{"text_format":"1","workbook":"xlsx","n_sheets":3,"sheets":["Levels","Interaction Grid","Interaction Probs"],"not_rendered":{"charts":0,"images":0,"macros":1,"external_links":0,"defined_names":0,"comments":0,"pivot_tables":0},"unopened":[],"bounds":{"document_bytes":16777216,"sheet_cells":100000,"rows_first":2000,"rows_last":500,"rows_between":2000,"halvings":0,"cell_chars":16384,"cell_head_chars":4096},"cells_cut":0,"cells_raw":0,"read":"whole","date_system":"1900"}

{"sheet":"Levels","index":0,"n_rows":9,"n_cols":9,"rows_kept":9,"cut":false,"hidden":false,"merged":[]}
[null,"Arsenal","Chelsea","Liverpool","ManCity","ManU","Southampton","Tottenham","WestHam"]
["initial level","l","m","h","l","m","l","h","h"]
["Prior of increasing",0.42799999999999999,0.92400000000000004,0.29799999999999999,0.90600000000000003,0.749,0.47699999999999998,0.41699999999999998,0.32800000000000001]
["Prior of decreasing",{"$f":"1-B3","v":0.57200000000000006},{"$f":"1-C3","v":7.5999999999999956E-2},0.70199999999999996,9.3999999999999972E-2,0.251,0.52300000000000002,0.58299999999999996,0.67199999999999993]
[]
["Prior data (1) or guess (0)",0,0,0,0,0,0,0,0]
[]
["Posterior increase",0.45538294945252478,0.92354710845770638,0.26992284461042942,0.90793891646380576,0.76941769308142138,0.46259485362279679,0.39680957033084724,0.30170861973108692]
["Posterior decrease",{"$f":"1-B8","v":0.54461705054747522},{"$f":"1-C8","v":7.6452891542293622E-2},0.73007715538957063,9.2061083536194244E-2,0.23058230691857862,0.53740514637720316,0.60319042966915282,0.69829138026891302]

{"sheet":"Interaction Grid","index":1,"n_rows":22,"n_cols":16,"rows_kept":22,"cut":false,"hidden":false,"merged":[]}
["Row effects column",{"$f":"Levels!B1","v":"Arsenal"},{"$f":"Levels!C1","v":"Chelsea"},{"$f":"Levels!D1","v":"Liverpool"},{"$f":"Levels!E1","v":"ManCity"},{"$f":"Levels!F1","v":"ManU"},{"$f":"Levels!G1","v":"Southampton"},{"$f":"Levels!H1","v":"Tottenham"},{"$f":"Levels!I1","v":"WestHam"},{"$f":"Levels!J1","v":0},{"$f":"Levels!K1","v":0},{"$f":"Levels!L1","v":0},{"$f":"Levels!M1","v":0},{"$f":"Levels!N1","v":0},{"$f":"Levels!O1","v":0},{"$f":"Levels!P1","v":0}]
[{"$f":"B1","v":"Arsenal"},null,1,1,1,1,1,1,1]
[{"$f":"C1","v":"Chelsea"},1,null,1,1,1,1,1,1]
[{"$f":"D1","v":"Liverpool"},1,1,null,1,1,1,1,1]
[{"$f":"E1","v":"ManCity"},1,1,1,null,1,1,1,1]
[{"$f":"F1","v":"ManU"},1,1,1,1,null,1,1,1]
[{"$f":"G1","v":"Southampton"},1,1,1,1,1,null,1,1]
[{"$f":"H1","v":"Tottenham"},1,1,1,1,1,1,null,1]
[{"$f":"I1","v":"WestHam"},1,1,1,1,1,1,1]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
[]
["Put a 1 in any of the interaction boxes - currently this is top down predation and competition only - but it doesn't need to be"]

{"sheet":"Interaction Probs","index":2,"n_rows":43,"n_cols":15,"rows_kept":43,"cut":false,"hidden":false,"merged":[]}
["Prob of column increasing given row is increasing",{"$f":"'Interaction Grid'!B1","v":"Arsenal"},{"$f":"'Interaction Grid'!C1","v":"Chelsea"},{"$f":"'Interaction Grid'!D1","v":"Liverpool"},{"$f":"'Interaction Grid'!E1","v":"ManCity"},{"$f":"'Interaction Grid'!F1","v":"ManU"},{"$f":"'Interaction Grid'!G1","v":"Southampton"},{"$f":"'Interaction Grid'!H1","v":"Tottenham"},{"$f":"'Interaction Grid'!I1","v":"WestHam"},{"$f":"'Interaction Grid'!J1","v":0},{"$f":"'Interaction Grid'!K1","v":0},{"$f":"'Interaction Grid'!L1","v":0},{"$f":"'Interaction Grid'!M1","v":0},{"$f":"'Interaction Grid'!N1","v":0},{"$f":"'Interaction Grid'!O1","v":0}]
[{"$f":"'Interaction Grid'!A2","v":"Arsenal"},null,0.45,0.2,0.45,0.2,0.2,0.2,0.2,0.5]
[{"$f":"'Interaction Grid'!A3","v":"Chelsea"},0.5,null,0.2,0.5,0.3,0.2,0.2,0.2,0.4]
[{"$f":"'Interaction Grid'!A4","v":"Liverpool"},0.2,0.45,null,0.45,0.25,0.2,0.2,0.2,0.3]
[{"$f":"'Interaction Grid'!A5","v":"ManCity"},0.5,0.45,0.5,null,0.5,0.5,0.5,0.5,0.3]
[{"$f":"'Interaction Grid'!A6","v":"ManU"},0.2,0.45,0.2,0.45,null,0.2,0.2,0.2,0.3]
[{"$f":"'Interaction Grid'!A7","v":"Southampton"},0.2,0.45,0.2,0.45,0.2,null,0.2,0.2,0.4]
[{"$f":"'Interaction Grid'!A8","v":"Tottenham"},0.2,0.45,0.2,0.45,0.2,0.2,null,0.2,0.4]
[{"$f":"'Interaction Grid'!A9","v":"WestHam"},0.2,0.45,0.2,0.45,0.2,0.2,0.2,null,0.4]
[{"$f":"'Interaction Grid'!A10","v":0},0.5,0.6,0.6,0.6,0.3,0.2,0.3,0.2]
["Some of this is automated - but can be manually overridden. If shaded grey, then there is no need to fill in, as not part of interaction"]
["Prop of column decreasing given row is increasing",{"$f":"B1","v":"Arsenal"},{"$f":"C1","v":"Chelsea"},"Liverpool","ManCity","ManU","Southampton","Tottenham","WestHam",0]
[{"$f":"A2","v":"Arsenal"},{"$f":"1-B2","v":1},{"$f":"1-C2","v":0.55000000000000004},0.8,0.55000000000000004,0.8,0.8,0.8,0.8,0.5]
[{"$f":"A3","v":"Chelsea"},{"$f":"1-B3","v":0.5},1,0.8,0.5,0.7,0.8,0.8,0.8,0.6]
["Liverpool",0.8,0.55000000000000004,1,0.55000000000000004,0.75,0.8,0.8,0.8,0.7]
["ManCity",0.5,0.55000000000000004,0.5,1,0.5,0.5,0.5,0.5,0.7]
["ManU",0.8,0.55000000000000004,0.8,0.55000000000000004,1,0.8,0.8,0.8,0.7]
["Southampton",0.8,0.55000000000000004,0.8,0.55000000000000004,0.8,1,0.8,0.8,0.6]
["Tottenham",0.8,0.55000000000000004,0.8,0.55000000000000004,0.8,0.8,1,0.8,0.6]
["WestHam",0.8,0.55000000000000004,0.8,0.55000000000000004,0.8,0.8,0.8,1,0.6]
[0,0.5,0.4,0.4,0.4,0.7,0.8,0.7,0.8,1]
[]
["Prob of column increasing given row is decreasing",{"$f":"B12","v":"Arsenal"},{"$f":"C12","v":"Chelsea"},"Liverpool","ManCity","ManU","Southampton","Tottenham","WestHam",0]
[{"$f":"A13","v":"Arsenal"},{"$f":"1-B2","v":1},{"$f":"1-C2","v":0.55000000000000004},0.8,0.55000000000000004,0.8,0.8,0.8,0.8,0.5]
[{"$f":"A14","v":"Chelsea"},{"$f":"1-B3","v":0.5},1,0.8,0.5,0.7,0.8,0.8,0.8,0.6]
["Liverpool",0.8,0.55000000000000004,1,0.55000000000000004,0.75,0.8,0.8,0.8,0.7]
["ManCity",0.5,0.55000000000000004,0.5,1,0.5,0.5,0.5,0.5,0.7]
["ManU",0.8,0.55000000000000004,0.8,0.55000000000000004,1,0.8,0.8,{"$f":"1-I6","v":0.8},0.7]
["Southampton",0.8,0.55000000000000004,0.8,0.55000000000000004,0.8,1,0.8,{"$f":"1-I7","v":0.8},0.6]
["Tottenham",0.8,0.55000000000000004,0.8,0.55000000000000004,0.8,0.8,1,0.8,0.6]
["WestHam",0.8,0.55000000000000004,0.8,0.55000000000000004,0.8,0.8,0.8,1,0.6]
[0,0.5,0.4,0.4,0.4,0.7,0.8,0.7,0.8,1]
[]
["Prob of column decreasing given row is decreasing",{"$f":"B23","v":"Arsenal"},{"$f":"C23","v":"Chelsea"},"Liverpool","ManCity","ManU","Southampton","Tottenham","WestHam",0]
[{"$f":"A24","v":"Arsenal"},{"$f":"1-B13","v":0},{"$f":"1-C13","v":0.44999999999999996},0.19999999999999996,0.44999999999999996,0.19999999999999996,0.19999999999999996,0.19999999999999996,0.19999999999999996,0.5]
[{"$f":"A25","v":"Chelsea"},{"$f":"1-B14","v":0.5},0,0.19999999999999996,0.5,0.30000000000000004,0.19999999999999996,0.19999999999999996,0.19999999999999996,0.4]
["Liverpool",0.19999999999999996,0.44999999999999996,0,0.44999999999999996,0.25,0.19999999999999996,0.19999999999999996,0.19999999999999996,0.30000000000000004]
["ManCity",0.5,0.44999999999999996,0.5,0,0.5,0.5,0.5,0.5,0.30000000000000004]
["ManU",0.19999999999999996,0.44999999999999996,0.19999999999999996,0.44999999999999996,0,0.19999999999999996,0.19999999999999996,0.19999999999999996,0.30000000000000004]
["Southampton",0.19999999999999996,0.44999999999999996,0.19999999999999996,0.44999999999999996,0.19999999999999996,0,0.19999999999999996,0.19999999999999996,0.4]
["Tottenham",0.19999999999999996,0.44999999999999996,0.19999999999999996,0.44999999999999996,0.19999999999999996,0.19999999999999996,0,0.19999999999999996,0.4]
["WestHam",0.19999999999999996,0.44999999999999996,0.19999999999999996,0.44999999999999996,0.19999999999999996,0.19999999999999996,0.19999999999999996,0,0.4]
[0,0.5,0.6,0.6,0.6,0.30000000000000004,0.19999999999999996,0.30000000000000004,0.19999999999999996,0]