New equation for threat

code/__HELPERS/maths.dm

@@ -13,6 +13,11 @@ var/list/sqrtTable = list(1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4,
                           8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10)
 */
 
+
+// Returns y so that y/x = a/b.
+#define RULE_OF_THREE(a, b, x) ((a*x)/b)
+#define tan(x) (sin(x)/cos(x))
+
 /proc/Atan2(x, y)
 	if (!x && !y)
 		return 0
@@ -35,6 +40,20 @@ proc/arctan(x)
 	else
 		return 0
 
+// -- Returns a Lorentz-distributed number.
+// -- The probability density function has centre x0 and width s.
+
+/proc/lorentz_distribution(var/x0, var/s)
+	var/x = rand()
+	var/y = s*tan_rad(PI*(x-0.5)) + x0
+	return y
+
+// -- Returns the Lorentz cummulative distribution of the real x.
+
+/proc/lorentz_cummulative_distribution(var/x, var/x0, var/s)
+	var/y = (1/PI)*ToRadians(arctan((x-x0)/s)) + 1/2
+	return y
+
 //Moved to macros.dm to reduce pure calling overhead, this was being called shitloads, like, most calls of all procs.
 /*
 /proc/Clamp(const/val, const/min, const/max)
@@ -191,6 +210,10 @@ proc/arctan(x)
 /proc/Tan(const/x) 
 	return sin(x) / cos(x)
 
+/proc/tan_rad(const/x) // This one assumes that x is in radians.
+	return Tan(ToDegrees(x))
+
+
 /proc/ToDegrees(const/radians)
 					// 180 / Pi
 	return radians * 57.2957795

code/datums/gamemode/dynamic/dynamic.dm

@@ -9,8 +9,47 @@ var/list/threat_by_job = list(
 	"Detective" = 3,
 )
 
+var/dynamic_curve_centre = 0
+var/dynamic_curve_width = 1.8
+
 #define BASE_SOLO_REFUND 10
 
+/proc/lorentz2threat(var/x)
+	var/y
+	switch (x)
+		// Left end of the tail, the lowest bound is -inf.
+		// 0 to 10.
+		if (-INFINITY to -20)
+			y = rand(0, 10)
+		// Porportional conversion from the lorentz variable to the threa.
+
+		// First, we use a rule of three to get a number from -40 to -30.
+		// Then we shift it by 50 to get a number from 10 to 20. 
+		// The same process is done for other intervalls.
+		if (-20 to -10)
+			y = RULE_OF_THREE(-40, -20, x) + 50
+		if (-10 to -5)
+			y = RULE_OF_THREE(-30, -10, x) + 50
+		if (-5 to -2.5)
+			y = RULE_OF_THREE(-20, -5, x) + 50
+		if (-2.5 to -0)
+			y = RULE_OF_THREE(-10, -2.5, x) + 50
+		if (0 to 2.5)
+			y = RULE_OF_THREE(10, 2.5, x) + 50
+		if (2.5 to 5)
+			y = RULE_OF_THREE(20, 5, x) + 50
+		if (5 to 10)
+			y = RULE_OF_THREE(30, 10, x) + 50
+		if (10 to 20)
+			y = RULE_OF_THREE(40, 20, x) + 50
+
+		// Right end of the tail, higher bound is +inf.
+
+		if (20 to INFINITY)
+			y = rand(90, 100)
+	
+	return y
+			
 /datum/gamemode/dynamic
 	name = "Dynamic Mode"
 
@@ -43,11 +82,19 @@ var/list/threat_by_job = list(
 	var/datum/stat/dynamic_mode/dynamic_stats = null
 	var/pop_last_updated = 0
 
+	var/relative_threat = 0 // Relative threat, Lorentz-distributed.
+	var/curve_centre_of_round = 0
+	var/curve_width_of_round = 1.8
+
+	var/peaceful_percentage = 50
+
 /datum/gamemode/dynamic/AdminPanelEntry()
 	var/dat = list()
 	dat += "Dynamic Mode <a href='?_src_=vars;Vars=\ref[src]'>\[VV\]</A><BR>"
 	dat += "Threat Level: <b>[threat_level]</b><br/>"
 	dat += "Threat to Spend: <b>[threat]</b> <a href='?_src_=holder;adjustthreat=1'>\[Adjust\]</A> <a href='?_src_=holder;threatlog=1'>\[View Log\]</a><br/>"
+	dat += "Parameters: centre = [curve_centre_of_round] ; width = [curve_width_of_round].<br/>"
+	dat += "<i>On average, <b>[peaceful_percentage]</b>% of the rounds are more peaceful.</i><br/>"
 	dat += "Executed rulesets: "
 	if (executed_rules.len > 0)
 		dat += "<br/>"
@@ -112,13 +159,30 @@ var/list/threat_by_job = list(
 	send2maindiscord("Dynamic mode threat: **[threat_level]**, rulesets: [jointext(rules, ", ")]")
 
 /datum/gamemode/dynamic/can_start()
-	threat_level = rand(1,100)*0.6 + rand(1,100)*0.4//https://docs.google.com/spreadsheets/d/1QLN_OBHqeL4cm9zTLEtxlnaJHHUu0IUPzPbsI-DFFmc/edit#gid=499381388
+
+	// Old equation.
+	//threat_level = rand(1,100)*0.6 + rand(1,100)*0.4//https://docs.google.com/spreadsheets/d/1QLN_OBHqeL4cm9zTLEtxlnaJHHUu0IUPzPbsI-DFFmc/edit#gid=499381388
+
+	// New equation : https://docs.google.com/spreadsheets/d/1qnQm5hDdwZoyVmBCtf6-jwwHKEaCnYa3ljmYPs7gkSE/edit#gid=0
+	relative_threat = lorentz_distribution(dynamic_curve_centre, dynamic_curve_width)
+	threat_level = lorentz2threat(relative_threat)
+	threat = round(threat, 0.1)
+	peaceful_percentage = round(lorentz_cummulative_distribution(relative_threat, curve_centre_of_round, curve_width_of_round), 0.01)*100
+
+	curve_centre_of_round = dynamic_curve_centre
+	curve_width_of_round = dynamic_curve_width
+
 	threat = threat_level
 	starting_threat = threat_level
+
 	latejoin_injection_cooldown = rand(330,510)
 	midround_injection_cooldown = rand(600,1050)
 	message_admins("Dynamic Mode initialized with a Threat Level of... <font size='8'>[threat_level]</font>!")
 	log_admin("Dynamic Mode initialized with a Threat Level of... [threat_level]!")
+
+	message_admins("Parameters were: centre = [curve_centre_of_round], width = [curve_width_of_round].")
+	log_admin("Parameters were: centre = [curve_centre_of_round], width = [curve_width_of_round].")
+
 	if (config.high_population_override)
 		message_admins("High Population Override is in effect! Threat Level will have more impact on which roles will appear, and player population less.")
 		log_admin("High Population Override is in effect! Threat Level will have more impact on which roles will appear, and player population less.")

code/modules/admin/admin.dm

@@ -687,6 +687,9 @@ var/global/floorIsLava = 0
 				for(var/datum/dynamic_ruleset/roundstart/rule in forced_roundstart_ruleset)
 					dat += {"<A href='?src=\ref[src];f_dynamic_roundstart_remove=\ref[rule]'>-> [rule.name] <-</A><br>"}
 				dat += "<A href='?src=\ref[src];f_dynamic_roundstart_clear=1'>(Clear Rulesets)</A><br>"
+			dat += "Parameters: <br/>"
+			dat += {"Curve centre: <A href='?src=\ref[src];f_dynamic_roundstart_centre=1'>-> [dynamic_curve_centre] <-</A><br>"}
+			dat += {"Curve width: <A href='?src=\ref[src];f_dynamic_roundstart_width=1'>-> [dynamic_curve_width] <-</A><br>"}
 		else
 			dat += "<A href='?src=\ref[src];f_dynamic_latejoin=1'>(Force Next Latejoin Ruleset)</A><br>"
 			if (ticker && ticker.mode && istype(ticker.mode,/datum/gamemode/dynamic))

code/modules/admin/topic.dm

@@ -1557,6 +1557,39 @@
 			mode.picking_specific_rule(midround_rules[added_rule],1)
 
 
+	else if(href_list["f_dynamic_roundstart_centre"])
+		if(!check_rights(R_ADMIN))
+			return
+
+		if(ticker && ticker.mode)
+			return alert(usr, "The game has already started.", null, null, null, null)
+		if(master_mode != "Dynamic Mode")
+			return alert(usr, "The game mode has to be Dynamic Mode!", null, null, null, null)
+
+		var/new_centre = input(usr,"Change the centre of the dynamic mode threat curve. A negative value will give a more peaceful round ; a positive value, a round with higher threat. Any number between -5 and +5 is allowed.", "Change curve centre", null) as num
+		if (new_centre < -5 || new_centre > 5)
+			return alert(usr, "Only values between -5 and +5 are allowed.", null, null, null, null)
+
+		log_admin("[key_name(usr)] changed the distribution curve center to [new_centre].")
+		message_admins("[key_name(usr)] changed the distribution curve center to [new_centre]", 1)
+		dynamic_curve_centre = new_centre
+
+	else if(href_list["f_dynamic_roundstart_width"])
+		if(!check_rights(R_ADMIN))
+			return
+
+		if(ticker && ticker.mode)
+			return alert(usr, "The game has already started.", null, null, null, null)
+		if(master_mode != "Dynamic Mode")
+			return alert(usr, "The game mode has to be Dynamic Mode!", null, null, null, null)
+
+		var/new_width = input(usr,"Change the width of the dynamic mode threat curve. A higher value will favour extreme rounds ; a lower value, a round closer to the average. Any Number between 0.5 and 4 are allowed.", "Change curve width", null) as num
+		if (new_width < 0.5 || new_width > 4)
+			return alert(usr, "Only values between 0.5 and +2.5 are allowed.", null, null, null, null)
+
+		log_admin("[key_name(usr)] changed the distribution curve width to [new_width].")
+		message_admins("[key_name(usr)] changed the distribution curve width to [new_width]", 1)
+		dynamic_curve_width = new_width
 
 	else if(href_list["c_mode2"])
 		if(!check_rights(R_ADMIN|R_SERVER))