RPI 2010-2011 V: The "Chase" to AC & Beyond

[DrDemento]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

Just to help ou I'm rooting for a cc loss to UAA on thursday.
Go Engineers!

That alone deserves a positive rep from me!

[engineerhockeyfan]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

Added them in today. They're weighted wrong though probability-wise, as KRACH doesn't seem to have a good way to estimate ties. I used the probability of a split when two games are played, but that's no where near the probability of a tie. It shouldn't matter too much for the actual analysis though, as the probability associated with each outcome are secondary to the result of RPI in that outcome for this. It'll also be easy/quick to re-generate my probabilities if someone has a better idea about how to predict ties.

After running for about an hour, the program is predicting that we have an 84.2463% chance of making the playoffs (+/- ~4%). The margin of error accounts for a number of probability-based biases. I have one computer calculating the result of each permutation in highest-to-least-likely order, and another randomly picking permutations. The random one is converging to around 82%, which is inline with the probability based method.

I'm glad the results "agree" with RPI92's pen-and-paper based 86% estimate.

Here's a data dump for the data processed so far, accounting for the 30.5% most probable permutations:

Ranking if we're "in" the tournament (84.2463% of total):
15 - 34.930720271277%
13 - 18.091683732382%
14 - 25.354367457376%
12 - 5.8607277621524%
11 - 0.0088531694667127%
Ranking if we're out of the tournament (15.7537% of total):
16 - 12.705547353595%
17 - 2.1967289450045%
15 - 0.85137130874607%

Rankings of 14 and lower where we don't make it will be found eventually, it simply hasn't processed scenarios where there are more than two outside-the-top 16 auto-bids. I'm also bemused it hasn't found any #10 rankings where we're in yet.

You guys are amazing, I thought my head was spinning before, now it just fell off.

[Ralph Baer]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

Added them in today. They're weighted wrong though probability-wise, as KRACH doesn't seem to have a good way to estimate ties. I used the probability of a split when two games are played, but that's no where near the probability of a tie. It shouldn't matter too much for the actual analysis though, as the probability associated with each outcome are secondary to the result of RPI in that outcome for this. It'll also be easy/quick to re-generate my probabilities if someone has a better idea about how to predict ties.

After running for about an hour, the program is predicting that we have an 84.2463% chance of making the playoffs (+/- ~4%). The margin of error accounts for a number of probability-based biases. I have one computer calculating the result of each permutation in highest-to-least-likely order, and another randomly picking permutations. The random one is converging to around 82%, which is inline with the probability based method.

I'm glad the results "agree" with RPI92's pen-and-paper based 86% estimate.

Here's a data dump for the data processed so far, accounting for the 30.5% most probable permutations:

Ranking if we're "in" the tournament (84.2463% of total):
15 - 34.930720271277%
13 - 18.091683732382%
14 - 25.354367457376%
12 - 5.8607277621524%
11 - 0.0088531694667127%
Ranking if we're out of the tournament (15.7537% of total):
16 - 12.705547353595%
17 - 2.1967289450045%
15 - 0.85137130874607%

Rankings of 14 and lower where we don't make it will be found eventually, it simply hasn't processed scenarios where there are more than two outside-the-top 16 auto-bids. I'm also bemused it hasn't found any #10 rankings where we're in yet.

Do you mean that in about an hour you ran 30.5% of the permutations or however many permutations it takes to have a total of a 30.5% chance of happening. The latter, since you started with the most likely ones, would represent much less than 30.5% of all of the permutations, however if you meant the former, it means that it only takes between 3 and 4 hours to run all of them.

[fr joe]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

It's also not over until Hokymom sings.

I'd rather hear Princeton SuperMOM sing. I'm sure Babo has a wondeful signing voice. I know I don't!

[Ralph Baer]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

I'd rather hear Princeton SuperMOM sing. I'm sure Babo has a wondeful signing voice. I know I don't!

me neither

[realet]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

Do you mean that in about an hour you ran 30.5% of the permutations or however many permutations it takes to have a total of a 30.5% chance of happening?

I presumed that was one standard deviation.

[RPI92]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

12 - 5.8607277621524%
11 - 0.0088531694667127%

There's a 5.869580931% chance of a third-band seed? I like those odds.

Good work RH. Keep that program running. Please be ready to kick it off again for a recalc as soon as Thursday's games are completed.

[Ralph Baer]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

I presumed that was one standard deviation.

My recollection is that about 36.5% of time one is between plus and minus one SD of the mean in a normal distribution.

[RHamilton]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

Do you mean that in about an hour you ran 30.5% of the permutations or however many permutations it takes to have a total of a 30.5% chance of happening. The latter, since you started with the most likely ones, would represent much less than 30.5% of all of the permutations, however if you meant the former, it means that it only takes between 3 and 4 hours to run all of them.

It was the latter, Ralph. Currently at 82.5972% odds with permutations accounting for 60.0% of the _probable_ outcomes processed. I'm not expecting much more downward drift, if anything I expect an upturn based on what I'm seeing from the randomly ordered solver.

[Ralph Baer]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

It was the latter, Ralph. Currently at 82.5972% odds with permutations accounting for 60.0% of the _probable_ outcomes processed. I'm not expecting much more downward drift, if anything I expect an upturn based on what I'm seeing from the randomly ordered solver.

Thanks. They better turn out the same when they are done. BTW, are you keeping track of where everyone fits in or just RPI? If so, you could post the results on the Princeton/Brown thread.

[realet]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

BTW, are you keeping track of where everyone fits in or just RPI? If so, you could post the results on the Princeton/Brown thread.

Or even better, he could send them to WaP and give us an exclusive.

Great work, RHam.

[manurespreader]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

I presumed that was one standard deviation.

Somehow I thought one standard deviation was 65%.
At any rate, looking at the teams from a subjective point of view... CC has Schwartz( the best freshman in D1 btw) back which is a big factor and got them the win last weekend, however AA plays well against them. I'm picking AA to continue that.
I don't see WMU winning a single game the rest of the way, The competition is too tough and all are highly motivated. I think Dartmouth splits.
God luck to your team, tough sitting in your position. Much easier to kibbitz.

[Ralph Baer]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

Somehow I thought one standard deviation was 65%.
At any rate, looking at the teams from a subjective point of view... CC has Schwartz( the best freshman in D1 btw) back which is a big factor and got them the win last weekend, however AA plays well against them. I'm picking AA to continue that.
I don't see WMU winning a single game the rest of the way, The competition is too tough and all are highly motivated. I think Dartmouth splits.
God luck to your team, tough sitting in your position. Much easier to kibbitz.

It has been a long time. I looked it up. It's about 68.27%, so you are correct.

[turk181]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

congrats to Chase & Nick (1st Team ECAC)....Allen (3rd Team) & Chase for one of 3 finalists for POY http://www.rpiathletics.com/

[FreshFish]

Re: RPI 2010-2011 V: The "Chase" to AC & Beyond

After running for about an hour, the program is predicting that we have an 84.2463% chance of making the playoffs (+/- ~4%). The margin of error accounts for a number of probability-based biases. I have one computer calculating the result of each permutation in highest-to-least-likely order, and another randomly picking permutations. The random one is converging to around 82%, which is inline with the probability based method.

I really respect all the work you've done, and I don't want this observation to come across the wrong way, and perhaps my perspective is skewed from having been a lifelong Cubs' fan.....

It seems to me you omitted an important variable from your calculations, especially when engineers are concerned! You can call it Maxwell's demon, you can call it Murphy's law, however you phrase it mathematically, in English it basically says "whatever can go wrong, will go wrong."

Or as Schrodinger's cat said right after the box was opened, 'however you view the superposition of probability wave states while the box was closed, once the box is opened all the probability waves except one collapse to zero, while one wave....ah!" and the cat stopped speaking......