## How to evaluate a player's offense, part II

If you haven't already, go read Part I. There will be a quiz.

Ready? Ready!

Before we start talking about OPS, let's step back and figure out exactly what it is we're trying to measure on offense. What we really want to measure is winning, but generally we use run scoring as a proxy - a player contributes to winning by contributing to run creation or run prevention.

Creating runs is a *team process*. If you remember nothing else, remember that. Everyone in the lineup is responsible for helping the team to score runs. Think of the lineup not as a lineup, but as a giant loop.

Any outcome of a plate appearance - be it a walk, a single, a home run, a sacrifice fly, what have you - contributes (or detracts) from a team's run creation process in three ways:

**Providing a baserunner.**- This is fairly self-evident, if underrated; you can't bat runners in if there aren't any base runners.
**Advance the baserunners.**- This is why a walk and a stolen base are nowhere near as valuable to a team as a double; walks can only advance runners if there is a runner on first, and a stolen base cannot advance the runner at all.
**Avoid making an out.**- Each team is alloted 27 outs per game, three per inning. There is no limit on the amount of runs you can score, so long as you don't use up all of your outs. Using up one of the team's outs is very costly.

This is why batting average is a poor measure of value; batting average does a poor job of telling us how well a player gets on base, avoids outs or advances runners. On-base percentage does a very good job of telling us how well a player gets on base and avoids making outs; slugging tells us how well he advances the runners ahead of him.

But OBP and SLG aren't equally valuable; two players with the same OPS aren't equally valuable if one player's OPS is based on a higher OBP and one player's is based on a higher SLG. Generally speaking, OBP is 1.8 times as valuable as SLG.

(Note: OPS+, as used on Baseball-Reference.com, avoids this problem by comparing OBP and SLG to the league average seperately before combining them.)

But we're not really interested in a player's OPS; what we're interested in is his contributions to team run production. We use OPS because it correlates well, but it doesn't actually tell us how many runs a player contributes.

There are two popular methods to do this: linear weights, and Runs Created. First we'll discuss Runs Created, one of many sabermetric concepts developed by Bill James. The basic Runs Created formula is as follows:

[(Hits plus Walks) * (Total Bases)] / (Plate Appearances)

Hey, I said simple, right? There are well over a dozen different variant Runs Created formulas, all of which figure in more inputs and do a better job of accuracy.

Here are the main problems I have with Runs Created, in all of its forms:

- Runs created has some technical quirks that tend to show themselves at the extremes - for example, it is possible for a home run to produce more than four runs when using Runs Created to estimate runs; it is not possible in real life.
- Runs created doesn't apply well on an individual level; it tends to overrate players with high OBP and SLG and underrate players with low OBP and SLG. Why? Because when a player gets on base, he relies on the players behind him - not himself - to drive him in; when a player hits, he drives in the runners who get on base ahead of him, not himself.

The latter complaint is usually resolved by introducing a "theoretical team" of league average players; this approach is the basis of James' theoretical team Runs Created, or Baseball Prospectus' Value Over Replacement Player. (You probably know it as VORP.) In practice, those sorts of formulas are very cumbersome to apply.

Linear weights gets around that problem by using the relative run values of each event on average. There's a multiplicity of ways to figure the appropriate values for each event, and you can figure linear weights for a variety of contexts (you can do custom linear weights values based upon season, league, even team if you're so inclined).

So let's compare the derived weights of each of the common events (walk, single, double, triple and home run) from OPS, as compared to the Batting Runs linear weights estimator:

OPS | BR | |

BB | 0.50 | 0.702 |

1B | 1 | 1 |

2B | 1.85 | 1.66 |

3B | 2.70 | 2.32 |

HR | 3.55 | 2.98 |

Out | -0.61 | -0.53 |

I went ahead and made everything relative to the single, which I assigned a value of one; that's purely for clarity's sake. It's pretty apparent OPS does a poor job of understanding the value of a walk. That said, those values are pretty close, which is why OPS works as well as it does.

So, linear weights. They're awesome. Learn them. Love them. Cherish them.

Tomorrow, part III - where we discuss the various flavors of linear weights, what they're good for, and where to find them, as well as how to apply linear weights to things that aren't hitting. (You want to account for stolen bases? We can do that!)

## Dude

I know you mentioned it earlier, but until you did I didn't realize that BR calculated OPS+ so intelligently. Cool beans.

Hey, so what about positional adjustments? Theriot with his OPS+ of 103 right now is very different than a first baseman with an OPS+ of 103, so how do we evaluate? OPS++ where we normalize to the shortstops and first basemen?

## What you first need are positional baselines...

...to adjust to. You can't use the average at each position; an average second baseman is less valuable to a team than an average third baseman. That's why the concept of the replacement player was created.

But you can't simply set an offensive threshold for replacement level - you need to account for defensive value as well.

All of this is tied into the Wins Above Replacement framework that I use, created by Tom Tango. That's where this series is building to - once you have offense and defense figured out, you have a value system for position players. That only leaves pitching.