Wednesday, February 3, 2010

The Optimized Bracket Adjustment

Before I get started on the OBA (optimized bracket adjustment) a few (more) words on yesterday's classification post. I want to demonstrate in real numbers the difference in the current method for moving down and my suggested alternative.

Let's say a player earns 4200 points during the 2010 season. The player is ranked semi-pro as a result. In the current system (assuming no higher scores are received) the player's scores remain the same in 2011 and 2012. For 2013 the score is reduced from 4200 to 3150 dropping the player's rank to D1. And in 2014 the score drops again to 2100 where it stays, leaving the player ranked D1.
Using my alternative take the same player and the same 4200 points earned in 2010. The score remains the same in 2011. In 2012 (assuming no new qualifying scores are received) the player's score drops to 3360 and the player is ranked D1. In 2013 the score drops to 2520 and player remains D1. In 2014 the score drops to 1680 with the player assigned a D2 rank and in 2015 it would drop to the D2 floor of 984 where it would remain--until sufficient new scores were earned to start the climb up the ladder over again.
The larger point is simply that any player who rises to semi-pro (or pro) status but is unable for whatever reason to maintain it is no longer a semi-pro (or pro) player by demonstrated ability and shouldn't remain one by rank. That player may retain semi-pro potential but that is very different than playing at a semi-pro level and their classification rank ought to reflect the fact.

The Optimized Bracket Adjustment modifies scores earned in sub-optimal brackets. In a bracket of 8 teams 50% of the field end up in the top 4. In a bracket of 20 teams 20% of the field end up in the top 4. Clearly the larger bracket has a higher degree of difficulty in achieving a top 4 result. In the 8 team bracket the winner receives a 100. Second gets a 77 and third gets a 64. (All numbers rounded.) Eighth place gets 10, seventh gets 23 and sixth gets 36. In the bracket of 20 teams the winner receives 100, second gets 85, third gets 80. Twentieth gets 10, nineteenth gets 15 and eighteenth gets 19. All scores revert toward the mean except the polar scores of 100 and 10.

My contention is that a win in a bracket of eight is not equivalent to a win in a bracket of twenty (or more.) All results aren't created equally and shouldn't be valued equally for the purpose of determining a player's classification. The OBA takes into account the disparity in the relative degree of difficulty between random bracket population sets. The OBA would assign an optimum number of participants to a bracket and any number less than the optimum would modify the final event scores received by the participating teams. It would NOT alter their place of finish and the purpose of the modified score is as it relates to the ratings that impact classification only. Any number of teams below the optimum is then recognized as being competitively insufficient to award maximum points. It would also be relatively easy to do. It could be accomplished at least 3 ways, 2 of which are; by altering the range of scores from the top down (meaning the max score would be less than 100) or by changing the mean score (by moving both the high and low score possible.) In either case it would only require a simple numeric change to the equation generating raw event scores. And depending on the program structure it probably wouldn't be all that difficult to include. (Easy for me to say.)

But, again, this is more of a quibble than an absolutely necessary modification. The OBA would be most useful in under-populated brackets that displayed little or no parity. The fact that the high score is removed from consideration goes a long way towards assuring only players who legitimately earn their rank receive it--particularly in under-populated brackets--and as I said in the first post the new system is a substantial improvement over the old one. Any perceived or real inequities in the system are unlikely to affect any significant number of players. All it really needs is a little more flexibility in allowing downward player movement.


raehl said...
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Baca Loco said...

I hear you, Chris. All I had to work with was the classification system as displayed. I'm happy to see there's been a tweak or two aimed in the direction I was looking.

As to five years down the road--you of all people ought to favor having a method in place, even if it reqauires future adjustment. But as I said, largely a quibble and one I won't complain about loudly or often. :)

Baca Loco said...

Glad I saw it before you pulled it though I have no idea why you pulled it.

raehl said...

The classification system has yet to stay the same for more than 2 seasons. In 2003 we had D1, D2, ProAm, Novice and Rookie. Now We're at Pro, Semi-Pro, D1, D2, D3, D4, D5 and D6/Beginner. What's it going to look like in 5 years? I don't think anyone knows. So worrying about what the current rules will do to players 5 years from now seems to be getting a bit ahead of ourselves. We'll have a much better idea what's going on 5 years from now 4 years from now, and can make changes as necessary then.

What's important right now is how the system works for 2010. Where it's become apparent it wasn't working for 2010 it's already been changed - Pro scores from prior to 2009 were dropped to a 48x multiplier from 64x to account for the lack of Semi-Pro back then and the decreasing Pro ranks. And the end-season threshold for bumping from Semi-Pro to Pro was bumped to be top 10% of scores instead of top 20% in every other division.

With regards to the OBA, 100 points in one division is worth the same as 50 points in the next division. So winning D3 is the same as getting just shy of middle-of-the-pack in D2, and the number of D3 (or D2) teams at that event doesn't really change the known strength of the best team.

(And I pulled it to rewrite it to hopefully be clearer then got distracted.)

anonachris said...

I haven't followed the rules, just this commentary.

But if someone proposes a 5 year plan. And someone else points out how it won't work in 5 years. The solution isn't to say, it's a good plan and we'll change it in 4 years.

Why not re-work it so you don't have to change it 4 years. Unless their reasoning is garbage, which Baca's might be.

The only reason I see not to is to save face. You can't release a change and then change it before you even start the previous change, especially not if some blogger gets on your case about it.

Which brings me to the real point of my comment. Why not just involve this Baca guy and run the decision by him for his input. He seems to know what he's talking about. And at least if you work his input into the solution before releasing it, you've already co-opted him and he's on your side and can't whine about it.

At the very least it wouldn't hurt. Either that or just start posting, "That's good advice, maybe you can tell me more about it, we'll look into it and take it into account."

Baca Loco said...

They'll never co-opt me I tell ya, never. They'd have to pay me first--and why bother when I'm gonna say something anyway?

With respect to movement down it does matter now--at least to the group of players who will be affected by the rules prior to 4 years down the road. Admittedly it's not an enormous group but it is a group that could potentially help improve the quality of play across the board.

a-chris--that's raehl on his best behavior and I, for one, appreciate the effort. :)

raehl said...
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raehl said...

No one proposed a 5-year plan. All that happened was a new system was put in place that works better right now than the previous system and better than any alternative on the table.

Someone pointed out that the current system might not work for a certain percentage of players in 5 years. They are almost certainly correct. But knowing that the current system probably won't work the best for everyone in 5 years is not the same as knowing what system will work the best for everyone in 5 years. Nobody has enough information to make a good prediction on that.

For example, 5 years ago was the start of the 2005 season. APPA was 18 months old at that point. We didn't have the length of data nor the league participation numbers then to even make a system like this possible. PSP was running Open, D1, D2 and D3 across XBall and 5-man and NPPL was about to have their largest season ever. Any system put in place then that attempted to work the best now would have failed miserably.

The current system should work very well for 2010. As has been done year after year, at the end of 2010, the system will be reexamined and any necessary changes ll be will made to make it better for 2011.

But back to your original issue: You don't rework the system to make sure it works the best for everyone in 5 years because you accept that you don't have the crystal ball necessary to make such a task possible, and thus accept that the best way to make a system that will work the best in 5 years is simply to wait 4 years.

Baca Loco said...

Now this is the raehl I'm used to. :D

Apparently the voices in your head are the ones suggesting re-working the system because I can't find where anybody else suggested it. As you've already addressed, at least in part, my issue with low pop brackets it can't be that. And the suggestion about changing the moving down mechanism is hardly a re-working of the whole system because it relies on the way you've already set it up.

Good to know the old faction is still here.

raehl said...

Split hairs much Baca?

"rework" doesn't have to mean "change completely" or even "change mostly". It can very well mean taking the current system and making it work differently - by say, changing the percentages and time frames that scores decrease in value. One might call that 'reworking'.