Rackets come in four flavors: Cash, Attack Boosts, Defensive Boosts, Job Boosts. Each Racket requires you invest Influence into it and then wait for a specified amount of time for the Racket to finish. Once the timer expires and the Racket is complete, you get back your Influence investment + the reward (cash or boost).
It's important to think of these Rackets as investments (rather than purchases) because you get 100% of your Influence back when you collect on the Racket. This is important because you only GAIN 1pt of Influence every hour. You don't get a refill on level ups like you do with Energy and Stamina.
So in other words, it would take you 24 real-time hours to GAIN 24 pts of Influence. So getting back your Influence investment by collecting is absolutely critical to being successful at Racketeering.
However, once a Racket is ready to collect, you have a very limited amount of time to collect on the racket before it is "busted" and you lose your Influence investment. Given the slow regen timer on Influence, the Influence loss from a "busted" job is much more hurtful than losing the cash or extra boost. 
Influence Skill Points
When you increase your Influence skill, you increase the amount of Influence you can "hold" at one time. The maximum amount you can you hold is 20% greater than the number of skill points you have invested. So if you have 20 Influence skill points, you can "hold" up to 24 Influence points at one time (24/20). However, just like an Energy Pack, you stop GAINING pts from the regen timer if your current Influence is greater than the amount of pts you have invested.
This means that with 20 skill points, the largest Racket you could invest in would have a 24 point cost. If the Racket you want to invest in has an Influence cost greater than that amount, then you'll need to increase the number of skill points. Otherwise, if it is equal to or less than 24, there is little reason to invest more skill points into Influence. This is critical because investing skill points above that number is wasteful and they could be better spent elsewhere.
Re-Investing Influence
The reason this is wasteful is because if you manage it correctly, you'll never exceed 24 pts. Lets say that the Racket you use most often requires 16 Influence. You would invest that 16 Influence into a Racket.
The regen timer ticks away gaining you additional Influence. When it reaches 16 again, you invest in a second Racket. Then you collect on your original Racket, gaining back the original 16 investment and immediately re-investing it back into a new Racket.
As long as your Rackets don't bust, your total amount of Influence invested in Rackets continues to increase. The only limitation is the total number of Rackets you have at the same time (based on the number of slots purchased - 20 max).
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