Who are Player J's helpers? ---- a test of the TASM

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Who are Player J's helpers? ---- a test of the TASM

I have not used the Test Against Selected Modulus (TASM) in a while, but a situation has arisen where it may be useful.
A certain player (let us call him Player J) is in the top 25 but has no wins. Certainly a typo. But that is not the case. Player J is striving to attain first place without any wins.
Now this is where the TASM comes in. The TASM (Test Against Selected Modulus) is designed to spot pgaâ€™s of a particular player. Who is helping Player J attain his goal?
The TASM works as follows. Player J has a percentage profile of 00-30-10-09-13-14-20. If there are only six other players with whom Player J has played games, their collective percentage profile would have to be the modulus of Player Jâ€™s, or 100-70-90-91-87-86-80. Divided equally among the six players, each J-helper would have a percentage profile of 16-12-15-15-15-14-13. The TASM compares a player against this profile (rather than the uniform distribution profile used by the TAPL). The smaller the TASM, the greater the possibility that the player is a pga of Player J.
The TASM is only an approximation. First, the number of helpers of player J may be less or more than six. Second, some helpers may help more than others. Third, many players have played more games than Player J and obviously cannot have helped Player J in all of them.
Here is a list of the top 25 players and their TASMâ€™s. The number of games per player have been normalized to match that of Player J. The smaller the TASM, the more likely a pga. It will be noted that Player J himself has a very large TASM. That is because he canâ€™t be a pga of himself!
12 amenphis 2486â—† 215 15% 17% 14% 15% 11% 15% 10% âˆ« 659 âˆ«
23 Obi-Wan Kenewbie 1695â—† 215 22% 11% 9% 13% 15% 13% 14% âˆ« 744 âˆ«
2 Vohaul 3610â—† 215 22% 16% 11% 16% 10% 15% 6% âˆ« 1617 âˆ«
7 lesplaydices 2679â—† 215 19% 17% 14% 12% 10% 6% 19% âˆ« 1662 âˆ«
4 Linch 3108â—† 215 22% 17% 16% 10% 14% 11% 6% âˆ« 1664 âˆ«
14 MadHat_Sam 2136â—† 215 21% 16% 8% 9% 10% 15% 18% âˆ« 1678 âˆ«
25 sticks&stones 1547â—† 215 24% 9% 12% 22% 12% 9% 10% âˆ« 1781 âˆ«
1 Zosod 4049â—† 215 23% 19% 11% 14% 13% 9% 8% âˆ« 1797 âˆ«
17 bcmatteagles 2041â—† 215 24% 15% 19% 16% 8% 8% 8% âˆ« 2096 âˆ«
11 fish28 2563â—† 215 15% 23% 16% 8% 14% 12% 10% âˆ« 2196 âˆ«
16 Hart 2084â—† 215 22% 18% 14% 13% 18% 9% 3% âˆ« 2436 âˆ«
9 wishbone 2656â—† 215 24% 18% 16% 9% 16% 12% 4% âˆ« 2487 âˆ«
13 seï¿½kin 2217â—† 215 18% 20% 12% 6% 18% 6% 18% âˆ« 2624 âˆ«
19 Phoenix37 2011â—† 215 30% 12% 11% 9% 9% 10% 15% âˆ« 2834 âˆ«
5 SodaPop 2948â—† 215 28% 12% 19% 13% 12% 4% 9% âˆ« 2912 âˆ«
15 uukrul 2115â—† 215 26% 19% 19% 9% 12% 9% 3% âˆ« 3641 âˆ«
24 DiceLord 1551â—† 215 24% 22% 14% 15% 10% 10% 2% âˆ« 3738 âˆ«
18 Vermont 2031â—† 215 27% 19% 19% 9% 6% 8% 8% âˆ« 3762 âˆ«
6 kissygirl 2794â—† 215 20% 25% 17% 14% 8% 7% 7% âˆ« 3766 âˆ«
21 Grisu 1916â—† 215 23% 25% 16% 5% 8% 8% 11% âˆ« 4452 âˆ«

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Player J sounds like the worst type of player to me. More worried about getting points than winning first place.

*bows to Player J's brilliance*

Wasn't Player J the one who made a huge thread and stated that first place gets too many points?

If Player J is brilliant, then that makes Stoudemire an unrecognized genius. Sorry Player J, if you are emulating Stoudemire, you only deserve utter banishment.

Please remind everyone what Stoudemire's experiment was. I don't think Player J was around when Stoudemire played.

skrumgaer:

"Under the current flag rules, you don't have to call for second"

True - I never said that wasn't the case. Calling for second, though, invariably produces better results, so it's more likely Player J did that (or will do that, after reading this post).

"The equal division of the 100-70-etc. is under the laws of probability. "

Explain to me how this assumption makes any sense given the circumstances. I'm an actuary - feel free to hit me with arguments based on advanced statistics.

azala:

I'm glad we both agree that what I said was true.

In regard to the laws of probability, as used by actuarians, when 215 games are played, and there is no division of labor among player J's helpers, there is no reason to expect any one of J's helpers to have a profile different from any other of J's helpers.

Q.E.D.

why is there an assumption that player J has helpers? he has the lowest first % in the top 25!

It would be interesting if everyone flagged early just to make Player J get 1st.

"there is no reason to expect any one of J's helpers to have a profile different from any other of J's helpers"

Like I said, in the 1-helper case, regardless of how they're distributed they should all do better than 16-12-15-15-15-14-13. The same principle is true as long as someone in the table is not in on the PGA. Those players not in on the PGA will rarely be allowed by the PGA to have significant influence on the game - making 16-12-15-15-15-14-13 unreasonably high. To assume that the expected value of profiles of PGA and non-PGA players are the same is ridiculous.

In the remaining case - when all the players left on the table are PGA toward J getting second place - from a behavioral standpoint all bets are off. Nobody really knows how they'll play, for example whether it's calculated to get some other player a lot of 1sts or 7ths or whatever (in which case, high TASM), whether it's sitting down with the intent of flagging immediately (how does that explain the low end of 00-30-10-09-13-14-20?), or whether they're playing a bunch of seemingly honest games with the condition that if J is in a two player match, he flags. You can say, technically, that the expected value for each player is 1/6 of the total - I didn't say you're wrong about that fact - but that doesn't mean you can derive reasonable conclusions from your test. The problem is that the list of possible motives simply generates too much variance from the expected profiles of the 6 other players.

That's why I say the value of the test is diluted by your assumption - the correlation between your calculated expected PGA'ers and the actual is uselessly low due to lack of information. About the PGA's - do we know what their secondary goals are? Do we know how they play amongst themselves? Making good progress on either of these questions is infinitely more beneficial to solving the problem than working with an assumption of perfect PGA-player equality.

On the other hand, it seems to me that you might be doing this test just for statistical fun, instead of deriving idiotic Leekstep-like conclusions from

(cont.)

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