It is unlikely to be the coil.

Have you disassembled and cleaned the unit?

Also replace the sleeve with a new nylon one.

You can also jumper over the switches in that circuit in order to see "full power" vs. power potentially through dirty switches.

Coils generally don't go bad. What you have is insufficient power to the coil itself, or possibly a bad coil sleeve. If the coil goes bad it will be a dead short and blow fuses.

You can get an A 21-500 from Pinball Resource. It will be more powerful than an A 22-550 as it is a bigger gauge wire with fewer turns.

You can verify all the switches are making good contact by taking a resistance reading from the coil lug to the common wire (yellow or black probably) on the far side of them. But none of this matters if the stepper isn't cleaned and moving freely

In EMs, the coil doesn't advance the stepper; it should be done by the return spring. At least on Gottlieb games that was the case. It was done this way because a spring has a known, repeatable force whereas a coil force can vary quite a bit with line voltage.

You can observe this when you operate the unit by hand and watching the behavior as you release the coil plunger. If spring advances the unit cleanly, then you may not be getting the proper pulse to energize the coil. That could happen if the LOCK-IN circuit on the OUTHOLE relay wasn't keeping the OUTHOLE relay energized.

Some other possibilities:

- The plunger may be mushroomed at the end where it slams into the coil stop. Make sure there are no sharp edges there.

- The stepper gear may not be staying put as the advance solenoid fires. What should happen is that the toothed gear is held in place by a ratcheting mechanism to keep it from rotating backwards. When the solenoid fires, the advance lever reaches across a gear tooth to the far side of the tooth and the spring pulls it to the next position when the solenoid relaxes. If the latch holding the gear isn't adjusted properly the gear may be rotating backwards as the advance lever tries to slide over it. When this happens the advance lever doesn't catch the next gear tooth and can't advance the gear.

- The advance lever that grabs the next gear tooth may be worn to the point where it can't reliably grab the gear tooth.

The adjustment screw could also be out of alignment causing the stepper arm to not reach far enough to grab the next tooth

Went through getting a Big Deal up and running a few months back and had an issue with the same stepper.

What finally got it 90% of the way there - cleaning it up and lubing the contacts.
The final bit - replacing the ancient metal coil sleeve. Surprising at what a difference it made.

In case anything in there helps out - here's an old thread that I had running while getting the machine going.

Good luck - it's a pretty decent EM in my book. Broke 1,000,000 for the first time recently. Felt pretty good. Double and max that bonus, then chase the extra ball. Seemingly simple, but so challenging at times.

sounds like you have a problem with a score motor switch either being dirty or not making full contact.on your game the score motor switch that pulses the coil for the player unit is located on the 3rd switch stack furthest from the front of the machine.Wms actually labels it #2 even though it is in the 3rd position.the switch that needs to be adjusted /cleaned is the 2nd from the bottom of that stack.make sure you tighten the 2 screws on the stack before you make any adjustment.next clean the contacts on both switches.finally turn the score motor by hand to make sure the switches are in proper adjustment.as always make sure the power supply is disconnected before you start working on the game.that should do it for you.

My mistake. Forgot to paste it in.
https://pinside.com/pinball/forum/topic/williams-big-deal-1977-score-reels-not-resetting

With regards to the issue that I was having - I had taken the bakelite plate off the stepper, cleaned it up, lubed it, etc. Pulled springs, made sure things werent gummed up and put it back together. Things seemed to work by hand just fine, but the stepped wasn't advancing right. It would go from player 1 to 2 just fine, but then not be strong enough to go from 2 to 3 or 3 to 4. Replacing the 40 year old metal sleeve did the trick.

Quite possibly not related (I'm just some guy that got a single EM up and running a few months ago.) but... you mention that the coil moves slightly, but not enough to move the actuator.

The final issue I had involved a score reel that wasn't working right. The coil for it would move slightly, but not pull in the arm to ratchet the wheel up. Caught the behaviour with some slo mo on my phone.

Turned out to be a switch on the 100 point relay that wasn't clean enough. Wild ass guess, but maybe check the switch that send the signal to the stepper telling it to advance? And as I write that, I see belbs316 saying something similar, as well as telling you where it is. Check that video - if that looks like the behavior you're seeing, I'd bet that belbs316 has pointed you in the right direction.

I unscrew the switch stack since, as you have seen, it is hard to get at the switches while they are in place.
There is quite a bit of travel for the switch stack in the score motor so you don't have to be super fussy about the switch gaps.
Personally I clean switches with isopropyl alcohol and use the flexstone file as well.

Unscrew the stack and tape it together so none of the parts fall off the bottom end of the screws.

Best way to clean is with a carbon steel dremel brush but if you don't have access to one a file will work okay.

After taking it off and putting it back on you'll need to double check all the switches in the stack to make sure they're still gapped properly

Yeah, it's no big deal taking a switch stack out. Just keep everything together & clean contacts with a wire brush in your Dremel. If you don't have a Dremel & wire brush, then get one. NOTHING works better & the brush technique is gentler on the contacts than a file.