Simple Sabermetrics: Linear Weights
By Clave Jones
Jesse Johnson-USA TODAY Sports
The premise of linear weights is that the events that lead to scoring runs are linear. It’s the adage of ‘moving the guys across the bases.’ Step 1 is 1st base, step 2 is 2nd, step 3 is 3rd, and the final step in this line of events is stepping on home plate.
Positive events that would move runners along this line are hits, walks and stolen bases, and those events get positive values. Negative events are outs and when a player gets caught stealing. These events are given a negative value.
Very simple, right? Hits are good; outs are bad. A hit moves guys along the bases; a strikeout can end the inning.
So that’s the linear part, how about the ‘weights.’ Well, a double is better than a single, and a homer is even better than that!
Let’s use an examples!
Over thousands and thousands of real life baseball games we know how many runs on average are scored in various states. Again, these are the average results from decades of data.
Is there a runner on second and the batter hits a home run? That’s obviously two runs. Are the bases loaded with no outs? Chances are good that you are looking at a ton of runs scored! Two outs and the bases are empty? It’s a good time to go get some nachos.
With decades worth of play-by-play data baseball fans can actually look at any hitting situation and find out the average run expectancy in that situation. This is a BIG deal as it allows us to measure the relative importance of dozens of hitting outcomes like walks and singles.
Let’s use real situations and players to illustrate the concept.
Norichika Aoki leads off the 6th inning with a single. We know from tracking thousands of baseball games that when a batter leads off the inning with a single that the team will put a run on the board about half the time (more precisely it’s .46 of the time). Things are looking good.
Aoki steals second, putting him halfway home, which obviously his chance of scoring up considerably.
Omar Infante has a rare strikeout and we should keep in mind that since each team only gets 27 outs total, every one is precious. It doesn’t matter though Eric Hosmer smacks a homer, scoring himself and Aoki!
Over thousands of baseball games we know that a homer scores 1.4 runs on average. Maybe a guy is on base, maybe they are loaded, maybe the pond is empty. But the average over thousands of games is about 1.4 runs scored per homer.
But it’s this linear sequence of events and the fact that a homer gets more weight than a single that forms the foundations of the saber concept of linear weights.
Below is how it’s calculated.
"((1B x .46) + (2B x .8) + (3B x 1.02) + (HR x 1.4) + (BB x .33) + (SB x .3) – (CS x .6) – (AB – Hits) x Normalizing Factor)"
You can see that positive events are first and they are multiplied by the number of runs they lead to on average. Next are the negative events which subtract the average number of runs. The normalizing factor is simply because the amount of offense changes subtly from year to year. One year runs might be slightly up, while another they might be slightly down. The value is typically .26.
OK, I have the basics.
This is an extremely important concept in saber metrics and many different metrics build off this basic concept. But linear weights isn’t talked about much on fantasy baseball sites. Why is that?
Well, while linear weights is beautiful in how it can help you understand the potential impact of each trip to the plate and how each trip to the plate builds off one another, but it doesn’t have much utility for fantasy baseball.
But this is quickly changing. Led by Fangraphs and their Ottoneau Leagues, point scoring is becoming more and more popular among fantasy baseball players. It is also the basis of daily fantasy baseball that is popping up all over the place.
You have an understanding of linear weights, but you can see that numbers like .46 would make for a seriously nerdy fantasy baseball experience, as if fantasy baseball isn’t nerdy enough.
That’s why the simple solution that most points leagues use is to round the weights, then multiply by 10. So .46 is rounded to .5 then x 10 equals 5. So instead of a single equaling .46 points in a points league, it becomes 5 points.
Looking at the formula above, you can see a double is weighted as .8 and a triple is 1.02. For simplicity those become 8 and 10. Since we’ve already found a hit is worth 5 points, so we score a double as an extra three to make it equal 8, while the triple is scored with and extra 5 to make it equal 10.
Below is a list of how many common points leagues are scored.
Batting
Hits (H) 5
Doubles (2B) 3
Triples (3B) 5
Walks (BB) 3
Home Runs (HR) 9
Stolen Bases (SB) 3
Out (Out) -1
Pitching
Innings Pitched (IP) 6
Saves (SV) 5
Holds (HD) 4
Strikeouts (K) 2
Hits Allowed (H) -3
Walks Issued (BB) -2
Home Runs Allowed (HR) -12
Give fantasy baseball points leagues a shot. As an experiment; try something new.