What do people use as the value of runs gained/lost from an IF or OF Error, + play, or - play?

Honestly, I use something I call modified OPS to value players. Basically this all works by the assumption that a hit is equal value, whether you are taking it away from someone or getting it yourself.

+ Plays = add one more hit to their season total (turning an out into a hit)
- Plays = remove one hit from season total (turning a hit into an out)
Errors = remove one hit from season total (turning hit into an out - even in the OF most of these are 1 base, though more are 2 bases than in the infield)
SB = add one total base to season total (doesn't change avg or OBP, but does change slugging)
CS = turn one hit into an out

I then can figure out the appx value of all contributors at that position and baseline my player against them (since it's easier to find someone who can get 10 + plays at 1B than SS). Haven't broken it down by runs gained/lost, but the same thought process should basically applied. Turning a single into an out (defensively) should have the same value as turning an out into a single (offensively).

Are we talking in hindsight? Are we looking for how to evaluate a player's statistics after they have played or are we talking about evaluating players based on their ratings and expected performance? I am sure there is some fully involved formula or theory about how a great defensive play saves a certain amount of runs, but I don't know what the formula is. Also, I am curious what people think regarding turning hits into outs while on defense vs. turning outs into hits while on offense. I am sure some would argue they are equal. Others may take one or the other side of the discussion. I would be interested in hearing those arguments.

Outside of the draft, I have rarely been in a situation where the guy that overplays a defensive position, but isn't a great hitter AND the guy that underplays the defensive position, but is a decent hitter are both available at the same price at the same time. Typically, the guy that can fake it at the defensive position and hit for 750+ OPS will get snatched up in free agency before the Rule 5 draft. Whereas, the guy that will offer the opportunity for 15+ plus plays and 7 less errors than the average replacement player at the position [but OPS's .625] is still available after Rule 5 for cheap.

Regardless of what the argument is regarding who the more valuable player is, I am taking the least expensive player because usually the difference is close to negligible.

bripat, agreed. Realistically I just use this as a first-level thing. I don't want to go through and check every plus, minus, and error so I just assume that they're the most common variety (turning a hit into an out or vice versa). That's the same reason I assume every error is a 1 base error. I went through one season and checked and less than 10% of errors were 2 base errors. They exist but there's a balance between getting the exact perfect result and the amount of time I have to spend. I use the above as a quick and dirty way to assess values, not to get a 100% accurate result.

By the same note, getting a single and then being CS is probably better than just recording an out since you may have advanced runners. Similarly, I'd rather have my guy hit a double rather than get a single and then a SB. It's an imperfect method, but it works for me.