Is there a highest (and lowest) possible WAR for a baseball player?

Do you mean theoretically or in practice? That is, can I imagine a pitcher that strikes out every hitter of every start? Or, conversely, one that never retires a batter but somehow is allowed to continue to pitch?

In practice they range from slightly negative to 8-ish being MVP-level. Anything over 10 is an all-time-great season.

i mean in theory (IOW mathematically)

There is no upper or lower limit, theoretically. (A batter who hits a home run every time up on a team that never records an out could record an infinite WAR. Likewise, two pitchers who never get tired and never allow a hit could run up an infinite pitching WAR in a single game. In the meantime, the pitcher facing the perfect batter could run up an infinite negative WAR and the batters facing the two perfect pitchers could also run up infinite negative WARs.)

Another question: does the quality of the pitcher’s team make a difference in the calculation? A team with a very bad offense will not allow a pitcher to get many wins, no matter how good he is. A team that scores a moderate amount of runs would probably stand to benefit the most from a good pitcher.

No. The OP is asking about the sabermertric stat Wins Above Replacement, not the tradition win statistic. In recent years more and more people have dismissed wins as a useless statistic for pitchers for just the reason you gave.

While WAR is theoretically infinite in either direction, I suppose we could apply some plausibility limits and see what the numbers might look like then. A batter with 700 PA and 700 HR (and who’s also Ozzie Smith at SS and Rickie Henderson on the basepaths), for instance. Or a starting pitcher who gets his 5 innings every turn of the rotation, no matter what, and has an ERA of 20 (or whatever). Would have to guesstimate anyway, of course.

Well, we would also need to know league-average offense and park factors. I think there are some WAR calculators out there, but I can’t pull them up right now.

Also, why would being Rickey on the bases matter if he gets 700HR in 700PA? I don’t think fast home-run trots are in the calculation.

What would a positional player’s WAR be if he set MLB records in the relevant stats?

Well, it would depend on his position and the league average.

The 2011 wOBA equation is: wOBA = (0.69×uBB + 0.72×HBP + 0.89×1B + 1.26×2B + 1.60×3B + 2.08×HR + 0.25×SB -0.50×CS) / PA

So if you take the records for each you would have the wOBA for that player.

As I said, there are a few spreadsheet tools out there to convert this to WAR based on what position they play and what their defense looks like (Fangraphs uses UZR for defense, I believe).

You’d max out around 20 wins, I think.

Theoretically, he could do that and not have a very good WAR at all, if he was terrible enough at everything that wasn’t HR/Avg/whatever else we’re counting as relevant. And either way the actual number would have to be based on what the rest of the league did, what position he played, what his park was like, and so on. You’re more valuable hitting 75 home runs in a league where the second place guy hits 45 than a league where 25 other guys hit 60, for instance. I suppose you could calculate what a .440/74/192 etc. season would be worth in the current major league for a league average fielder/runner, in a neutral park, on a .500 team and at a certain position, but I don’t have the tools to do that.

It would be… quite high. Maybe this is the best way to look at this, to get an idea of what a really high number means: at the end of April in 2004, Barry Bonds was on pace for .472/71/155 with a .696 on-base and a 1.132 slugging (275 walks). Close enough, really. That month was worth 2.7 wins with the bat in 23 games, so over 162 that’s 19 wins. My initial guesstimate was 25 wins for the all-record guy, and I think that’s probably about right, if he sets records in fielding and baserunning and stuff.

I asked because QB passer rating is linked to single-season records. BTW, I forgot about the fact he’s compared to the league as a baseline.

Of course there has to be a logical upper limit as a team only plays so many games. If a team plays 162 games, the player’s WAR cannot, logically, be higher than 162 minus the replacement level of wins, which varies a little but is in the low 40s; even if the guy is out there by himself, pitching no-hitters without a defense and homering over and over every time he goes up and leading himself to 162 straight wins, he’s still just (162-replacement) WAR. If you calculate that a guy has 180 WAR in a 162-game season there is something wrong with your equations.

I imagine it’s possible WAR COULD return a value above 162, but that would be a failure in the system.