Right, just back from testing. Did them using the following settings:
Battlefield
10 stock
Unlimited Time
Wolf(me) Original costume
Bowser (lvl 3 CPU) Original Costume
Ganon (lvl 3 CPU) Original Costume
Pokeballs only on high
The purpose of these tests were to find if there was any relation between the two blue circlets on the field, and whether they affected Pokemon spawn. Three tests were done. The first battle went as follows:
NOTE: For ease of typing, I will use a legend and the shortened form of each Pokemon found. The code is:
Gr:Groudon
Ky: Kyogre
Mo: Moltres
En: Entei
Sui: Suicune
Ho: Ho-Oh
Lu: Luiga
Lat:Latias & Latios
Deo: Deoxys
Man: Manaphy
Mew: Mew
Cel: Celebi
Ji: Jirachi
To: Togepi
Met: Metagross
Me: Meowth
Mu: Munchlax
Gu: Gulpin
Pi: Piplup
Bo: Bonsly
We: Weavile
Tor: Torchic
Gar: Gardevoir
El: Electrode
Go: Goldeen
St: Staryu
Sn: Snorlax
Ch: Chikorita
Be: Bellossom
Wo: Wobbuffet
All:
Mu-Go-Sui-Go-To-To-We-En-Sn-Ch-Sn-Gu-We-Go-We-Go-Go-Mu-We-Gu-Be-Gu-Go-Me-Gu-To-Met-Be-Me-Sn-Lat-Be-Me-Gar-El-Cel-Sui-Wo-Be-Wo-
Gar-Mew-El-Gar-Lat-Go-We-Sn-Sn-Be-Go-Gu-Sn-Go-Bo-Be-Met-Lat-El-Be-Wo-We-Lat-Gu-To-To-Me-Wo-Wo-St-Tor-To-Sn-Lat-We-Tor-Me-Wo-Man-Ch-To-Tor-Pi-Pi
Legendary Specific: a-a-Sui-a-To-To-a-En-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-a-To-a-a-a-a-Lat-a-a-a-a-Cel-Sui-a-a-a-
a-Mew-a-a-Lat-a-a-a-a-a-a-a-a-a-a-a-a-Lat-a-a-a-a-Lat-a-To-To-a-a-a-a-a-To-a-Lat-a-a-a-a-Man-a-To-a-a-a
Notes:
-85 Pokeballs were thrown, 11 Legendaries( 18 including Togepi)
-Pretty sparse, legendary-wise. Mostly Lats and Togepis.
-My first Celebi, Mew, and Manaphy sighting! ^_^ Of course, the Mew gave me a sticker since I have all the other CDs >_> Manaphy worked, by the way.
-None of the Electrodes failed.
-I always threw the Pokeball in a standing position, straight down.
-I did not record which circlet the Pokeball was thrown on, nor which Pokeballs were hijacked by CPUs and thrown places other than the circlets. This may cause problems.
- A majority of the legendaries (including Celebi and Manaphy) were spawned on the left circlet. However, this may be due to me throwing a majority of the Pokeballs there.
The second test uses the exact same settings as before, but was more planned out. I recorded which circlet the ball was thrown, as well as if the ball was thrown somewhere other than the circlets, and alternated between circlets. The second test is as follows:
NOTE: Numbers will represent which circlet, if any, the ball was thrown on.
1-Left circlet
2- Right Circlet
3- Off (did not fall on circlet)
All:
Go3-Lat2-Pi1-El2-Me1-Ch2-Mo1-Sn2-Ky1-Be2-Mu1-Ch2-Pi3-Met2-Me1-Me2-Gu1-Pi2-Gu1-St2-Wo2-Sn1-Wo2-Lat1-St2-Ch1-Lat2-Go2
-Lat1-Me2-To1-Be1-Mu2-Ky1-Mo2-St1-Lat2-Tor1-Go3-Sn1-Lat2-St3-Go1-To2-Ga1-Deo2-To1-Gu2-El1(delayed)-Go2-Go1-Be2-El1-Ga3-Met1-Me2-Deo1
Legendary:
a-Lat2-a-a-a-a-Mo1-a-Ky1-a-a-a-a-a-a-a-a-a-a-a-a-a-a-Lat1-a-a-Lat2-a
-Lat1-a-To1-a-a-Ky1-Mo2-a-Lat2-a-a-a-Lat2-a-a-To2-a-Deo2-To1-a-a-a-a-a-a-a-a-a-Deo1
Area:
1

i1-Me1-Mo1-Ky1-Mu1-Me1-Gu1-Gu1-Sn1-Lat1-Ch1-Lat1-To1-Be1-Ky1-St1-Tor1-Sn1-Go1-Ga1-To1-El1(delayed)-Go1-El1-Met1-Deo1
2:Lat2-El2-Ch2-Sn2-Be2-Ch2-Met2-Me2-Pi2-St2-Wo2-Wo2-St2-Lat2-Go2-Me2-Mu2-Mo2-Lat2-Lat2-To2-Deo2-Gu2-Go2-Me2-Be2
3:Go3-Pi3-Go3-St3-Ga3
Area and Legendary:
1:Mo1-Ky1-Lat1-Lat1-To1-Ky1-To1-Deo1
2:Lat2-Lat2-Lat2-Lat2-To2-Deo2-Mo2
3:None
Notes:
-58 Pokeballs were thrown, 12 legendaries( 15 including Togepi)
- I did pretty well, defending the Pokeballs from the CPUs.
- Out of the 5 balls that were off, 2 were Goldeens.
- Latios seem more common in the right circlet.
The third test added the middle factor into the mix. The Pokeballs were thrown first on the right, then the middle, then the left, then middle, then right, etc.
NOTE:
Slightly altered code:
1: Left
2: Right
3: Middle
4: Off
All:
Mu4-En1-To3-Bo2-Wo3-Mu1-Lat3-Lat2-Go4-Ga3-Bo1-Wo3-Mew2(lololol)-Wo1-Go3-Met4-Pi2-Bo3-El1-Ga4-Pi3-Sn2-Wo3-Lu1-Bo3-Me2
-Go3-Me4-Ch4-Ga4-Tor1-Ky3-We2-Go3(hit)-Be4-Go4(hit)-Mu2-Ga2-Tor1-Lat3-St4-Me3-Ho3-Go1-Me3-We2-Sn3-Met1-We4-Mu4-Wo3-Go3
-Wo3-Gar1-To3-Mu1-St3-Wo4-Wo2-El3-Wo1-Mo3-Deo2-Lat3-Lat1-Lat3-Bel3-St3-En1-Me4-Gar3-To2-Ch3-Mu1-Wo3-Gar4-Be1-To3-Bo2-Wo3
-El1-Pi3-Mu2-El4(delay)-Go4-Lat3(hit)-Go1-Bo4(hit)-Pi3-Ch2-Gu3-We1-Gu3-To2-Mo3
Legendaries:
a-En1-To3-a-a-a-Lat3-Lat2-a-a-a-a-Mew2(lololol)-a-a-a-a-a-a-a-a-a-a-Lu1-a-a
-a-a-a-a-a-Ky3-a-a-a-a-a-a-a-Lat3-a-a-Ho3-a-a-a-a-a-a-a-a-a
-a-a-To3-a-a-a-a-a-a-Mo3-Deo2-Lat3-Lat1-Lat3-a-a-En1-a-a-To2-a-a-a-a-a-To3-a-a
-a-a-a-a-a-Lat3(hit)-a-aa-a-a-a-a-a-To2-Mo3
Area:
1:En1-Mu1-Bo1-Wo1-El1-Lu1-Tor1-Tor1-Go1-Met1-Gar1-Mu1-Wo1-Lat1-En1-Mu1-Be1-El1-Go1-We1
2:Bo2-Lat2-Mew2(lololol)-Pi2-Sn2-Me2-We2-Mu2-Ga2-We2-Wo2-Deo2-To2-Bo2-Mu2-Ch2-To2
3:To3-Wo3-Lat3-Ga3-Wo3-Go3-Bo3-Pi3-Wo3-Bo3-Go3-Ky3-Go3(hit)-Lat3-Me3-Ho3-Me3-Sn3-Wo3-Go3-Wo3-To3-St3-El3-Mo3-Lat3-Lat3-Bel3-St3-Gar3-Ch3-Wo3-To3-Wo3-Pi3-Lat3(hit)-Pi3-Gu3-Gu3-Mo3
4:Mu4-Go4-Met4-Ga4-Me4-Ch4-Ga4-Be4-Go4(hit)-St4-We4-Mu4-Wo4-Me4-Gar4-El4(delay)-Go4-Bo4(hit)
Area and Legendaries:
1:En1-Lu1-Lat1-En1
2:Lat2-Mew2(lololol)-Deo2-To2-To2
3:To3-Lat3-Ky3-Lat3-Ho3-To3-Mo3-Lat3-Lat3-To3-Lat3(hit)-Mo3
4:None
Notes:
-95 Pokeballs were thrown, 16 Legendaries( 21 including Togepi)
- I did a horrible job of controlling the match, as shown by the extremely large Off number of Pokeballs. And yet, none of them legendaries.
-(hit) simply means that the ball was used to hit an opponent (or in all cases, me

)
-Don't be fooled by the big list of middles; I'm comparing circlet to middle, not left to right to middle. The discrepancy was added to even out the chances of the left or right affecting the outcome.
-A lot more Latioses were found in the middle area.
- A Mew, yet again, appeared on the right Circlet.
Don't know how this might help, but use it at your whim. I'll think I'll conduct some more tests tomorrow. Oh, and yes, I am requesting to help you conduct research. Proper format, please!