Good formula for average finish? (1 Viewer)

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What would be the best way to determine what everyone's average finish is for our tournaments?

I see plenty of threads that discuss formulas for league points but nothing for average finish. Would the same type of formula apply? I don't think it's fair to add up their finishes and divide by the number of tournaments they attended as we often don't have the same turnout. Quick example... player A finishes 8th in a 16 person tournament while player B finishes 8th in an 8 person tournament. Both of their averages would be 8 which to me isn't fair since player A finished in the top 50% while player B finished last.

I've been toying with this equation... place finished/total # of players, I then add up all their points and divide by the number of tournaments attended. Then I just sort them lowest to highest. This seems to give me a good ranking system in regard to place finished against the field but not necessarily what their average finish is. With this equation last place would always be valued at 1 no matter how many attendees I have.

Is there a good way to figure out average finish with it still being fair?
Should I scratch the idea of average finish and just go with a ranking system?
What would you do?

Other info if it helps...
We always have the same buy-in
We don't do rebuys/addons
Maybe once every other year we do a deep stack tournament otherwise it's always the same starting stack
We usually have attendance between 8 and 16
This is more out of curiosity than anything. I don't have enough interest (from my players) to actually track it for league play
 
Another option would be to add up the points from the X number of weeks, or conversely drop the points from the worst Y number of weeks for each player.
 
I threw some numbers in my spreadsheet but this is what it looks like now
Average finish.JPG
 
We used to award one point for every player you outlasted and total the points for the year. 16 player tourney you could score up to 15 points, 6 players max would be five.
 
It seems to make sense to earn one point for every player you outlast, but I think it makes sense still to give additional weight to the top three spots in the tournament either way. Getting 8th of 16 players is far easier than getting 1st out of 8 players, and with no weighting they would earn the same number of points. I would give additional weight to 3rd place no matter the player count, additional weight to 2nd place, and a heavy weight for the winner. I might also reward consistent attendance by giving additional points to players who make it to most games. Maybe some sort of bonus for 50% attendance or better, then an additional bonus for 75%-80% or better, and a big bonus if you make every game.
 
Perhaps we are looking at this backwards. We are trying to find a way to add points to harder accomplishments. Maybe this should be like golf, where lower scores is better. Take each player in each tournament and make a fraction. Top half is position finished and bottom half is total entries. A first place finish in a 8 player tourney is .125 ( 1/8 ) while first place in a sixteen player tourney is. 0625 ( 1/16 ). Use this formula to get a number for every player in every tourney, and your best player will have the lowest average number.
 
So my goal here is to find each persons average finish, so yes the lower the score the better. My current formula is exactly what @tabletalker7 mentions. I'm curious if this is the best method or if there's something better out there.

I don't want to add points for attendance or remove their worst or best finish as this would throw off the results I'm looking for. The only weight that I think should be applied here is to the finishing position compared to the size of the field.
 
What would be the best way to determine what everyone's average finish is for our tournaments?

I see plenty of threads that discuss formulas for league points but nothing for average finish. Would the same type of formula apply? I don't think it's fair to add up their finishes and divide by the number of tournaments they attended as we often don't have the same turnout. Quick example... player A finishes 8th in a 16 person tournament while player B finishes 8th in an 8 person tournament. Both of their averages would be 8 which to me isn't fair since player A finished in the top 50% while player B finished last.

I've been toying with this equation... place finished/total # of players, I then add up all their points and divide by the number of tournaments attended. Then I just sort them lowest to highest. This seems to give me a good ranking system in regard to place finished against the field but not necessarily what their average finish is. With this equation last place would always be valued at 1 no matter how many attendees I have.

Is there a good way to figure out average finish with it still being fair?
Should I scratch the idea of average finish and just go with a ranking system?
What would you do?

Other info if it helps...
We always have the same buy-in
We don't do rebuys/addons
Maybe once every other year we do a deep stack tournament otherwise it's always the same starting stack
We usually have attendance between 8 and 16
This is more out of curiosity than anything. I don't have enough interest (from my players) to actually track it for league play
Answering the original question....

The easiest way to calculate the 'average finish' of each player over a series of unequal events is to add up the fractional finishes for each player and divide by their respective number of events -- and rank the scores from lowest total (best) to highest total (worst). So a player finishing 1st in an 8-player event scores 1/8 (0.125), while last place scores 8/8 (1.0).

This system can be used to determine either average score or cumulative score. The last-place finisher always scores 1 point, and the first-place finishers score lower points the larger the event.

If you prefer to use a larger-to-smaller numbering scale, simply deduct each player's fractional score from F+1 (field size +1). For example, 1st place in an 8-player event scores 8.875 (8+1-0.125) while 8th place scores 1.000 (8+1-1). In this version, the last-place finishers still always score 1 point, and the first-place finishers score higher points the larger the event.
 
The easiest way to calculate the 'average finish' of each player over a series of unequal events is to add up the fractional finishes for each player and divide by their respective number of events -- and rank the scores from lowest total (best) to highest total (worst). So a player finishing 1st in an 8-player event scores 1/8 (0.125), while last place scores 8/8 (1.0).

This system can be used to determine either average score or cumulative score. The last-place finisher always scores 1 point, and the first-place finishers score lower points the larger the event.
So in your eyes I had it right.

You say the easiest, is there a more complex equation that would be more accurate?
 
So in your eyes I had it right.

You say the easiest, is there a more complex equation that would be more accurate?
There is, but it wanders from the 'average' score to a more performance-based metric. The problem with tracking average scores is that it equates an overall average performer (with little-to-no chance of winning) with an all-or-nothing performer (who is actually capable of winning). I don't think they are actually equal players, but the system would have you believe it so.
 
I've come to the realization that with a variable number of players that I'll never come up with an accurate average. I guess the best I can do is settle for a ranking system. If nothing else it gives us a good idea of where people usually finish. Or at least who has better or worse finishes.
 
I've come to the realization that with a variable number of players that I'll never come up with an accurate average. I guess the best I can do is settle for a ranking system. If nothing else it gives us a good idea of where people usually finish. Or at least who has better or worse finishes.

I’ve kept track of results in a two-table tourney going back many years. Turnout has ranged from 8 to 20 players, typically around 14.

For my own interest—not for a points/prize system—my spreadsheet uses a number of slightly different metrics.

(A) In the money. The number of players ITM varies per session, depending on game size, so this kind of bakes in an adjustment for degree of difficulty. For many players, I think this is the most important stat: Was the session profitable?

(B) Raw average placing. Here, I just divide where they placed by the number of tourneys they played. This number is problematic, as the OP has noted, over a small sample size. But my database of tourneys now includes something like 250 events with a pretty stable cast of regs. So over time, the difference between placing 5th in an 18-person tourney vs. 2nd in a 9 person one kind of smooths out.

(C) Adjusted average. This is a formula I came up with which focuses more on how many people the person finished ahead of than how close they came to first, with some other factors to try to make it more fair/realistic. TBH I haven’t revised the formula in a long time, so I’d have to dig into the spreadsheet to remember how the heck this works.

(D) Wins. I also keep track of just how many firsts someone has.

(E) Money per session. How much $$$ they win or lose per session. This produces much the same result as ITM, but not exactly. I also track total net profit/loss, which is much more dependent on how often they play.

The interesting thing is that over time, the rankings for each metric pretty much converge. Over a season or even a year, you get different results. But long term it comes out very close to identical no matter how you slice and dice it. The top 4-5 players is almost exactly the same each way. Likewise with the bottom rungs.

A few specific things have come out, though, when I’ve fiddled with and scrutinized the spreadsheet.

For example, I notice that there are 3-4 players who are definitely well above average, ranking between 5th-8th in a pool of about two dozen regs. But though they are better than 2/3rds of the fields, they cash less and win less than you’d think. When I’ve then thought about these players’ styles, they tend to be on the nitty side—which means they last longer than average—but fail to play aggressively in the middle and mid-late stages. So as blinds go up, their nittiness leads to short stacks near the bubble, and getting ITM less.

Another example: I noticed that there are a few players with above-average wins, and also 2nd place finishes… but well below average rankings overall. These are the more aggressive, loose, bingo-y tournament players. They are more likely to either build a big stack early by taking chances, or to bust early for the same reason. There’s another problem with averaging.

Anyway. Maybe none of that is helpful. But I think the takeaway is: If you collect data long-term, you can run the numbers multiple ways, compare results, and then decide what are the most valuable metrics for your group. Not helpful for League purposes, but maybe it would be of interest to the group if they are competitive about the poker equivalent of an OBP or WHIP in baseball.
 
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I've kept track of the last 35 tournaments and I've noticed that the raw average and my weighted rankings do come out pretty close for the regulars. What seems to throw a wrench into the mix is the guys that have only attended a few tournaments. I think I need to implement a minimum number of tournaments attended to get them out of the mix. But then thinking about it I guess their numbers are valid even if they played once and finished first. Just hate seeing that guy at the top. I need to find a better formula for my weighted rankings as well. We had a small turnout the other day (only 5 of us) I took it down and scored .2 which I felt hurt me in the weighted standings. But I guess that's the nature of the beast when I have a formula that weighs in the number of players.
 
This is going to be a problem for any statistical analysis with a small sample size, covering an activity or experiment where there is a lot of variance in the results. I probably wouldn’t even pay it much mind until you get to 50 or even 100 tourneys logged. A good poker player can go months without a tournament win even in small MTTs. It just happens.

But in the meantime, you could make three charts: One for those with lots of appearances, another for just those with only a few, and a third which includes everyone. Maybe make the cutoff for the first for those with 50% of games played, the second 10% or less.
 
I wonder if basing on the tournament winnings will be a fairer result for comparison. It tougher to place 1st out of 20 (entry+rebuy) as compared to placing 1st out of 10 (entry + rebuy)
 

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