Several studies including one by Princeton University show a direct correlation between police staffing (number of officers) and the amount of crime.

A Camden study wrongly showed that reduced police funding reduced crime. But digging into the study, the reduced crime came from more police officers that were being paid less after the city broke the police union and changed the compensation and work rules. In essence when looked at in terms of boots on the ground, it in fact confirmed the Princeton study.

So, the greatest correlation is between "boots on the ground" and crime not police funding and crime. There are lots of ways to waste tax dollars even if they are spent on law enforcement.

Officers cost money, so there is also a direct but less significant correlation in absolute spending levels. However, as an example, the city of LA is increasing police officer compensation by $24K a year (that won't reduce crime, but it will increase police funding costs). However, if this higher rate of pay translates into attracting more and better police officers, that will translate into lower crime.

At a more anecdotal level, my brother substantially reduced crime by deploying police officers on the streets without cars as Mayor of Jersey City. Again, the more numerous visible presences of police officers empowered with the authority to stop crime worked dramatically. He used to say, it won't stop "crimes of passion", but it has a direct impact on "crimes of opportunity".

My nephew with an advanced degree in statistical analysis did a study on police departments and found that it is true funding alone is not a guarantee of lower crime... your point. Police departments can waste money like any other government bureaucracy.

But inadequate funding in a crime prone area is a guarantee of higher crime rates. Crime is a "job" and like every job/business, it comes with associated risks and rewards.

Increasing police presence increases the risk of being arrested and if the consequences are appropriate the "cost of crime" to the criminal. This tilts the risk reward equation and drives down crime rates. Each incremental police officer added to the streets on average is less effective than the previous one (but still has a marginal beneficial impact). Each police officer taken off the street produces a similar negative result. If your police department is overstaffed, you should have low crime and high costs, if your police department is understaffed you should have high crime and low costs. If it is just right, you should have what the community considers "acceptable crime" levels and "acceptable" costs.

Meanwhile, "catching" criminals is only half the answer, your criminal justice system must have an effective way to match the crime with a fair penalty to the thief. There are many other variables that impact crime rates, but it is simple not true that "boots on the ground" police officers combined with a justice system that imposes costs that fit the crime on the criminal doesn't lower crime.

Video games are not a good basis for measuring human behavior. The risks rewards of the game simply cannot be made to equate with real life.