if the game scoring is fairly linear, such as on many modern Sterns.

    Some game scores, like Fish Tales or Creature, take a giant jump if the player manages to get to super jackpots. The top player's score might by 5 - 10x the next player's because of that.

    Personally, I'd never use natural log because any scoring system has to be simple and intuitive for the players. What I might do if ties are a problem is simply use them in just that case. But to me, a simpler method would be to just calculate the median or average, and then compare how players did versus those. So if player 1 performed against the median on four games as follows: +5%, -8%, +20%, +7%, then their overall performance was +23% vs the median. If that's better than someone they tied with, they win the tie-breaker.

    #3 6 years ago

    I don't think you should use a transformation of any kind during in a tournament setting. It makes the scoring too mystical and players won't have a clue what's going on. Any benefits you gain would detract from the fun.

    The ifpa system isn't much different than your "linear one", except the point scale is inverted (more points the better you do). Most people find this intuitive. The bonus system is cool too. Getting a top score on one game can help you out big time if you aren't playing as well on other games. It can also be devastating to your overall score if someone tops you. What fun!

    If ties are your only problem, consider having a one ball playoff on a random game. Only do this when it matters, otherwise ties are okay. It's quick, it's easy and it's fun. Data transformation= not fun.

    #4 6 years ago

    Don't use logarithms to calculate scores. It will confuse everyone but you!

    You could use a similar system where the score drops by 10% for each position, rounded to the nearest integer:

    1st = 100
    2nd = 90
    3rd = 81
    4th = 73

    etc

    FYI the 100-90-85-84-83... system was first used at the PAPA 7 World Championship and is the general standard for the types of events you describe. Linear scoring does not reward high scores very well, so I don't recommend it.

    #5 6 years ago

    Thank you for the feedback!

    So what I'm hearing here is that: while the math behind the approach above is sound, it will confuse people who doesn't get the math behind it. That seems like a good reason though. I'm probably the most math-competent person there during our tournaments, and I don't want to appear as though I'm trying to 'bake' anything.

    The only reason I used the (1st=1pt,2nd=2pt,3rd=3pt,...) scoring was because I inherited the format from someone else, that's all. It worked OK for another director's monthly tournament here in Milwaukee, but he did everything on paper originally, and I think that scoring scheme made it easier for him to reason about things, but he routinely has tons of ties and it made the end of the tournament messy and time-consuming for some.

    On a week night (when I hold the tournament), I think its nice to limit the amount of time players might be required to stick around, especially since they might have to get to jobs the next day. 1-ball tie breakers are okay to me, but when my friend suggested this scoring method that would effectively reduce the tie-space to almost non-existent, I was interested.

    I already announced that I'd do the logarithmic scoring for tomorrow to my players. I'll try it and see what happens. If people are super-confused by it as the above might suggest, I'll write up a macro to use one of the other scoring assignment systems suggested above for next month.

    #6 6 years ago

    Well, since log 2 + log 3 = log 6, you might still end up with ties...! Choosing to add logarithms is also equivalent to doing the same 1-2-3 scoring system you did before, and *multiplying* the score ranks instead of adding them. That's a way to get what you were after while still keeping it understandable to others in the group.

    Good luck and enjoy.

    #7 6 years ago
    Quoted from bkerins:

    Choosing to add logarithms is also equivalent to doing the same 1-2-3 scoring system you did before, and *multiplying* the score ranks instead of adding them.

    That's not what I am planning on doing. If I'm confusing bkerins with my explanation (and considering that he essentially explains math for a living), then this is definitely not a good scoring scale for me to use at this time, and I'm going to abandon it for tonight. I'll use my lunch break to code up a macro for the IFPA scoring. If other tournaments are using it, my players should learn how to play in that scoring model, since they may see it elsewhere sometime (most of the players haven't competed much outside of local tournaments). I'll just have to deal with ties.

    ----------------------------

    Here's an actual example of what I was planning on doing.

    I plan on taking ln(actual player score on the machine) as the player's individual machine points.

    Example: Qualifying round using logarithmic scoring for 3 machines + 5 players. Each player is only allowed a single attempt at each machine.
    Game: Theatre of Magic
    Player 1 score: 529,761,950
    Player 1 points: ln(529,761,950) = 20.08794
    Player 2 score: 92,800,080
    Player 2 points: ln(92,800,080) = 18.34596
    Player 3 score: 280,981,090
    Player 3 points: ln(280,981,090) = 19.45380
    Player 4 score: 813,318,400
    Player 4 points: ln(813,318,400) = 20.51663
    Player 5 score: 113,005,270
    Player 5 points: ln(113,005,270) = 18.54295

    Game: No Good Gofers
    Player 1 score: 5,884,010
    Player 1 points: ln(5,884,010) = 15.58775
    Player 2 score: 29,844,530
    Player 2 points: ln(29,844,530) = 17.21151
    Player 3 score: 4,039,850
    Player 3 points: ln(4,039,850) = 15.21151
    Player 4 score: 9,892,370
    Player 4 points: ln(9,892,370) = 16.10727
    Player 5 score: 16,968,270
    Player 5 points: ln(16,968,270) = 16.64686

    Game: Rollergames
    Player 1 score: 2,781,420
    Player 1 points: ln(2,781,420) = 14.83847
    Player 2 score: 3,193,370
    Player 2 points: ln(3,193,370) = 14.97656
    Player 3 score: 1,443,770
    Player 3 points: ln(1,443,770) = 14.18277
    Player 4 score: 4,579,070
    Player 4 points: ln(4,579,070) = 15.33701
    Player 5 score: 1,417,480
    Player 5 points: ln(1,417,480) = 14.16439

    Qualifying accumulated points (add TOM, NGG, RG points together)
    Player 1 points: 20.08794 + 15.58775 + 14.83847 = 50.51416
    Player 2 points: 18.34596 + 17.21151 + 14.97656 = 50.53403
    Player 3 points: 19.45380 + 15.21151 + 14.18277 = 48.84808
    Player 4 points: 20.51663 + 16.10727 + 15.33701 = 51.96091
    Player 5 points: 18.54295 + 16.64686 + 14.16439 = 49.35420

    Qualifying ranking (ordered from most accumulated points to least):
    1st -> Player 4 (51.96091) ADV to finals
    2nd -> Player 2 (50.53403) ADV to finals
    3rd -> Player 1 (50.51416) ADV to finals
    4th -> Player 5 (49.35420) ADV to finals
    5th -> Player 3 (48.84808)

    EDIT: After looking over my response to Bowen again, I think the problem is with *my* understanding of taking ln(x) than his. My bad. I'll just use the IFPA scoring. Hope I didn't bother everyone.

    #8 6 years ago

    Bowen's statement is still correct. Addition of logarithms is equivalent to multiplication of the things prior to taking the logarithm.

    In any case, the players will need to have a good understanding of the scoring system in order to determine effective strategies on the fly, and to validate that the results are error-free. Anything that involves fractions of a point is likely to cause confusion, so I would not recommend it.

    #9 6 years ago
    Quoted from jpolfer:

    That's not what I am planning on doing. If I'm confusing bkerins with my explanation (and considering that he essentially explains math for a living), then this is definitely not a good scoring scale for me to use at this time, and I'm going to abandon it for tonight. I'll use my lunch break to code up a macro for the IFPA scoring.

    Pm me your email and I'll send you the ifpa excel template, with excel macros already written. No need to reinvent the wheel.

    #10 6 years ago

    For those of us that use LibreOffice Calc, here's the BASIC function listing:


    Function IFPAPOINTSFROMRANK(rank)

    If rank = 1 Then
    IFPAPOINTSFROMRANK = 100
    End If

    If rank = 2 Then
    IFPAPOINTSFROMRANK = 90
    end if

    If rank >= 3 Then
    Dim adjusted as Integer
    adjusted = 88 - rank
    If adjusted >=0 Then
    IFPAPOINTSFROMRANK = adjusted
    Else
    IFPAPOINTSFROMRANK = 0
    End If
    End If

    End Function

    #11 6 years ago
    Quoted from jpolfer:

    I've been using linear scoring (top qualifier on a game gets 1pt, 2nd -> 2pts, 3rd -> 3pts, etc), and then add up the player's points to get a total. This works, except it tends to generate ties,

    We use this system. In order to avoid ties, we decide and announce in advance which game will break ties. If two players finish
    1-2-2-1 and
    2-1-1-2
    on machines A-B-C-D, they both score 6 points. If machine A is the tie-breaker the first player wins. Works with 3+ players finishing with the same score.

    Attributing points based on score, even with ln(x) correction, gives a strong bias towards a single high performance. Bad idea for games with unbalanced scoring.

    #12 6 years ago

    Do what you like! Just ... why are you calling it IFPA scoring? It's not their system and they don't even use it in their own world championship tournament.

    Using raw scores instead of scaled scores (100-90-85-etc) puts a heavy emphasis on "exponential scoring" games like CFTBL or Spiderman, while reducing the emphasis of "linear scoring" games like Monopoly. A player with a breakaway score on an exponential scoring game can break this system and run away with #1 regardless of their other play.

    #13 6 years ago
    Quoted from bkerins:

    Just ... why are you calling it IFPA scoring?

    That's the term used in the Scott Danesi software package for the (100-90-85-84-...) scoring scale.

    #14 6 years ago

    Scott has it incorrectly labeled.

    Best of luck with your event.

    #15 6 years ago

    It's a common point allocation for Herb-style tournaments, nearly all of which are for IFPA (wppr) points. That's probably where it came from.

    One thing I forgot to add is that if time permits and they'll not drag out too long, go ahead and do tie-breakers. Most players I've met would rather their fate be decided via actually playing it out vs a formula. That said, I understand where you're coming from as far as weekday events and wanting to keep the event to a reasonable length. I use a formula for PAGG for that reason.

    Always remember that there are a lot of acceptable formats for IFPA that are very time-manageable, such as Pin Golf or time-limited games. I expected a lot of complaining with time-limited formats, but it turns out the players love them.

    Another thing is if you use a format with a qual and final, it's likely the 'serious' players will make the final and everyone else will be able to leave at a more reasonable hour. The finalists tend to be more serious players and are willing to stay late for pinball, even if it costs them an hour of sleep.

    #16 6 years ago

    KISS is my motto.

    Just pick one game up front that is the "tie breaker game".

    That game has added importance during the round robin. Any ties in rank points default to how each player performed on game X.

    Keeps Is Simple Stud.

    Players like simple and even the above avg pinball player is easily confused in the competition setting for some reason.

    #17 6 years ago
    Quoted from jpolfer:

    What I'm wondering about is: what are some guidelines around selecting a scoring scale to translate a player's individual game score into a point score?

    Here is my opinion on the matter: You should never translate a player's actual game score into anything other than a placement (whether that be a placement in a match or a placement against all the other scores recorded on a machine). If you are doing anything that involves directly awarding credit for points scored in a game instead of a ranking of the player's score, your format is bad and rewards insane scores on games like CFTBL and JM too strongly. Additionally, the formula you propose also makes games with higher scores worth more points, similar to the early NY PAPA tournaments. As I understand it, what you refer to as "round-robin" is really like a one-ticket-per-game NW Champs/HERB/whatever qualifying round. In that case, the only way scores should be compared to each other is by ranking. That is to say that in all of these situations for the top 3 players' results for a given game, players should be given the same amount of tournament qualifying points (100/90/85/... or 100/99/98... or 10/9/8... or whatever scale you choose to use):

    Top: 15 billion
    Second: 10 billion
    Third: 2 billion

    Top: 1.2 million
    Second.0 million
    Third: 800,000

    Top: 41,000
    Second: 40,000
    Third: 31,000

    If you have 3 machines and only 5 players, you are likely to have ties with whatever reasonable ranking formula you use for this style of tournament. The way you proposed to solve this problem only solves the problem by introducing a false level of granularity which isn't really representative of players' performances. If you have enough time, I suggest playing more games, or playing off tiebreakers (which are unfortunately inevitable at a small scale event like this).

    The "open qualifying/HERB" or restricted-ticket-open-qualifying tournament format works better with more players. If you have somewhere between 10-20 players, I recommend using Brackelope's Knockout format to run your event. We have three weeklies at different venues in Seattle that use the Brackelope software, and casual players have been happy generally because they are guaranteed a few rounds of play in the worst case and have no trouble understanding the formula. Additionally, head to head matches are always fun, and there is no direct conversion from game points to tournament points involved with the Brackelope Knockout format. Brackelope also works well for larger events, but I personally prefer the HERB or Pinburgh styles of tournament at that level.

    Hope your events work out! Always great to hear of more people starting up tournament scenes all around the world! Please feel free to contact me privately (or publicly) if you have any questions or would like more information.

    #18 6 years ago

    Definitely agree with the last point. Events are difficult to run and thank you for doing so. Let us know what other questions you have or contact me through messages.

    #19 6 years ago
    Quoted from mhs:

    Scott has it incorrectly labeled.

    Bowen is wrong too, as Pinburgh 2003 was the first event (that I remember) using the 100-90-85-84-... scoring scale

    #20 6 years ago
    Quoted from bkerins:

    Using raw scores instead of scaled scores (100-90-85-etc) puts a heavy emphasis on "exponential scoring" games like CFTBL or spiderman, while reducing the emphasis of "linear scoring" games like Monopoly. A player with a breakaway score on an exponential scoring game can break this system and run away with #1 regardless of their other play.

    As a recent example of this, the recent Australian champs used a sum-of-raw-scores scoring method over four games (two avengers LE, two metallica pro).

    One player won the competition strictly on the back of a good game of Metallica. With literal zeroes on the other games he still would have won overall. This was, unfortunately, one of the first games played by any player.

    #21 6 years ago
    Quoted from Zaxxis:

    Bowen is wrong too, as Pinburgh 2003 was the first event (that I remember) using the 100-90-85-84-... scoring scale

    Ah yes! Pinburgh 2003 was also the first tournament organized by the "new" PAPA

    To Excalabur: Yes, exactly. That doesn't make the event much fun to participate in or to watch.

    #22 6 years ago

    Thanks for the feedback everyone.

    I used 100-90-85-... scoring for the last tournament, and the tournament went well. I'm going to stick with it and see how it goes for the conceivable future.

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