In 4, 2, 1, 0 if you win two you are guaranteed to move on, even if you lose the last one outright. That extra bonus point for wins makes a ton of difference.
If you are in a four player group and you go 1st, 1st, 4th, and another player goes 2nd, 2nd, 1st, I think the 2nd player SHOULD win. That is exactly what happens in IFPA (7,5,3,1) and Pinburgh(3,2,1,0) scoring. Only in PAPA(4,2,1,0) scoring does that create a tie-breaker. I would argue that in that scenario with 2 players taking only 3rd and 4ths throughout the match, that the match was pretty lopsided to begin with.
Edit: I see now that the tie-breaker would be meaningless unless it was the final match.
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I 100% disagree. Winning outright against players of the caliber weāre talking about is an enormous accomplishment, and I want a system that motivates players to swing for the fences and win not just ādo good enough to make up for it in the next gameā.
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@djreddog - I know you like to grade out at 100% TGP, so whatever you end up doing, make sure that you know what the TGP of the format is going to end up being so that you can adjust qualifying to add in an extra round or two if needed to get things up to 100%.
If you keep qualifying the way youāve been (7-Round Match Play, 14 of 25 TGP), youāre targeting Finals to be a least 11 TGP.
I know the guidance that Iāve gotten from the IFPA in the past is that if itās a non-standard format, itās the number of games played by the winner, which if you have a format like the Curling Finals may not reach the 11 TGP Threshold, so you would need to add another round of two of qualifying to make up the different in order to plan for āworse-case situationsā where the 1-seed ends up winning all of their games.
Sounds like thereās some debate into whether how valuable certain positions should be relative to one another.
A few years ago we had a more casual event but wanted a very quick Finals Format with the goal of having 16 people participate but finishing the event as quickly as we could because of time constraints.
We decided to do a two-round Match Play Finals, but wanted to minimize the number of ties. 100% not the best way to decide the true best player of the event, but I dug up an old spreadsheet that looked at all the permutations for two games with each of the following scores:
- 4-2-1-0 Scoring
- 3-2-1-0 Scoring
- 6-3-1-0 Scoring
- 7-4-2-0 Scoring
- 5-3-2-1 Scoring
- 5-3-1-0 Scoring
- 1-0-0-0 Scoring
- 1-1-0-0 Scoring
- 8-6-4-2 Scoring
PAPA scoring 4/2/1/0 has 5 out of 24 permutations result in tiebreakers
Marburg scoring 7/4/2/0 has 3 out of 24 permutations result in tiebreakers
In PAPA, getting 2nd twice results in a tie with someone who got a 1st and 4th.
In Marburg, getting 2nd twice is more valuable than someone who got a 1st and 4th.
Our goal for that specific event was avoiding tiebreakers and wrapping up quickly, so thatās what we were trying to optimize on.
Someone with some time and Excel savvy could expand what was done here to look at how this flushes out across three or four games across different scoring schemes, but since I had a starting point I thought it may be worth sharing.
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I think itās time for a return to the original PAPA 10-5-1-0 scoring.
So Iāve always heard that 4-2-1-0 scoring is preferable to 3-2-1-0 scoring because it reduces ties, but Iāve never actually questioned this assertion. I decided to run some tests.
For a single four player match, there are 24 possible outcomes. This means for a 3 game round, there are 13,824 possible outcomes.
Using 3-2-1-0 scoring, ~44.1% of those outcomes results in any tie. 18.4% of all outcomes result in a tie for first, and 17.4% result in a tie for second.
Using 4-2-1-0 scoring, ~42% of outcomes results in any tie. 12.2% of all outcomes result in a tie for first, and 17.9% are ties for second.
I found this to be pretty interesting. 4-2-1-0 scoring does result in fewer ties overall, but only marginally so. Ties for second are what we worry about most in early rounds, because those have to be broken. Yet, the probability of second place ties are the same for both scoring methods. Ties for first arenāt really a problem, because usually that just means both players move on, and the tie only has to be broken in the last round. Three-way ties for first are pretty rare (3% in 3-2-1-0 and 1.7% in 4-2-1-0).
Anyway, 4-2-1-0 scoring does provide some benefit in terms of reducing the probability of ties. Iām on the fence though in terms of whether itās all that meaningful.
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Are these for tiebreakers for the final round (for final placement) or earlier rounds (only tiebreakers that affect who advances)? Also, you may want to double check your math. Iām pretty sure there should be 13,824 (24^3) possible outcomes.
And for 3 games you can fix the player finish order for game 1 then you only have to consider the number of permutations in the remaining 2 games, so 24^2 = 576.
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For a 4 player final: (naming the winner of player 1 A, 2nd place B, etc.)
1 game played there is just 1 outcome
2 games played there are 24 possible outcomes
3 games played that increases to 576 (24x24)
4 games played that increases to 13824 (576x24)
I have created a spreadsheet that calculates all of the possible outcomes for a 3 games final, and calculates percentages of ties, once any scoring system is inputted. I wasnāt able to think of a way to accommodate a 4 game final other than brute force - which Iām not putting that amount of time in!
(Happy to share this via email with someone, so that they can then post it as a Google doc - as I donāt know how, or if anyone wants me to run it with any other scoring system)
Some screenshots of the most popular scoring systems (blue is a 2 game final, green a 3 game final)
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dāoh, youāre right. The permutation function I used defaulted to not allowing repeats. Updated original post ā good catch!
The results are actually for any three game group. But this is a good point ā depending on the number of groups there are, those āmarginalā differences may be more significant over an entire tournament final.
If youāre interested in the brute force method, hereās the R code. I originally started this to be able to determine the āoutsā and win probabilities for any given person depending on the number of games remaining, but hacked it for the present discussion.
library(tidyverse)
# Starting parameters
start.scores = c(0,0,0,0)
matches = 3
scoring = "4-2-1-0"
player_score <- function(outcome = 1,player = 1, match.scores){
return(match.scores[outcome,player])
}
# create matrix of possible outcomes in a single match
match.pos <- permutations(n = 4,r = 4,repeats.allowed = F) #rows = possible outcome, columns = player, value = position
# create matrix of possible scores in a single match, given scoring method
match.scores <- match.pos
if(scoring == "3-2-1-0"){
match.scores <- match.pos-1
match.scores <- abs(match.scores -3)
}else if(scoring == "4-2-1-0"){
match.scores[match.scores == 4] <- 0
match.scores[match.scores == 1] <- 4
match.scores[match.scores == 3] <- 1
}else if(scoring == "5-3-2-1"){
match.scores <- match.pos-1
match.scores <- abs(match.scores -4)
match.scores[match.scores == 4] <- 5
}else if(scoring == "7-5-3-1"){
match.scores[match.scores == 1] <- 7
match.scores[match.scores == 4] <- 1
match.scores[match.scores == 2] <- 5
}
#create matrix of all the possible paths, given the number of matches remaining.
paths <- permutations(n = nrow(match.pos), r = as.numeric(matches),repeats.allowed = T)
n.possible.outcomes <- nrow(paths)
#for the paths of each player, compute their score given that path.
p1 <- paths
p2 <- paths
p3 <- paths
p4 <- paths
for(i in 1:matches){
p1[,i] <- player_score(paths[,i],1,match.scores)
}
for(i in 1:matches){
p2[,i] <- player_score(paths[,i],2,match.scores)
}
for(i in 1:matches){
p3[,i] <- player_score(paths[,i],3,match.scores)
}
for(i in 1:matches){
p4[,i] <- player_score(paths[,i],4,match.scores)
}
# create a matrix showing the final score of each player, for all possible paths
final.scores <- matrix(nrow = nrow(paths),ncol = 4) #matrix showing scores for each player after each outcome
final.scores[,1] <- apply(X = p1,MARGIN = 1,FUN = sum) #note each column is a player
final.scores[,2] <- apply(X = p2,MARGIN = 1,FUN = sum)
final.scores[,3] <- apply(X = p3,MARGIN = 1,FUN = sum)
final.scores[,4] <- apply(X = p4,MARGIN = 1,FUN = sum)
# add starting values
for(i in 1:4){
final.scores[,i] <- final.scores[,i]+start.scores[i]
}
# get the final placement, for all possible paths (note, ties use "max" method. E.g., if scores are 6,6,6,1, the ranks are 1,1,1,4)
final.placement <- t(apply(X = final.scores,
MARGIN = 1,
FUN = function(x) length(x)+1-rank(x,ties.method = "max")))
ties <- mean(apply(X = final.placement,MARGIN = 1, FUN = function(x) n_distinct(x)<4))
first.ties <- mean(apply(X = final.placement,MARGIN = 1, FUN = function(x) sum(x == 1) > 1))
first.ties.no.break <- mean(apply(X = final.placement,MARGIN = 1, FUN = function(x) sum(x == 1) == 2))
first.ties.three.way <- mean(apply(X = final.placement,MARGIN = 1, FUN = function(x) sum(x == 1) == 3))
second.ties <- mean(apply(X = final.placement,MARGIN = 1, FUN = function(x) sum(x == 2) > 1))
print(paste("Scoring Method:",scoring))
print(paste("Total permutations:",n.possible.outcomes))
print(paste("total ties:",ties))
print(paste("first ties:",first.ties))
print(paste("first ties, no break: ",first.ties.no.break))
print(paste("first ties, three-way: ",first.ties.three.way))
print(paste("second ties: ",second.ties))
Discussing a 4 player 3 game final format tonight which reduces the no. of ties and have come up with something a bit different.
Hear me out.
A 4 player 3 ball 3 game final has 36 balls played in total.
Why not try a 4 player 9 ball game on a single game?
As good as GUARANTEED no ties at the end of the 36 balls.
The game used would have to be chosen carefully, no one wants to see 9 balls on GoT for example, but other games it may suit well.
I can see it changing the strategy people would have to employ on certain games, it would almost certainly mean Wizard Modes would be reached, which would never normally be seen, and force people to go for them.
Im definitely going to try this at the next comp I run, and see how it goes.
Games up for consideration include DI, AcDc, ST, TWD, WPT, TSPP, JJP PotC, DP.
Games discounted include SM, GB, GoT, GotG, LotR.
Wellā¦ canāt argue that itād be a different approach.
First immediate thought that comes to mind is that if a participant doesnāt know the selected game, or just isnāt good at it (sometimes certain playfield geometry just throws some people for a loop, for example)ā¦ that participant is probably screwed.
Second thought is that it could turn into a terrible slog for both participants and spectators. āWell, here we are, starting our 3rd hour of this same freakinā long game of XYZā¦ā I think when something goes on for a long time like that, everyone appreciates more variety.
If you or your players are WPPR chasers, this may negatively influence the TGP of your event (depending on what else is involved in the overall tournament)ā¦ if Iām not mistaken, although games with less than 3 balls get penalized, games with more than 3 balls cap at 100%, and this would count as a single game.
But hey, if you try it, let us know how it went. 
Thanks for this!
I currently have this exact same goal.
Hereās a 3-game version:
Three-Game Finals Possibilities
I added some extra columns that show how many expected extra games would need to be played to break ties for advancement and for the final round. I also included the concept of only breaking ties in the final round if the tie is for 1st place (required for valid IFPA results) or if itās a 3-player tie (because 2-player ties are actually positive expected WPPRs overall among the tied players). This lets you further reduce the need for tiebreaker games in situations where theyāre not needed and not beneficial.
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