The M61 (the gun the Phalanx is built around) apparently has a 80% dispersion of ~5 milliradians (see this amazing reddit post complaining about DCS - note that

The M61 (the gun the Phalanx is built around) apparently has a 80% dispersion of ~5 milliradians (see this amazing reddit post complaining about DCS - note that the evidence points to a range of values - I think 5 milliradians is a fair summary https://old.reddit.com/r/hoggit/comments/eyddn3/m61_and_gau8_dispersion_values_are_wrong_what_ive/ https://old.reddit.com/r/hoggit/comments/eyddn3/m61_and_gau8... ). At 1500m that works out to a 75cm radius (I'm pretty sure its radius...) disc. Assuming your firing at a missile flying right at you, and assuming a Cold War era threat (so say a Kh-22 fired from a Tu-22M), you're talking about a 92cm diameter target (46cm radius) that you're trying to hit. In reality, things are worse because in addition to dispersion, your actual point of aim of your stream of bullets will be effected by external factors (like wind). You can see how in the scenario layed out above, you do actually have what seems to be a reasonable chance of landing a few hits when you're spewing out hundreds of rounds within seconds. But you can also see how quickly the odds go to crap as you push the range further and further. I think that gets to the reality of what the "effective range" value is. It is a rule of thumb designed to help weapons officers quickly determine how best to react in a scenario. Remember that CIWS was envisioned to be deployed in a scenario where USN ships would be subject to saturation attacks by supersonic anti-ship missiles from multiple bearings and sources. Phalanx itself only has a magazine of ~1000 rounds, which is good for maybe only 10s of firing, so you really do need to conserve ammo.