Depressing title, but let's face facts, the Bulls are going to spend like a small market team. This doesn't preclude them from getting a couple superstars Miami style and ramping up spending. Even a small market team will spend to do that, but it does preclude them from winning Dallas Mavericks style by having one great player and then adding tons of expensive roleplayers around him.
To win as a small market team comes down to salary allocation. You need to stock your team with players that are underpaid relative to their worth in order to build a team that has more value than the ones with much higher salary. If you've read the book (or seen the movie) moneyball, a basketball solution is somewhat less likely to work easily.
Unlike baseball where your offensive stats should translate to any team, basketball requires too much teamwork to look at numbers in a vacuum. Your shooting percentages and other statistics rely significantly on your cast, scheme, and situation rather than simply the your own ability.
This doesn't mean that investing in some statisticians wouldn't help, but they would need proprietary data unavailable to us in order to operate in a useful manner. They'd need to track things like "help defends", "shot alters", "shot creates", "percentage on good looks", "percentage removing bailouts", "double teams drawn", "hockey assists", etc...
Since we don't have the type of data to truly analyze the impact of a player, I'm going to only note that investing in such a program would likely be quite helpful. Without having such data ourselves, the results are beyond the scope of what we can discuss here though.
With the tools we have, there are a few types of players that are always underpaid, and the Bulls need a plan to target these types of players.
The first, the NBA superstar. Everyone wants as many superstars as they can get and the maximum contract is one of the pieces of the CBA which destroys true competition for players. Max players end up having to agree to the same salary regardless of where they go and thus will always choose the city they like to play in most rather than having a true open competition for their bidding. The true superstar will also make 10 million or so less than he would on the open market.
Obviously, if you can get a superstar, you go for it. I don't think anyone is missing out on that point. Of course, not all max players are superstars, in fact most of them aren't. Some max players are guys who are overpaid (Joe Johnson) or worth about their contract (Carmelo Anthony / Chris Bosh perhaps) rather than being fabulously underpaid (Dwight Howard, LeBron James, Dwyane Wade, Kevin Durant, Derrick Rose, Chris Paul, etc.. )
The underpayment of superstars combined with a willingness to spend is what makes the Heat so deadly. LeBron and Wade combine to make probably 30 million per year less than they would on a true open market, throw in the fact that their owner is willing to spend a near unlimited amount of money, and the Heat are probably playing with a "fair market cap" of close to 120 million assuming they don't make any other really poor signings [which they generally won't because other players will go to Miami for a discount due to the great weather and likeliness of winning a title].
Assuming the Bulls will grab a superstar if they can, there isn't really much room to go in terms of discussing that. However, it's the reason why you take a chance on Dwight Howard even without a commitment. Though reading up on the news from what Orlando wants, I find it somewhat unlikely the Bulls could trade for Howard now anyway since Orlando wants lottery picks and prospects rather than veterans. The Bulls are in short supply of those things.
Speaking of lottery picks, we have group number two of our underpaid players. The rookie deals. When fighting out the CBA, one group of players isn't at the bargaining table. The ones who've yet to enter the league. In a move which should surprise no one, that group of players was absolutely screwed over by the owners and existing players. Rookies are locked into four year deals at bargain basement prices. It's common for a superstar rookie to provide 20+ million in value while making 5 million in salary.
Only the rookies that are drafted in the top 10 and are complete busts ever end up notably overpaid, because after the top 10 or so, they make role player eighth man type money anyway and by the end of the first round, their salary is in the 10th man range. Basically, if a draft pick is good enough to stick in the NBA, he's on a value contract.
So the second primary way to increase the value of your team is by making sure you have a steady influx of draft choices. Granted, too many rookies will leave your team without enough experience and most rookies are only underpaid by a couple million per year, so you aren't making up a huge gap.
In order to build a championship caliber team around draft choices you'll need to luck into a few that are superstar level and end up in that 10-15 million dollars per year underpaid range. That's a tricky thing to do as those types of rookies are typically only available at the very top of the draft in scenarios where teams are unlikely to give up their picks. This is the model the Oklahoma City Thunder are presently working under, and we'll see what happens when everyone is due an extension.
Will they be able to keep Durant, Westbrook, Harden, and Ibaka? Probably not if they care about staying under the luxury tax. Possibly so if they don't. Given how close they are to winning a title, maybe their owner will go all in to keep the core together, but will he also go all in to add pieces around it? Tough to say.
The final group of player that is likely underpaid is the guy who takes an obvious pay cut because he wants to play for a championship team. The ring chaser. The Bulls haven't had much luck pursuing ring chasers. Even when they landed Rip Hamilton last off-season, they certainly didn't get him at a discount. They paid full price, maybe more than full price, to add him to the team. I believe Chicago's lack of commitment to winning and status as 4th horse in the race will grant diminishing returns here. They'll still get better minimum players than Minnesota or Cleveland, but they won't compete for them with the teams they need to.
So what are the Bulls doing presently? Right now, they're in no man's land. They aren't pursuing the superstar (Dwight Howard), they aren't pursing potential high end rookies (trading Deng for Harrison Barnes), they aren't pursing draft picks for their expirings (the Gordon trade I noted that could have potentially given us a high lotto pick from Detroit). They're pursuing a conservative strategy aimed at keeping together a good team.
After watching their bench get decimated this off-season, the Bulls are clearly looking for a team that can make a deep playoff run while not breaking the bank. Increasing their odds of winning the title by 10-20% simply isn't worth 20 million dollars of profit to them. If the Bulls have a bunch of statisticians working for the team, I'd bet they aren't analyzing isolation stops, shot alters, and double teams drawn to evaluate underpaid players and instead are evaluating how much profit can increase per win or per round and weighing whether adding salary is a good fiscal investment rather than good basketball.
Even the Bulls best chance of winning a title under the salary cap won't be taken advantage of because it risks profit too much. If Dwight Howard is traded for and leaves then the Bulls will lose a ton of profit attempting to rebuild. If they trade Deng for a high lotto pick they'll lose profit in the next season or two as they rebuilt. Not only is the team unwilling to risk salary to improve, but it's unwilling to risk great to attempt to become elite because the profit margin between great and elite isn't that large while the risk of falling from great to good or average or bad is immobilizing.
In short, if the Bulls want to win while being financially prudent it will involve taking significant risks in terms of bringing in the types of players that are most likely to be underpaid. Thus far, the Bulls have been unwilling to take those risks.