First off, as a fan, lasts nights game was incredibly entertaining and one I will not soon forget. However as someone who focuses on in-game strategy as much as anyone there is a fairly large dent in my kitchen table that closely resembles my forehead. As I break down some decisions made by both coaching staffs I will start with this:

1. Do not judge any decision by the outcome of that decision

2. The luck surrounding every decision is much more impactful than the decisions themselves.

Lineups:

Before the first pitch was thrown Tuesday night Yost and Melvin already had their stamp on this game. While lineup optimization means very little in a one game playoff it is still annoying to say the least, and why do something wrong when you can do it right. The glaring problem with the A's lineup is Sam Fuld. Hitting one of your worst hitters in the second spot is ridiculous, even with the platoon split Fuld is one of the A's worst hitters hitting in a spot reserved for one of your best. On top of Fuld hitting second is the question whether he should be playing at all. Melvins options were

A) Fuld in LF, Moss DH, Dunn Bench

B) Fuld Bench, Moss LF, Dunn DH

While their are benefits of Fuld and his defense over Moss in the OF and Dunn in DH, their offense over Fulds defense would give the A's a slight advantage. Now having Dunn on the bench for a pinch hit late in the game is very much defensible however he never saw the field which makes the decision a little more puzzling.

While hitting Eric Hosmer in the 4th spot against a left handed Jon Lester is not optimal, the Royals just didn't have many great options. I would have liked to see Josh Willingham come into the lineup however in doing so you would force a sub par defender into the field just as playing Adam Dunn would have. The far bigger problem, but remember still a small factor, is hitting the speedy SS at the top of the lineup. Alcides Escobar projects as the Royals worst hitter in the lineup, how hitting him infront of your best hitters makes any sense to anyone is beyond me.

Bullpen Usage:

Allowing Jon Lester to face the Royals for a 3rd and 4th time. Although with a 4 run lead in the 8th, it shouldn't matter who is pitching, it is well documented that every pitcher gets worse and worse the more times they face opposing hitters. By this point in the game every reliever the A's have will be more effective than Jon Lester regardless of how Lester has pitched in the past. The second big mistake Melvin made was his handling of Fernando Abad. Melvin allowed Dan Otero to face Hosmer and Colon and then brought Abad in to face Gordon. The correct decision regardless of what happened would to allow Abad to face Hosmer, Colon and Gordon. The platoon advantage gained on Hosmer far outweighs the one lost on Colon who is a bad hitter regardless of who is throwing.

I had zero problem with the pulling of James Shields, the man he chose to replace him with however may have not been the correct choice. Ventura had thrown 73 pitches just a few days ago, and has very little history as a relief pitcher. If you ignore the result of this decision by Yost it is not nearly as bad however I would lean towards using one of their very effective relief pitchers in that spot.

Small Ball:

The sacrifice bunt is one of the most argued topics in the sabermetric and "old school" worlds, however there are misconceptions on both sides. The biggest point that is very rarely mentioned is that you should never do what the other team is expecting you to do. To simplify it as much as possible, if the defense is playing you to bunt, you swing, if they are playing you to swing away you bunt. Obviously there are exceptions depending on the hitter, but the main factors include, hitters ability, hitters speed/bunting skills, and defensive alignment. The Escobar sacrifice of Dyson to second is an example of a good batter to chose to bunt, however I would assume the A's were playing in at that point. The part that people seem not understand is when you have a runner like Dyson, who is stealing at a 84% clip, why would you not steal second rather than bunt him over giving up an out. This is the precise moment where the stolen base has its most value. over the course of a season, small ball strategies do not create a good offense but the Royals stealing 7 bases, while getting caught only once, helped them created almost a full run in a single game which is massive! (You can have your own opinion on the awkward 1st and 3rd play with 2 sub par base runners in Hosmer and Butler)

While all of these decisions by Melvin and Yost do not make a significant difference in the win expectancy of either team, when you add them all up they certainly did not help. I find it crazy that these men are actively reducing their teams chances of winning and no one is doing anything about it.

Never underestimate the amount of luck involved in this game

For more information regarding in game strategies, check out "The Book", http://www.insidethebook.com/ as it heavily influences most thoughts I ever have on game theory.