ADC1115 Resolution question

Hi everyone,
I have a question regarding the resolution of the ADC1115. It is supposed to have 16Bit, or as I have heard 15Bit because one bit is used for something else. Now, I really don't care if I'd have 15 or 16, but using a linar potentionmeter at 5V input I only get a Max of 1600 on the output of the standard sketch using single ended input. Makes sense, as in the sketch is sais the gain is at 3mV/bit- so 1600 would make 16000,003= 4.8V.
But - at 15Bit on a +/-6V Base I would be expecting something like 32768/12= 2730Units/Volt. So at 5V I should get a fullscale of 4
2730= 10920. What am I getting wrong here?

I am a bit confused here...

Thanks for any input and here just if someone need it - the standard sketch:

#include <Wire.h>
#include <Adafruit_ADS1015.h>

// Adafruit_ADS1115 ads;  /* Use this for the 16-bit version */
Adafruit_ADS1015 ads;     /* Use thi for the 12-bit version */

void setup(void) 
{
  Serial.begin(9600);
  Serial.println("Hello!");
  
  Serial.println("Getting single-ended readings from AIN0..3");
  Serial.println("ADC Range: +/- 6.144V (1 bit = 3mV/ADS1015, 0.1875mV/ADS1115)");
  
  // The ADC input range (or gain) can be changed via the following
  // functions, but be careful never to exceed VDD +0.3V max, or to
  // exceed the upper and lower limits if you adjust the input range!
  // Setting these values incorrectly may destroy your ADC!
  //                                                                ADS1015  ADS1115
  //                                                                -------  -------
  // ads.setGain(GAIN_TWOTHIRDS);  // 2/3x gain +/- 6.144V  1 bit = 3mV      0.1875mV (default)
  // ads.setGain(GAIN_ONE);        // 1x gain   +/- 4.096V  1 bit = 2mV      0.125mV
  // ads.setGain(GAIN_TWO);        // 2x gain   +/- 2.048V  1 bit = 1mV      0.0625mV
  // ads.setGain(GAIN_FOUR);       // 4x gain   +/- 1.024V  1 bit = 0.5mV    0.03125mV
  // ads.setGain(GAIN_EIGHT);      // 8x gain   +/- 0.512V  1 bit = 0.25mV   0.015625mV
  // ads.setGain(GAIN_SIXTEEN);    // 16x gain  +/- 0.256V  1 bit = 0.125mV  0.0078125mV
  
  ads.begin();
}

void loop(void) 
{
  int16_t adc0, adc1, adc2, adc3;

  adc0 = ads.readADC_SingleEnded(0);
  adc1 = ads.readADC_SingleEnded(1);
  adc2 = ads.readADC_SingleEnded(2);
  adc3 = ads.readADC_SingleEnded(3);
  Serial.print("AIN0: "); Serial.println(adc0);
  Serial.print("AIN1: "); Serial.println(adc1);
  Serial.print("AIN2: "); Serial.println(adc2);
  Serial.print("AIN3: "); Serial.println(adc3);
  Serial.println(" ");
  
  delay(1000);
}

An ADS1115 is an A/D to read a voltage, not a ratio.
So it's not the best tool for a ratiometric pot.
Leo..

// Adafruit_ADS1115 ads;  /* Use this for the 16-bit version */
Adafruit_ADS1015 ads;     /* Use this for the 12-bit version  <<< you're set up for the 12 bit version*/

Try this:

Adafruit_ADS1115 ads;  /* Use this for the 16-bit version */
// Adafruit_ADS1015 ads;     /* Use this for the 12-bit version */