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With few exceptions, running backs generally score more fantasy points in wins than in losses.  For example, Adrian Peterson has averaged 22.2 FP/G over the last four years in wins, and 14.8 FP/G in losses, in a 0.5 PPR scoring system.  Those numbers rank Peterson in the top four in both categories, but obviously he's been much more valuable in wins.

Some players, however, have particularly extreme splits. As Jason Lisk points out, Alfred Morris is one of those players.  Since Morris isn't much of a receiver, he gets his value from carries and touchdowns, and both of those tend to be higher in wins. Over the past two seasons, Morris has averaged 17.1 FP/G in wins and 11.1 FP/G in losses. Marshawn Lynch is another player who is more valuable in wins: fortunately for him, those are more prevalent in Washington state than Washington, D.C. Since 2010, Lynch has averaged 17.3 FP/G in wins and 9.7 FP/G in losses.

So which running backs are most impacted by their team's fortunes? I looked at the top 50 running backs in Footballguys.com rankings, and then excluded rookies and others players with small sample sizes.  I was left with 37 running backs, and I calculated their FP/G (using 0.5 PPR) in wins and losses since 2010.  Here's how to read the table below. No running back fared so much better in wins relative to losses as Doug Martin.  The Tampa Bay back has played in seven wins and averaged 24.5 FP/G in those games, the highest average among the 37 running backs in this study.  Martin has played in 15 losses, and averaged just 12.1 FP/G in those games, the 10th best ranking. That's a difference of 12.4 (24.5 - 12.1) FP/G.

What can we take away from the above table?

• Martin has averaged 129 rushing yards, 39 receiving yards, and 1.0 touchdowns per game in wins, and just 67 rushing yards, 18 receiving yards, and 0.4 scores per game in losses. We're dealing with small sample sizes with Martin, of course: his 251-yard, 4-TD game against Oakland is one of just seven wins, so take those numbers with a grain of salt.  Martin is a good receiving back, and with a regime change in Tampa Bay, I'm not sure we can put too much faith in his historical averages.
• Jamaal Charles has the second most drastic split, and that might surprise you. Then again, Charles has averaged 40 receiving yards per game in wins and just 18.0 in losses. Part of the reason for the split: over half of Charles' losses came during the 2012 season, when the Chiefs quarterbacks were unable to do much of anything.
• DeMarco Murray, on the other hand, is a player whose split probably tells us something. The Cowboys are very quick to abandon the run when trailing, and that's a trend that's continued for a few years. Murray has averaged 17.3 rushes in wins but just 11.8 in losses. When healthy, Murray is a top RB1 for fantasy purposes, but there's always the risk that Jason Garrett and the offense goes pass-heavy if Dallas falls behind early.
• The Ravens don't necessarily have the same reputation as Dallas when it comes to abandoning the run, but Baltimore does have a tendency to be much more run-heavy in wins than in losses. Ray Rice has recorded 19.5 carries per game in wins and just 12.4 in losses over the last four years. Rice is a good receiving back, but he also has averaged more receiving yards per game in wins. The Ravens runner used to be a top fantasy back, but after a miserable 2013 season, Rice is more likely a flex play in 2014. When deciding whether to play him, you may want to check the Vegas spread.
• Chris Ivory has averaged more than twice as many fantasy points in wins than he has in losses. That trend should continue this year, as look for the Jets to give Chris Johnson the majority of snaps when New York is trailing. If the Jets are expected to win a game, Ivory is likely a solid fantasy player and could pick up 15 carries and goal-line touches: if the Jets are expected to lose, Ivory could wind up having no fantasy value that week.
• Ryan Mathews hasn't posted as severe a split as Ivory, but he's another player whose value is tied to his team's success.  When San Diego is losing, Danny Woodhead or Donald Brown may wind up on the field more than Mathews.

If you scroll to the bottom of the table, you'll notice that four running backs averaged more fantasy points in losses than in wins.  What's going on there?

• Trent Richardson was productive on a bad team in Cleveland in 2012, and terrible on a good team in 2013. As a result, his split is more about Richardon's season-to-season variation than anything else.
• Rashad Jennings has been a role player in Oakland and a third down back, as a result, he's seen more playing time in losses than in wins. The same goes for Giovani Bernard, but both players enter 2014 as their team's top running backs.
• As for LeVeon Bell? The Steelers big back is quietly productive in the passing game: he topped 60 receiving yards in two of the five Steelers losses in which he played, but maxed out at 52 yards in Steelers wins.  Bell also has scored more touchdowns in losses than in wins, although that's probably more fluky than anything.

As a general rule in guiding your "Who Do I Start" decisions, you want to break ties in favor of players on teams you expect to be victorious.  On average, those players will score more touchdowns, get more touchdowns, and gain more yards. Some players, though, are even more extreme than this general rule.  Players like Morris, Lynch, Murray, Rice, and Ivory are more likely to have their best games when their teams are successful.  If a team has another back on the roster who is more likely to see time when the team is trailing -- say, New England with Shane Vereen, San Diego with Woodhead, Philadelphia with Sproles, or the Jets with Johnson -- the pass-catching back may surprise with some of his best games when the team is trailing early.