The Wrights are an old and respectable family of Reno and under the lead of Orville Wright they managed to become a major family in the power structure of New Reno. Though the interference of Ethyl Wright's Temperance Union limited their involvement with the more lucrative operations of the city, namely gambling, prostitution, and drugs. However, as the Republic stepped up its attempts to expand north and the drought hit, 2241 proved to be a difficult year for the family. Profits from the sale of booze to the other families, their only major cash source, were falling, forcing the family to consider watering down the product to increase production and major expansion of the distribution. More importantly, Richard Wright, the youngest child of Ethyl and Orville, overdosed on Jet. The family did not believe in the story and had their suspicions that someone had a finger in Richard's death. Their suspicions were correct, as Louis Salvatore was attempting to turn them on the Mordinos - the source of all Jet in the city - to wipe out one family and weaken another, allowing him to make a bid for control of Reno.
After New California's expansion north, the Wrights successfully made their own bid for power, becoming one of the three major families in the city, alongside the Bishops and the Mordinos. As the Mordino power base crumbled due to the shrinking of the drug market and the emergence of the Jet antidote, the Wrights asserted their control. However, before they managed to entrench themselves, the power vacuum was filled by the Van Graffs. The two sides remained in a stalemate ever since, as the Bishops and the Republic waited for them to exhaust themselves and sweep in.
The Wrights are the only Reno family that are an actual family. All of its enforcers have blood ties to the family. The power is concentrated in the hands of true blood Wrights, who number around twenty.
The Wrights do not operate a casino like the other families. Instead, they focus on small-time gun running and the manufacture and distribution of alcohol and are the biggest supplier of booze and other vital beverages in the New Reno area. The combination of low numbers (they aren't as likely to hire outside contractors as the other families) and no stake in the lucrative gambling, drug, and prostitution operations made them the weakest of the four families in 2241.
On the other hand, smaller numbers make Wrights extremely loyal to each other and allow for keeping family members clean and away from recreational drugs. The definition of those does not encompass alcohol.
The Wrights contest the other four families and their attempts to take control of New Reno. They are the weakest of the four families and considered pitiable by other families. Still, the Wrights are a proud group. Their bonds go deep and are the reason why Wrights hate slavers unconditionally: They allegedly lost one of their daughters to slavers.