**Net Win Values for Various Events**

The first set of numbers are for basic events: outs, singles, doubles, triples, home runs, and walks. The numbers for ‘singles’ here include ROE (reached on error) and ‘walks’ include hit-by-pitches:Basic Events

Runs/Game | HR | T | D | S/ROE | W/HBP | IW | Out | |

1921 - 2017 | 4.74 | 0.1429 | 0.0780 | 0.0597 | 0.0363 | 0.0311 | 0.0078 | -0.0233 |

since 2003 | 4.78 | 0.1384 | 0.0794 | 0.0594 | 0.0354 | 0.0292 | 0.0097 | -0.0232 |

Before tapering off somewhat over the last several years, run-scoring was at near-all-time highs for the past decade. In contrast, run-scoring was historically low in the 1960s and much lower than recent levels in the 1970s and 1980s. Hence, the results for the Retrosheet Era as a whole are associated with a lower average run-scoring environment (4.74 runs per 9 innings) than the results over the past decade (4.78 runs per 9 innings). The gap between these two time periods has closed quite a bit in recent years, however, as run scoring has declined considerably in recent seasons while the earliest seasons being added by Retrosheet are during the fairly high-scoring 1930's.

Because of this, positive offensive events – home runs, triples, etc. – are more valuable over the longer time period. What I find interesting, however, is that the win value of an out is remarkably similar in both columns of the above table. Thinking about it, this makes perfect sense, however. The number of outs per game doesn’t change with the run environment; only the number of non-outs changes.

Baseball events are more typically valued in terms of runs as opposed to wins. The next table compares win values from my work with linear weights run values. The Linear Weights Run Values here are taken from the

Event | HR | T | D | S/ROE | W/HBP | IW | Out |

Net Win Value | 0.1356 | 0.0742 | 0.0558 | 0.0356 | 0.0298 | 0.0094 | -0.0236 |

Linear Weight Value | 1.394 | 1.055 | 0.772 | 0.465 | 0.315 | 0.176 | -0.278 |

Runs per Win | 10.3 | 14.2 | 13.8 | 13.1 | 10.6 | 18.8 | 11.8 |

I think that two numbers in particular are worthy of comment here.

First, home runs are somewhat more valuable in terms of wins than in terms of runs. For example, the Linear Weights Run Values suggest that a single and a triple are worth more (1.52 runs) than a home run (1.39 runs), whereas the win values suggest just the opposite: the home run (0.1356 wins) is worth more than the combined win value of a single and a triple (0.0356 + 0.0742 = 0.1099 wins). The same is true of a home run vis-à-vis two doubles (run value of 1.54 runs vs. win value of 0.1117).

Why might this be? Well, first, I should acknowledge that it could just be a fluke of the data (although these specific relationships are true, as far as I can tell, for every league for which I have calculated Player won-lost records). More likely, I think there is something to this result. Specifically, I think the key is that a home run always generates at least one run, whereas, while, for example, a triple produces more than one run on average, there are cases where a team will fail to score any runs in an inning despite hitting a triple.

The key to winning baseball games is to score runs (and prevent the other team from scoring – this argument works exactly the same in that respect from a defensive standpoint). There are two factors which affect the number of runs scored: the expected number of runs scored, which is measured by the Linear Weights Run Value, and the probability of scoring one or more runs. A home run produces a higher probability of scoring (100%) than other types of hits and, hence, has a greater impact on winning, even controlling for the expected number of runs scored.

The other event which has markedly different run and win values is the intentional walk. Based on linear weights, an intentional walk is worth approximately 55% of an unintentional walk. The win value of an intentional walk, on the other hand, is only 31% of the value of an unintentional walk. While I should again acknowledge the possibility that this is a data fluke, I think that this suggests that major-league managers generally do a pretty decent job of issuing intentional walks appropriately and that Linear Weights run values likely overstate the true cost of intentional walks (and understate the strategic abilities of major-league managers).

Different types of outs have different win values. Ground balls, fly balls, and especially bunts, can lead to baserunner advancements, but ground balls can also lead to double plays. Net win values for batting out by the type of out are shown in the next table.Outs

Any Out | K | All BIP | Bunt | GB | FB | LD | |

1921 - 2017 | -0.0233 | -0.0214 | -0.0238 | -0.0168 | -0.0249 | -0.0224 | -0.0277 |

since 2003 | -0.0232 | -0.0217 | -0.0238 | -0.0186 | -0.0255 | -0.0220 | -0.0249 |

A few comments seem appropriate.

First, as noted above, the win value of an out is remarkably constant over time and across run-scoring environments. This is true across all types of outs shown here with the arguable exception of bunts.

Second, a strikeout is actually slightly less costly on average than an out on a ball-in-play, although the difference is fairly minor.

The most costly type of out is actually a line-drive out, since these practically never result in base advancement and can frequently lead to double plays.

The least costly type of out, on the other hand, is a bunt out. Bunt outs are also the ones whose value varies the most over time. Some of this difference could, however, be due to the level of data reported by Retrosheet. For most seasons, the only plays that are identified as bunts are sacrifice bunts. Sacrifice bunts will be less costly than other types of bunt outs (e.g., failed sacrifice bunts, double plays on sacrifice attempts), however. Hence, the true win value of bunts may be understated in early years.

The next table looks at all balls-in-play by hit type, regardless of what the final outcome of the play was. Information on the hit type of non-outs is not given for most years of Retrosheet play-by-play data. Hence, these figures are only shown here since 2003. For this table, all home runs are considered "Fly Balls"; in truth, some home runs may be more properly characterized as line drives.Balls in Play by Hit Type

All BIP | Bunt | GB | FB | LD | |

since 2003: Including Home Runs | 0.0017 | -0.0045 | -0.0093 | 0.0030 | 0.0244 |

since 2003: Excluding Home Runs | -0.0036 | -0.0045 | -0.0093 | -0.0137 | 0.0244 |

If one includes home runs, then putting the ball in play is a net positive offensive event. If the ball stays in the ballpark, however, then a ball-in-play is a net positive for the defense. The same is true of fly balls.

Ground balls and bunts are net negative offensive events, much more so for ground balls. In contrast, the Linear Weight run values calculated by Studenmund in the

Finally, the old Little League saying, "A walk's as good as a hit" isn't true (a walk is about half as valuable as an average hit). But, it turns out that a walk (win value of 0.0292) is about as good as a line drive (win value of 0.0244).

The next table shows net offensive values for stolen bases, caught stealings, and advancements on wild pitches and passed balls.Baserunning

Stolen base numbers here include all baserunner advancements on stolen-base attempts, including defensive indifference, balks, and errors on pickoffs. Caught stealing figures include successful pickoffs as well.

SB | CS | WP | |

1921 - 2017 | 0.0180 | -0.0376 | 0.0273 |

since 2003 | 0.0167 | -0.0345 | 0.0263 |

Event | SB | CS | WP |

Net Win Value (2002 - 04) | 0.0163 | -0.0361 | 0.0253 |

Linear Weight Value | 0.178 | -0.440 | 0.25 |

Runs per Win | 10.9 | 12.2 | 9.9 |

There are a few interesting results here. First, the ratio of win value and run value for stolen bases and caught stealing is similar to those for other events. This is in sharp contrast to intentional walks, the other events that I treat as purely contextual, and suggests that stolen base attempts are not particularly high-context, in general.

While the win values for stolen bases and caught stealing vary across run-scoring contexts, the breakeven success rate for stolen bases is actually much more stable – 67.7% over the 1921 - 2017 time period, 67.4% from 2003 - 2017. For most of the Retrosheet Era, the actual success rate for stolen bases has tended to be fairly close to, but slightly below, this level (including pickoffs) – 63.3% from 1921 - 2017.

More recently, stolen base attempts have been a net positive event since 2007 or so. Over the past decade, the actual stolen base success rate, 68.7% has been extremely close to (and slightly better than) the breakeven rate, 67.4%. Perhaps major-league teams and players are getting smarter about the timing of their stolen base attempts.

The average win value of a wild pitch is around 50% greater than the average win value of a successful stolen base. While this may seem wrong at first blush – both of these events simply advance a baserunner by one base – the reason is actually pretty simple. Wild pitches and passed balls are much more evenly distributed across bases, whereas the vast majority of stolen bases are by baserunners on first base. From 2000 – 2008, for example, there were a total of 206 stolen bases with either a runner on third base, runners on second and third, or the bases loaded (i.e., situations where the runner on third would have to advance for anybody else to advance). In contrast, there were 1,871 wild pitches and passed balls in these same base-states.

Going back to the first table, with singles, doubles, triples, and home runs, one can calculate the net win value of advancing an additional base. Note that these differences should be greater than the value of stolen bases or wild pitches, since these would involve additional baserunner advancement as well (that is, part of the added value of a double over a single is that a runner on second is practically guaranteed to score on a double but is less likely to score on a single).

Value of Reaching | 1st Base | 2nd Base | 3rd Base | Home Plate |

1921 - 2017 | 0.0363 | 0.0234 | 0.0183 | 0.0649 |

since 2003 | 0.0354 | 0.0241 | 0.0199 | 0.0590 |

Not all bases are created equal. Reaching first base (via walk) is more valuable than moving from first base to second base. Moving from first base to second base is more valuable than moving from second base to third base. But moving from third base to home plate is by far the most valuable base advancement.

Because moving from third base to home plate puts a run on the scoreboard. As I noted above, in observing that the win value for home runs is greater than the run value, increasing the probability of a run scoring – to 100% in this case – is crucial to increasing the team’s odds of winning the game.

The range of net win values in extreme run-scoring environments - the 1968 and 2000 American Leagues - is explored here.

Basic net win values by for the 2010 National League are shown here. Values for other years can be found by editing the values after the "?" in that link.