I'm generally going to follow the methods used in this thread over at Tom Tango and MGL's blog. I am also relying heavily on the player salary scale estimates here, which usually seems to work quite well.
John Fay reports that the Reds offered $2.7 million. In general, players make ~40% of their free agent value in their first season of arbitration eligibility, which means the Reds are claiming that he's got the value of a $6.75 million free agent. Based on Tango's salary scale, that pegs their valuation of Phillips as a 1.5 Win Above Replacement (WAR) player.
Phillips countered with $4.2 million, valuing him as equal to a $10.5 million free agent, which would pay for 2.5 WAR.
Phillips had what might have been his career year last season, but also might have been a breakout season. Hard to tell. Recent stats:
I'm going to be simple-headed here and project that Phillips will play at ~his 2-year average next season. This corresponds well to his Marcel and CHONE projections. So that puts him at ~48/2 = 24 RAR next season, or about 2.4 WAR on offense.
Defensively, the Fans see him as excellent, 15 FRAA via the Fans Scouting Report, or 1.5 Fielding Wins Above Average (FWAA). PMR has him at 5+35 = +40 runs over the past two years, or 2.0 FWAA per season. ZR, on the other hand, has him at "just" +4 runs over the past two years, or 0.2 FWAA/season. Using my (rather arbitrary) weighting system, I'd estimate his fielding as 0.375*2 + 0.375*0.2 + 0.25*1.5 = +1.2 FWAA per season.
He gets no bonus (nor penalty) for his defensive position, and I'll assume no aging for his age-27 year. That puts his estimated value at 2.4+1.2 = ~3.5 WAR next season. This puts his value at 40% of $15.4 million = $6.2 million for next season.
Maybe I'm vastly overvaluing him somehow, but these numbers indicate that even his counter offer is well below his actual arbitration value. I'm guessing that Phillips will win his case if he has good representation.
The Reds are offering Belisle $1.0 million. That means they're valuing him as a $1 million / 40% = $2.5 million = 0.5 WAR player.
Belisle countered with $1.65 million. That would assume that he's a $1.65 million / 40% = $4.1 million = ~1.0 WAR player.
Belisle's a little hard to project--especially in terms of his IP--because he just began serving as a full-time starter in the majors this past season. Here are his recent stats:
The thing that's really interesting about Belisle's 2007 season is that his FIP was so drastically different from his ERA. When putting together my writeup on him for the THT Preview (out in stores in February!), I noted that 6 of his 26 home runs allowed last season were for 3 or more runs (including 3 grand slams), which is unusually severe. Couple that with an 0.326 BABIP, and you've got trouble.
If we use standard RAR to estimate 2007 his value, that puts him at ~1.4 WAR. However, if we instead use FIP-Runs (described here), his value shoots up to a very respectable 2.6 WAR.
I think the safest thing would be to assume that he'll end up somewhere in between those figures next season--maybe 2.0 WAR? 2.0 WAR as a free agent is worth $8.8 million. So, $8.8 million * 40% (first year eligible for arbitration) puts him at $3.5 million in 2008.
Even if we just projected his 1.5 WAR value from last season into 2008, that puts his value at 40% of $6.6 million = $2.6 million in 2008. Again, I lean toward Belisle's argument, as even it seems to be undervaluing him.
Update: I discovered an error in my FIP-Runs calculation for Belisle, which cost him a half-win by that estimate. Sorry! :( The analysis still holds.
The fact that I'm estimating that both of these players will be underpaid in '08 raises some doubts about the validity of the assumption that players get 40% of their free agent value in their first year of arbitration eligibility. The only empirical work on this that I know of is this quick analysis based on Victor Wang's prospect value study, but by those data it was dead-on.
In Phillips' case, it looks like his defense is basically being ignored, and the Reds are a bit pessimistic about his offense. With Belisle, it looks like both the Reds and he are a) putting lots of weight on his scary 2007 ERA, and b) aren't fully appreciating how bad a replacement-level pitcher is when used as a starter.