Mana is one of the two main resources in Magic, along with cards, and one of the most effective ways to win games of limited is to gain an advantage in this resource. Most games of limited have a fairly set pace in the early turns. Each player draws a card, plays a land, plays a spell, then passes. If you can be the first person to break this pace by playing two spells in a turn, you swing the tempo of the game in your favor, and your opponent is now a play behind. In a normal game of limited, this generally won't happen until a player hits five or six mana, as most spells in a normal draft deck will cost two or three. However, if you have cards that only cost one in your deck, you can make this kind of play as early as turn three or four and make it difficult for your opponent to recover from being behind.
Why don't we all just play one mana spells? Unfortunately, most one mana spells are bad. You don't actually gain a tempo advantage if your second spell is a Chaplain's Blessing. We have a certain standard our cards must meet to be worth playing in our deck. The cards we are looking for are specifically those which can trade for an opponent's card while gaining us a mana advantage. If we can cast Dead Weight on a Crow of Dark Tidings, we've gained a 3:1 mana advantage, meaning our opponent effectively wasted two of their mana. This is why I tend to like a card like Dead Weight more than a card like Throttle, which can almost never generate this much mana advantage and often is cast at a disadvantage. However, most people know that Dead Weight is a good card, so valuing it highly will not get us much of an edge. The edge comes from understanding the value of cheap cards that other people evaluate incorrectly. So what kinds of cards are these?
Combat tricks are some of the most frequently printed cheap cards, and also some of the most often misunderstood and misplayed. R&D prints both one and two mana tricks, and most players look at the cards as being interchangeable. They're both instants, they both make your creatures win combats, they're both cheap. But that last point is not as clear-cut as it seems. A combat trick that costs two is twice as expensive as a combat trick that costs one. If we go back to the situation we were trying to set up, where we cast two cards on turn three or four, a one mana trick allows us to play a second two drop on turn three or a second three drop on turn four. The two mana trick does not do this, it allows us to play a second two-drop on turn four, at which point two drops are very much starting to lose their value, and we cannot play two spells on turn three at all. The other problem with the two mana trick is that tricks often trade for two-drop creatures, and in this case we did not gain the mana advantage we were looking for. One mana tricks also leak a lot less information, as it is very suspicious to be two mana off of your curve. When we have five mana and just play a three drop and pass with three cards in hand, most aware opponents will play around tricks if they can afford to. In the same position if we play a four and pass it's much more reasonable that we might not have had a way to spend our last mana, and it may cost them too much to play around our trick, leading them to cast a removal spell into it or make a poor attack.
For these reasons, I evaluate the two different costs of tricks at a massively different rate. The good one mana tricks I take at about the C+ level, over replaceable creatures as long as I'm on track to hit a good creature count. The two mana tricks I take at the D+ level, below any card that I would be happy to maindeck, and often leave them out of my maindeck when I do end up with some. Some decks need tricks more than others, particularly high creature count aggressive decks that do not end up with removal, and in that kind of draft I will start to take two mana tricks, but I almost never take them in the first two packs of a draft. In formats or color combinations which don't have good one mana tricks, I stay away from playing the kinds of decks that normally want tricks, as the lack of truly cheap spells is a serious drawback to winning via mana advantage.
Most people can tell when a one mana aggressive creature is good. Something like Loam Lion is a blatantly good card and will be taken highly. The times when we can gain an advantage are when cards that are traditionally not very good, such as one mana 1/1s with keyword abilities, become good because of synergies. This most often comes in the form of an early play that can make a one drop more threatening, such as the Ordeals of Theros, the Ethereal Armor deck in triple Return to Ravnica, or the support mechanic in Oath of the Gatewatch. Most limited players completely ignore these bad-looking creatures and let them go around the table, leaving room for the players who see the support cards first to have some of the most ridiculous fast starts of the format.
On the other side of the aggression coin, we have creatures we can get at a discounted rate because they are very poor attackers. If we are able to build a deck which always wants to be blocking, we get to have a big board impact for our one mana. These are cards that the opponent will always eventually have to trade for a more expensive creature if they are the beatdown. This offers defensive decks great defensive speed, preventing them from taking damage in the early game. It also allows decks playing card draw or other forms of slow card advantage to quickly recover the tempo loss of those cards by rapidly deploying their now full hand. If we trade off our three drop and then on turn four have to cast Divination to find our next play, we will take a large chunk of damage and end up a turn behind in the pace of the game. However, if we can cast Divination and then drop a Typhoid Rats in the same turn, we keep pace with our opponent while getting ahead in cards. These cards often go very late in drafts, as many decks can't afford to play cards that aren't proactive. When we find these cards in a format, we can benefit from them being undervalued by building control decks that can utilize them.
Situational or Conditional Answers
Though most people are on the same page about Lightning Axe being a fantastic spell, R&D also prints cheap reactive cards that are considerably less glamorous, and we can make use of those as well. For a recent example, we can go back to Battle For Zendikar draft. Most players had Touch of the Void as the best red common. It was very consistent, always did what you wanted it to do, and played into several synergies in the block. But also at common in red was the card Outnumber, a card which players valued considerably less and often would leave in their sideboards because they were afraid of the situation where they didn't have enough creatures for it to kill their intended target. For the players who saw Outnumber going late, they were able to adjust by valuing creature count and token-making creatures more highly to make their Outnumbers into Lightning Bolts, and construct very powerful decks of 17-18 creatures and 2-3 Outnumber.
But your conditional answers don't need to be that strong to be worth playing. Some of my favorite cards to sideboard in limited are narrow one-mana answers. Essence Flux may not be a card you generally want to maindeck, but if an opponent shows you several expensive removal spells like Throttle and Sleep Paralysis, Essence Flux is now a counterspell that generates 4:1 mana advantage or better. When my draft is going well and my colors seem open, I often take high impact sideboard cards like this over maindeck playables. They will sometimes allow you to win games you would otherwise lose by providing big swings in mana, whereas a card like Lamplighter of Selhoff may be a better card to maindeck, but could be replaced with dozens of other cards without significantly affecting your chances of winning or losing most games. Having outs to doing something powerful is often better than having guarantees of doing something average.
Putting it All Together
The point of understanding how cheap spells function to swing games is to ultimately build better decks. The way we do this is by identifying an underdrafted cheap card and then favoring archetypes that can make use of it. For a fantastic example of this, we can look at Fabrizio Anteri's approach to GP Barcelona, in which he had a dominating performance playing a single archetype in both his sealed and two drafts. Fabrizio Anteri is one of the top limited GP players in the world right now, with six top eights and three wins in limited alone in the last three years, and he has often shown a fondness for cheap spells. In Barcelona, Anteri identified that other players were not valuing the one-mana white cards in the format very highly, specifically the commons Strength of Arms, which could generate a powerful combo kill with the common Uncaged Fury, and Thraben Inspector, which could combine with human synergies and pump effects to be much more effective than a usual 1/2 while replacing itself. In his first draft on day two, he exploited this weakness, drafting a heavily white deck with nine one cost spells. This was the one mana slot in his final deck:
With this start to his curve, Anteri was able to play multiple spells per turn early in every single game and crushed the draft. He then went on to draft RW again in the top eight and win the tournament, using the same strategy of highly valuing the one-mana combat tricks, despite RW not being generally considered a strong or synergistic archetype.
This is our goal when identifying the good cheap spells in a format, to find a hole in the conventional wisdom of the format where our understanding of mana advantage gives us the edge we need to win. First, identify the cheap cards in the set which are potentially high upside. Second, look for other cards in the set which could support an archetype around them or could be weak to them. Third, raise them in your pick orders and playtest your new strategy. If the format supports it, you will be rewarded with powerful tempo plays and the draft wins that go with them.