Against this archetype, I don't recommend dropping Goblins into play. These decks just have so many ways to answer them ranging from: Golgari Charm, Toxic Deluge, Batterskull, Terminus, Supreme Verdict, Engineered Explosives and plenty of other cards. The Tendrils of Agony from the sideboard will get you a lot farther against these decks as you likely have enough time to build into a high storm-count.
In post-board games, it's better to slow the game down as that is what the opponent is trying to do as well. It's best to side out copies of Chrome Mox as it's inherently a faster card since its card disadvantage at the cost of the mana it provides – meaning over a longer game that its less valuable. It also doesn't help with the game plan of using Past in Flames as a means of card advantage. It's important to keep in mind that these decks are likely siding in Flusterstorm, which can be problematic, especially if you're going for the natural storm kill with Tendrils of Agony in hand. That said, if they don't have Flusterstorm, you've likely won the game.
A strong play against them is to Burning Wish for Past in Flames and make them counter it or lose. Meaning, try to build up "ritual-effects" over cards like Lion's Eye Diamond with cantrips and Infernal Tutor. Lion's Eye Diamond also has the downside of causing you to go all-in, if you're able to keep a few cards in hand after attempting to win, there's a good chance you'll have another shot in a few turns.
Bringing in Defense Grid is great against these decks, they don't have a fast clock and it will create a lot of awkward situations for them where they'll have to choose between casting spells or being able to interact with you. Against Shardless BUG or 4c Control, Defense Grid isn't as it's best as they have Thoughtseize or Hymn to Tourach and Abrupt Decay and/or Kolaghan's Command. That said, they do have Leovold, Emissary of Trest which can make things a little awkward. How Leovold, Emissary of Trest works against storm combo is that you target them with Tendrils of Agony and then Leovold, Emissary of Trest will trigger for each copy of storm. Often resulting in the opponent drawing into ten to twelve cards. This can become very difficult as they're prepared to fight back with either Flusterstorm or Mindbreak Trap. If you can't manage to get a Defense Grid into play, I highly recommend Empty the Warrens over using Tendrils of Agony. Alternatively, if you find that you don't like Defense Grid at all due to the amount of discard or their answers to permanents, I recommend bringing in Rending Volley.
For more information on how to beat Miracles, please read AJ Kerrigan's article linked below.
Against these control decks playing white, I bring in Rending Volley. These are specifically in the deck for this reason, without Counterbalance and Sensei's Divining Top, control decks have turned to Ethersworn Canonist to lock you out of the game. From there they try and protect it. Rending Volley is the most cost-efficient option in Grixis colors as an uncounterable answer. It can also answer Meddling Mage or even Stoneforge Mystic if need be! You can also use Burning Wish for Grapeshot, then play multiple artifacts to remove Ethersworn Canonist from the battlefield.
Copies of Ponder are usually sided out against Miracles as a way to find room, TES doesn't have a lot of "flex spots" and these control decks are known to bring in up to three copies of Pyroblast. This limits their effectiveness against TES. Sideboarding for this matchup can be difficult as there are so many cards we would like to bring in, but the entire deck feels useful in some way.
For more information on how to beat 4c Control & BUG Leovold, please read Alex Poling's article linked below.
08-06-2017 Albert Lindblom (alli) vs atdawn_theysleep with 4c Control (Round 4) on Magic Online (MTGO)
08-06-2017 Albert Lindblom (alli) vs Momsen with 4c Control (Round 3) on Magic Online (MTGO)
07-04-2017 Fighting Miracles in the Post-Top Era by AJ Kerrigan on theepicstorm.com
05-04-2017 Romario Neto vs Anuraag Das with UWr Stoneblade on Legacy Premier League
04-20-2017 TES Matchup Battles: 4c Control by Alex Poling on theepicstorm.com
04-17-2017 Nick Linder vs. Gabriel Meier with Miracles at Gameplace in Lucerne, Switzerland
03-18-2017 Bryant Cook vs. Joe Stempo with 4c Control at Eternal Extravaganza VI in Washington, DC
02-02-2017 TES Matchup Battles: Leovold Sultai by Alex Poling on theepicstorm.com
08-04-2016 Fighting the Miracles Menace by AJ Kerrigan on theepicstorm.com
04-22-2016 Steven Fierro vs. Fred Chen with Deathblade at Fire & Dice in Woodland Hills, CA
09-04-2015 Xantid Swarm Vs. The Metagame by Bryant Cook on theepicstorm.com
08-22-2015 Joey Valente vs. Corey Armstrong with Shardless BUG at Fire & Dice in Woodland Hills, CA
08-11-2015 Jordon Robbins vs. Jon Ha with Miracles at Ready to Play Trading Cards in Columbia, SC
01-10-2015 Bryant Cook vs. Zane Knapp with Esper Deathblade at StarCityGames: Philadelphia, PA
08-10-2014 Bryant Cook vs. Lloyd Kurth with Shardless BUG at StarCityGames: Syracuse, NY
06-13-2014 Bryant Cook vs. Reid Duke with Miracles at StarCityGames Invitational: Columbus, OH
08-27-2013 Bryant Cook vs. Harry Corvece with Shardless BUG at StarCityGames: Baltimore, MD
06-23-2013 Matthew Bevenour vs. Brad Nelson with Esper Deathblade at StarCityGames: Philadelphia, PA
03-17-2013 Bryant Cook vs. JD Nir with Esper Stoneblade at StarCityGames: Washington, DC
05-12-2012 Bryant Cook vs. Sam Roukas with BUG Control at Jupiter Games in Binghamton, NY
02-11-2012 Bryant Cook vs. Tariq White with Stoneblade at Jupiter Games in Binghamton, NY