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There is a Quite a Rumble over Rate Evaluation in the Cafe

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Postby Chrisy Moltisanti » Tue Oct 31, 2006 6:59 pm

Amazinz wrote:Alright, I read through some of what you linked to but it's too much to digest in one sitting. The main problem with the first part of your post is that the writer is making the assumption that A > B and to make a long story short this is not true in regard to what you are trying to accomplish.

A simple formula you can use is (Made*Attempts)/Made [or Made^2/Attempts].

B: 450^2 / 500 = 405
A: 190^2 / 200 = 180.5
C: 300^2 / 600 = 150
D: 40^2 / 100 = 16


Hmm, player D. Let's say in your example that player D takes twice as many attempts (or has twice as many AB at the same rate). Player D's rate obviously is far below the mean in the example and yet we're now giving him twice as many points, despite the fact that his attempts at that rate would hurt basically twice as much? (80^4/200 = 32)
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Postby Amazinz » Tue Oct 31, 2006 7:11 pm

Yes, it's true. It's not perfect just a quick and dirty formula I use to rank ratios but when you consider the scale those 32 points are insignificant.
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Postby Chrisy Moltisanti » Tue Oct 31, 2006 7:32 pm

Amazinz wrote:Yes, it's true. It's not perfect just a quick and dirty formula I use to rank ratios but when you consider the scale those 32 points are insignificant.


K bump that to 500 attempts and it's real big issue.

Care to disclose the best way to do it? Anyone?
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Postby Amazinz » Tue Oct 31, 2006 7:39 pm

Here is each player you originally listed plus a player for each who took twice as many shots but at the same rate. The formula has been changed slightly to take into account attempts more.

((Made^2)/Attempted)-(Attempted-Made)

Code: Select all
Made   ATT   %       V   
190   200    0.95    170.5
380   400    0.95    341
450   500    0.90    355
900   1000   0.90    710
300   600    0.50   -150
600   1200   0.50   -300
40    100    0.40   -44
80    200    0.40   -88
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Postby Chrisy Moltisanti » Tue Oct 31, 2006 8:00 pm

Amazinz wrote:Here is each player you originally listed plus a player for each who took twice as many shots but at the same rate. The formula has been changed slightly to take into account attempts more.

((Made^2)/Attempted)-(Attempted-Made)

Code: Select all
Made   ATT   %       V   
190   200    0.95    170.5
380   400    0.95    341
450   500    0.90    355
900   1000   0.90    710
300   600    0.50   -150
600   1200   0.50   -300
40    100    0.40   -44
80    200    0.40   -88


Aside from using standard deviation based valuation that seems pretty solid. Are you familiar with incorporating z-scores in to data evaluation?
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Postby Amazinz » Tue Oct 31, 2006 8:11 pm

I understand it but I am not a fan of using Standard Deviation for fantasy values. I prefer to use baselines.
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Postby Tavish » Wed Nov 01, 2006 3:04 pm

It is impossible to judge values for a rate stat for a particular player, don't let websites and magazine try and tell you any different.

The problem with the original post is that it does nothing to try and define what value actually is. Straight percentages have almost nothing to do with a particular player's value. Under the constructs laid out in that post if Shaq went 1 for 1 in 3-pt shots on the year he would be more valuable than if Kobe went 99 for 100.

Value in these cases is simply the impact a player has on the team total. Simple to define, but impossible to measure in a projection formula. The reason being is that a player's impact on the team total depends on the team itself. Lebron's 3pt percentage will have a much greater impact on a team made up of entirely of low post players than it would on a team made up of entirely perimeter players. His value fluctuates during the draft and during the season with each roster move.

The closest you can get is to determine values according to a league average mark (or if you are dead set on a specific strategy you can tailor the league average to that level).
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Postby Chrisy Moltisanti » Mon Nov 06, 2006 6:58 pm

Thanks Amazinz. And thanks Tavish, you are a good man (I've read many of your posts over the years). :-)

I'm going to come up with my own theory on how to best project weighted values based on percents. If you would critique it when I'm ready it would be much appreciated.
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Postby The Loveable Losers » Thu Nov 09, 2006 11:27 am

I'm not a statistician...I know numbers but I slept through my statistical methods class in college.

That said it seems to me that the M^2 / A isn't a bad formula as something quick and dirty but it lacks a comparison to the average shooting percentage.

Just to toss something out there for discussion with the people that do know stats how would this be as a starting point?
PP = Player Percentage = M / A
LP = League Percentage = M / A for the starting players in this league
PA = Player Attempts
LA = League average attempts for starting players in this league
x = Some coefficient to make the scale meaningful
Rank = sign(PP - LP) * (abs(PP - LP) ^ (x * PA / LA))

That way you're comparing the player's shooting percentage to the average shooting percentage for your league and you're comparing the player's attempts to the league attempts at that position. The sign and abs parts are because if you try to take a negative number to those odd powers you're going to get errors from your calculator. But basically a league average shooter will rank with 0 points regardless of how many attempts they have. Assuming that x is a reasonable number a bad shooter with very few attempts will rank very close to 0. A good shooter with very few attempts will also rank very close to 0 (again, assuming a good choice of x). But the value of a good shooter will ramp up the higher the PA/LA ratio is and the cost of a bad shooter will similarly ramp up along that scale.

Finally, you could choose different values for LP and LA if you're looking at different scenarios/strategies. This addresses Tavish's comments. To take a baseball example let's say I'm trying to value the era/whip of pitchers and I'm looking at it from a weekly average standpoint. I might value the pitchers based on what ratio of their projected innings pitched (PIP) versus the total innings pitched for the team in a week (TIP). Most teams in the league might have a TIP around 60 so a pitcher expected to average about 8ip per week (your typical starter) would make up 8/60th of the innings pitched (which would be part of our exponent in the valuation formula). But let's say my team is going to go with a minimum ip strategy and only pitch 14ip per week. Now my valuation of that player's era is using 8/14 as part of the exponent meaning that in my era/whip strategy slight variations in era have much larger significance for my values than it would for other teams' values. This makes sense...if I'm punting wins/k's in a h2h league to focus on era/whip then era/whip will be exponentially more important to me.
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