Boosting will cause the $2$ seed to always bust

Once again, there are four teams remaining in a bracket: the $1$-seed, the $2$-seed, the $3$-seed, and the $4$-seed. In the first round, the $1$-seed faces the $4$-seed, while the $2$-seed faces the $3$-seed. The winners of these two matches then face each other in the regional final.

Also, each team possesses a “power index” equal to $5$ minus that team’s seed. In other words:

• The $1$-seed has a power index of $4.$
• The $2$-seed has a power index of $3.$
• The $3$-seed has a power index of $2.$
• The $4$-seed has a power index of $1.$

In any given matchup, the team with the greater power index would emerge victorious. However, March Madness fans love to root for the underdog. As a result, the team with the lower power index gets an effective “boost” $B,$ where $B$ is some positive non-integer. For example, $B$ could be $0.5$, $133.7,$ or $2\pi,$ but not $1$ or $42.$

As an illustration, consider the matchup between the $2$- and $3$-seeds. The favored $2$-seed has a power index of $3,$ while the underdog $3$-seed has a power index of $2+B.$ When $B$ is greater than $1,$ the $3$-seed will defeat the $2$-seed in an upset.

Depending on the value of $B$, different teams will win the tournament. Of the four teams, how many can never win, regardless of the value of $B$?

As shown in the prompt, if $B \lt 1$ then $2$ will beat $3$ in the first round. On the other side of the bracket, $1$ will beat $4,$ since $4 \gt B+1$ in this case, so in the final round we have $1$ beating $2$ since again $4 \gt 3 + B$ when $B \lt 1.$ So, since whenever $B \lt 1,$ $1$ will win the championship. On the other hand, whenever $B \gt 1$, $2$ will lose to $3$ in the first round. Therefore, $2$ will never win the championship.

Whenever $B \in (2,3),$ $3$ will beat $1$ for the championship, since $2 + B \gt 4.$ Whenver $B \gt 3,$ $4$ will beat $1$ in the first round and then go on to beat $3$ for the championship. Thus, there are values of $B$ for which $1$, $3$ and $4$ will win the championship. So out of the four remaining teams, only one of them (the $2$ seed) will never win.