Or you can look at the record because it reflects everything you just said and is ultimately what matters as it is objective.
No it isn't, because you have to subjectively judge what the record should have been, given the personnel on the roster. Even then, the estimate of what the team's record should have been is subjective, and varies depending on what the team's goal was for that season.
For example, the Bobcats are currently 19-61. Should Coach Dunlap be fired for this record? According to you, yes, this is absolute and a bad record equates to a bad coach. But the reality is that a judgement based purely on record depends on whether you think they have won more or less games than their talent level indicates. But given the Bobcats are rebuilding, the team's goal at the start of the year was almost certainly to improve the young players on the roster. When you factor this in, then you probably allow Dunlap some slack in the W column. However, even so, the final judgement on Dunlap also depends on whether he has done a good job of developing his young players, both through teaching them at training and by giving them minutes during games. Ultimately, the W column reflects his abilities as a game-day coach, and player development reflects his abilities as a teaching coach. A head coach should be good at both, and that's how Dunlap's season will be judged, not just his W-L record.
How do we apply this to Corbin? The first question, the season-long elephant in the room, about which we Jazzfanz have bickered with each other (and with ourselves) over the season, is what was the goal of the season, as set by management (i.e. Greg and KOC)? It either had to be "improve on last season and finish higher than the 8th seed" or "develop the young players, who cares about the W column". Given we traded for Mo and signed Foye, then kept both Jefferson and Millsap all season, I'm leaning to option (a), but whichever it was (or should have been), the fact we can only finish in the 8th seed at best right now is an indicator of failure - we are no better than last season, can only be worse, and have done very little to improve our youth either. And we can easily point to game-day failures on Ty's part to explain our appalling road record, such as our losses in Cleveland, Milwaukee, and Philadelphia, plus I'm sure there were others, I recall a post someone made that included a list of at least a half-dozen such losses, and I agreed with every one being on Ty's poor decision-making. So our record is less than expected, and we are at least 6 games shy in the W column thanks to our head coach - 6 wins which would give us 48 wins and the 6th seed right now, plus a shot at a 50-win season.
The second question is how is he as a development coach? There have been one or two things that indicate teaching has been happening in practice - Kanter stopped bringing the ball down after an o-board, and Burks became a PG, for example - but the court time of the young players has been too erratic for them to make any real strides. When they have played, their improvement has been evident, but too often has been followed by a 5-10-minute cameo appearance in subsequent games, when they have clearly earned more court time. Again, even allowing for the fact that the front office apparently did not make player development his priority this season, in my subjective view, Corbin did not do enough to develop the younger players in the team.
In summary, Corbin is a poor game-day coach, and a poor development coach, who has neither improved our standings in the present nor developed our youth for the future. He needs to be replaced before we waste another season.