How can I get S?

I took a peek at the game and while we don't know the exact statistics and algorithms that form the ranking, some of the following may have played a part.

Relic shield charges every 40 seconds, and you start with 2 charges. Considering starting at 2 minutes you use both charges, and then use a charge every 40 seconds, in an 18 minute long game you should have had 26 minions - that's without upgrading the item. When you upgrade to Targon's Brace, you get recharge every 30 seconds, and when you upgrade to FOTM, you get recharge every 20 seconds. This all taken into consideration your CS does look quite low for playing a tank support that's utilizing the gold-share passive of the item you chose to buy. This is also hurting your game as your gold is a good 3-4 k (almost 60-80%) lower than the rest of your team's gold - support items are cheaper but you're going a tank build - meaning you need as much gold as you can get.

You didn't do a whole lot of Turret damage. I know that you're the support, but you only did around 600 damage to turrets/objectives in the game - and it looks like that may be all to turrets. Especially as a tank support you gotta get in there and make sure you're dealing damage to the turret with your ADC - since you're melee you'll be focused giving your ADC time to back off the turret - which lets them get a couple extra AAs in before they back off.

Even considering the fact you didn't have a sightstone, your ward placement is slightly low. You didn't buy any vision wards (control wards), and you only placed 7 trinket wards in an 18 minute long game. Like the Relic Shield, the yellow trinket loses its value quickly if you let it sit on full charge for long periods of time - you can keep a charge for a pinch but always make sure you aren't sitting on full charges without good reason.

You took barely more damage than Jinx, even though your max health was likely greater than hers. As the tank support, you should be trying to get the enemy team to focus you. I know you can't control the ADC's pathing, decisions, etc. but there's ways to get them to focus you instead of the ADC. Run towards them slightly so you're easier to hit than the ADC. Do something to ensure that your ADC is taking as little damage as possible both from champions and minions.

Around 7 minutes in, Jax ganked for you and him and Jinx killed both the enemy laners. That should've been a very easy tower if you all three were there (barring some info I'm not seeing on the match history), but for some reason the bottom tower didn't fall until 11 minutes in. I'm not sure if you'd backed or what, but trying to get first turret as early as possible will help greatly.

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To be quite honest, it's extremely likely that not all of what I've said applies to the ranking system of A/S/S+/etc. but in my opinion it's all still some decent advice to think about. Hopefully you can get that S next time :P

If you are playing support, you will likely be graded on your vision score or number of wards placed. I make this assumption because I have played a LOT of support games. Even when my KDA is not that great, I am still able to get S's pretty easy in games where I am able to ward alot.

Since the game is only 18 minutes long though, It is hard to tell. It could also be comparing your CS to every other Nautilus player.