NOTE: In order for this article to make much sense, I strongly suggest reading my previous article, which covers the math and creation of Player Run Value (PRV).

Since my last article was somewhat theoretical, in its creation of Player Run Value, I thought it important to get more tangible and describe how PRV could be used to determine a player’s offensive value. The first thing to note is that PRV is not in terms of Plate Appearances, so we would expect players that play more often to have higher PRVs than those that play less. PRV assess a player’s total expected offensive contribution to their team, based on their batting statistics, namely walks, hit by pitch’s, and the various kinds of hits. For those with a deeper sabermetric knowledge, this statistic works like Wins Above Replacement (WAR) which tracks the total wins contribution of a player, not their contribution over a playing-time metric, like Plate Appearances, Innings Pitched ect. The league average PRV for non-pitchers in 2016 looks like this;

The league average PRV was 58 runs with a standard deviation of 51 runs. This is a pretty large variation and, considering more than half the league failed to register more than 1.5 Plate Appearances per game, that’s not really informative stuff for analyzing most players that we care about, in the same way you wouldn’t judge a player’s Batting Average based on only a few at bats. If we instead make a cut off at some arbitrary value, like 2 plate appearances per game, to select only what “everyday-type” players should be producing. At 2 PA per game a player would have amassed 324 PAs over the course of a season to qualify, and the average and standard deviation look like this;

Admittedly this suffers from selection bias, because bad players don’t get 324 PA in a season, only good players get that many, but there is a range of talent in everyday players and really what we want to know is what constitutes good players, so this works. The average “everyday” player is worth about 112 runs with a standard deviation of about 32 runs, this is much more useful in assessing everyday player’s value. Here are the best players in terms of offensive runs production in the 2016 season;

# | name | prv |

1 |
Mookie Betts |
183.3 |

2 |
Nolan Arenado |
178.4 |

3 |
Josh Donaldson |
177.9 |

4 |
Jose Altuve |
177.8 |

5 |
Freddie Freeman |
177.2 |

6 |
Kris Bryant |
176.3 |

7 |
Mike Trout |
174.7 |

8 |
Robinson Cano |
173.3 |

9 |
Miguel Cabrera |
173.1 |

10 |
Joey Votto |
172.7 |

None of those names are surprising; everyone on the list is a team centerpiece and are all certainly expected to be on that list. Ironically, the only name on that list that may not be familiar to every one is the guy who produced the most offense Mookie Betts. Betts had a breakout year for the Red Sox last year, was an All-Star, Gold Glover, Silver Slugger, and came in a close second in MVP voting, right behind some guy named Mike Trout, and is certainly a name to keep an eye on.

PRV is a good way to see what players produced the most offense in absolute terms, but what about putting them all on the same scale? Here we introduce PRV per PA or just PRV/PA. Here’s the averages league wide for non-pitchers;

Average: .184 Runs/PA Standard Deviation: .060 R/PA.

Now among qualified batters (PA>323);

Average: .210 STDV: .023

PRV/PA is an equalized version of the statistic and gives us a good idea of how many runs a player will generate per plate appearance. So in 2016, the average “everyday” player was worth about 1 run per roughly 5 plate appearances (5*.210=1.05 runs). Now, which players generated the most expected runs per plate appearance?

# | name | PRV | PRV/PA |

1 |
David Ortiz |
171 |
0.2739 |

2 |
Daniel Murphy |
156 |
0.2687 |

3 |
Trea Turner |
87 |
0.2678 |

4 |
Mike Trout |
175 |
0.2565 |

5 |
Nolan Arenado |
178 |
0.2563 |

6 |
Freddie Freeman |
177 |
0.2558 |

7 |
Joey Votto |
173 |
0.2551 |

8 |
Miguel Cabrera |
173 |
0.2550 |

9 |
Trevor Story |
106 |
0.2543 |

10 |
Josh Donaldson |
178 |
0.2540 |

Again, none of these names are very surprising, each of these players are known for their offensive prowess, one note would be that Trea Turner, just barely qualified with exactly 324 Plate Appearances. If we were to apply the same standard the MLB uses for the batting title (502 PA) we get a top 10 that looks like this;

# | name | PRV | PRV/PA |

1 |
David Ortiz |
171 |
0.2738 |

2 |
Daniel Murphy |
156 |
0.2687 |

3 |
Mike Trout |
175 |
0.2565 |

4 |
Nolan Arenado |
178 |
0.2563 |

5 |
Freddie Freeman |
177 |
0.2558 |

6 |
Joey Votto |
173 |
0.2551 |

7 |
Miguel Cabrera |
173 |
0.2550 |

8 |
Josh Donaldson |
178 |
0.2542 |

9 |
Charlie Blackmon |
163 |
0.2535 |

10 |
Kris Bryant |
176 |
0.2522 |

This highlights how impressive David Ortiz was at hitting, the man was playing in his last year before retirement in 2016, and still registered as the best hitter, in terms of run production per plate appearance, of anyone in the league. The top 4 are all more than 2 standard deviations away from the mean. In layman’s terms, if one standard deviation is statistically different from the average, two full standard deviations is really different. These batters are not simply a fluke but rather are really are just that good; while it certainly didn’t take the creation of an entirely new statistic to find this out, using PRV gives us a complete picture of these hitters. Looking at these numbers, each of these players are worth more than 1 run every 4 plate appearances, if you consider that 4 Plate Appearances is a pretty reasonable number per game, these players give their team a significantly better chance of winning by generating about 1 run per game on average. One other thing to note is that Betts just barely missed the top 10 coming in 11th place.

If we look at this at the team level, we need to recognize a nuance to how we interpret the number. For an individual player, their PRV is a measure of all offense generated, both hit and scored, since a team is a beneficiary of both ends, meaning every RBI is also a run scored, we need to look at the statistic a little differently. Team PRV doesn’t explicitly predict the number of runs scored, but instead measures the Run Value of an offense, so if two teams have the exact same number of hits+walks but one has more Home Runs and the other has more Singles, the Home Run hitting team would be worth more. Similarly a two teams with the exact same number of Hits+Walks but the team with more Walks and the other with more Singles, the team with more Singles would have a higher team PRV. This allows us to measure each offense in terms of their ability to generate offense but is not explicitly predicting runs scored. Here are the top 5 offensive teams by PRV

Team | Wins | Runs | PRV |

Red Sox |
93 |
878 |
1401.199 |

Rockies |
75 |
845 |
1356.649 |

Cubs |
103 |
808 |
1310.863 |

Cardinals |
86 |
779 |
1307.283 |

Diamondbacks |
69 |
752 |
1290.719 |

What is interesting about this data is that the Diamondbacks were among the best teams in terms of offensive potential, and yet were 11th in the league in actual runs scored, suggesting some significant under-performance. It’s also interesting to note that the Rockies and Diamondbacks, both sub .500 teams in 2016, have come out on fire in the 2017 season, posting the 2nd and 3rd most Wins in the NL by the All-Star break, both with offenses that largely remained intact over the off-season.

Here are the 5 worst PRV teams;

team | wins | runs | PRV |

Phillies |
71 |
610 |
1119.382 |

Padres |
68 |
686 |
1131.717 |

Athletics |
69 |
653 |
1162.693 |

Braves |
68 |
649 |
1164.673 |

Royals |
81 |
675 |
1179.921 |

No big surprises on this list, none of these teams were known as offensive powerhouses. The Royals, the only .500 team on this list are better known as a craftier team, using great base-running, defense and pitching to win games, not necessarily out-slugging their opponents.

Putting PRV in terms of Plate Appearances makes less sense on a team level; all teams have played 162 games and the better an offense is, the more plate appearances they will have by virtue of them not hitting into as many outs, and increasing their PA/inning ratio. Moreover not much changes in terms of rankings when looking at PRV/PA, other than the Cubs and Diamondbacks dropping out of the top 5 and the Tigers and O’s moving into the top 5 (the Cubs led the MLB in PA in 2016). Both the Tigers and O’s had less productive offenses in terms of run totals, meaning that we lose some important information by putting PRV in terms of PA for teams, so PRV by itself is really the way to go. It may also highlight that the O’s and Tigers tended to trade more outs for offense, thus reducing their Plate Appearances, relative to the Cubs and D’backs. This may have deeper implications as to what styles of of offenses are more effective at generating runs, teams with sluggers or teams with good plate discipline, but that’s an analysis for another time.

Finally, what makes PRV a better statistic for analyzing a player’s offensive value? First off, PRV, though derived from RBI and Runs Scored, uses the league average situation for hitting to determine run value. What I mean by this is that things like RBI’s and Runs Scored are largely dependent on where a player is batting in the order, and what specific hitters are hitting around them. For instance a player batting 4th in the order will likely be batting with more base runners on than a batter in the 1st spot, who starts every game with an At Bat with no one on, thus the batter in the 4th spot has a much greater chance for RBIs than the one in the 1st spot. This doesn’t make the 1st batter less valuable to that RBI though, in fact, both the 1st and 4th batters are equally responsible for that RBI, but all of the credit goes to the 4th batter. Similarly, the 1st hitter has a greater likelihood of being driven in because they are followed by the best hitters on the team, but that doesn’t mean that they are any more or less responsible for being driven in than the 4th hitter, yet they get full credit for a Run Scored. So by setting both these batters against the league average batting situation, we eliminate the situational dependency of the RBI and RS statistics, and get to the real value of these batters. For additional information on this check this article out. What PRV does is it allows us to determine the offensive value of a player that may be depressed if they play on a bad team, or inflated if they are on a good team, against the exact same standard of playing for a theoretical perfectly average team.

PRV is also a better statistic than, say, the traditional slash line of AVG/OBP/SLG because it makes the implied run value of these stats explicit. The slash line implies that Batting Average, On Base Percentage and Slugging Percentage statistics correlate to runs being scored, but leaves this connection up to the imagination of the viewer. For instance one person may think 10 additional points of OBP is worth 10 runs per season, and someone else may think it’s worth 50 runs per season, which can lead to wildly different interpretations of players, depending on the person (to be clear it is actually about 25 runs). Compare this to PRV where it is quite clear that each player’s PRV is explicitly worth X number of runs per season, so each additional point of PRV is worth an about 1 run.

In sum, using PRV as an individualized statistic is a great tool for analyzing a player’s offensive contribution. PRV is better than RBI or Runs Scored because it is not situationally dependent, instead using the league average situation as the basis for the Run Value of a player. PRV is also a better statistic than the traditional slash line of AVG/OBP/SLG because it is explicitly about runs generated, not implied offensive value. Also, by generating the weights of each batting outcome in a different manner than most other sabermetrics, PRV tends to be a better predictor of runs than those statistics. PRV is a great offensive metric because it measures the sum of a player’s contribution, independent of situational hitting, or other variables outside of a player’s control and ought to make it into the statistics repertoire of baseball fans and sabermetricians everywhere.

Let’s go Bucs.

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