Linear_Weights
Linear_Weights
Sunday, May 19, 2019
?Bill James has developed a batter version of Game Score, using Runs Created as the core. Naturally, if I were to do the same, I'd use Linear Weights as the core. David Smyth would likely use BaseRuns as the core. Anyway, this thread is two tangents on something Bill noted here:
That didn’t really work; I got everybody in the range between zero and a hundred, but I had to compromise a little on the proportional value concept, and even then the average game was about 17.
Which is to be expected, unlike pitching. Why is that? Because for a pitcher, if the average RA/9 is 4.50, then the range in any game is going to be around 0.00 to 9.00 more or less. In other words, it's pretty balanced. For a hitter, it's not like that. Treating an out as -0.25 runs, then going 0-4 is minus 1 run. Treating a HR as +1.4 runs, then getting 4 HR is +5.6 runs. In other words, it's a very skewed relationship, about a ratio of 1:5. And if you have the average as 0.1667, then a 0 is -.1667 from average and a 1 is +.8333 from average. And .8333/.1667 = 5. So, it was inevitable that the average couldn't possibly come in at a 50 like Pitching Game Score.
The second tangent is this:
A homer has a run value of about 1.65 runs, a single about .70 runs each, an out has a certain cost; it totals up to a number not too far off from 2.50.
Which is actually wOBA. wOBA is the run value of the positive event, relative to the negative event. A HR being +1.40 and the out being -0.25 makes the HR 1.65 above out. A single is +.45 runs relative to the average plate appearance, and so 0.70 above the out.
(wOBA transforms that with a simply multiplier to get it onto an OBP scale.)
So, I think Bill's method probably works. Since I'm a believer in wOBA and Linear Weights, if I were to do a batter Game Score, I'd focus on those metrics. I'll leave it to the aspiring saberists to work it out if they want to.
Tuesday, May 14, 2019
?Good stuff from Craig, showing how balanced Strasburg is with the pitches noted (4 seamer and curve). One of the interesting things is that we'd expect (per pitch) that the run values to be identical. Or, if it's not identical, it would be somewhat close. If it's not, then the batters have simply decided to sit on one pitch more than the other, which should make them a bit exploitable. Kluber for example has an impressive breaking pitch (whatever you want to call it), and so, batters are getting nothing out of it, while they are having reasonable success on his fastball. They've likely decided to give him the breaking pitch and sit on the fastball. Which is why he throws his breaking pitch so much in comparison. (Though really we'd want to look at 4 seamer and sinker.) Anyway, fascinating topic as the batter and pitcher are dancing around the strike zone.
Tuesday, March 26, 2019
?When I look at all called pitches in 2018, the run value of a strike, in the count it is thrown in +5.9 runs per 100 pitches, while the run value of a ball is -6.2 runs. That difference is 12.1 runs. It is also 12.1 runs when I look at 2015-2018
However, called pitches thrown in the heart of the plate don't really impact the value of the difference between a called strike and a called ball, since virtually all the pitches in this region are called strikes. Similarly, most called pitches in the Chase zone aren't really a concern. And none of the pitches in the Waste zone are of any concern.
When I focus on The Shadow Zone, the run value of a called strike is 12.7 runs in 2018 and 12.6 runs in 2015-18 (it's even closer than that: 12.67, 12.63 respectively).
In terms of catcher framing, about 86% of the contribution comes from the Shadow Zone, 6% from the Heart and 8% from the Chase. If I use THOSE weights, then the run value of a called strike is 12.6 runs.
Since I like round numbers, I'm going to propose that the run value of a called strike is 12.5 runs per 100 pitches (0.125 runs per pitch). Comments appreciated.
Friday, February 01, 2019
In this post, Hareeb makes this observation:
As it turns out, properly removing park factor noise (wRC+) is more important than capturing sequencing (Runs Scored).
I never really thought about it, but it seems like an insightful observation. Could we have figured that out without doing a regression? Let's see. I've never done this before, so let's see where it takes us.
As Hareeb reminds us, high runs scored is based on:
- high offensive talent (think true talent wOBA + true talent baserunning)
- timing of good events
- run-friendly parks?
Which is the most impactful? We can try to make a decent estimate. Let's take them one at a time.
Spread in team talent (offense and defense)
- One standard deviation in win% is about .072, which means that we can infer that one SD is .060.
- And since offense = defense, then we can estimate that one SD of win% attributed to offense is 1/root2 of .060, or .042.
- And since 10 runs ~ 1 win, then one SD of true talent run scoring per game is 0.42
- So over 162 games, that's 1 SD = 68 runs of true talent (or 1 SD = 82 runs of observation)
Spread in sequencing
- Roughly speaking, one SD of random variation of wOBA over 162 games is: 0.5 x root(38PA x 162G) = 39, which we can scale to runs by x0.8 = 31 runs
- If we add the random variation of wOBA to the true talent of team, we get one SD = 74 (root of 68^2+31^2)
- We are still short 34 runs, which is probably the effect of sequencing. I don't necessarily like this "leftover" approach, but we just need a decent starting point
Spread in parks
- One SD in park factors is probably 5%, which means that with ~ 4.5 x 162 = 729 runs, 5% is 36 runs
Sooooo... spread in parks and spread in sequencing and spread in random variation are.... all about very similar, with parks taking the slight lead! At least using this approach.
Hareeb points out that:
- wOBA + minimizing park effect = wRC+
- wOBA + park + sequencing = Runs Scored
And since wRC+ beat out Runs Scored, that means neutralizing park effects has more impact than ignoring sequencing! A brilliant observation. And given my approach, I would have expected something pretty close to that (though not necessarily to that magnitude).
Fantastic, I learned something new!
Wednesday, January 09, 2019
?This is going to be math. Alot of math. But easy math if you are patient with me. So, take your time, and dive in. Or leave now. You have been warned.
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Saturday, January 05, 2019
?At its core, WAR is simple:
- for pitchers, it's a function of runs and innings
- for batters, it's a function of wOBA and PA
When you do that, you can get a quick WAR calculation. This is how quick WAR compares to WAR as shown on Fangraphs and Baseball Reference. (Click to make bigger.)
?
Monday, December 31, 2018
?
(Click to make bigger.)
Warning: This is a two-axis chart. There are some of you who through horrible experiences have decided you will never look at such a chart. You should get off this merry go-round now.
Thank you for coming willingly. On the left is wOBA. You will see two solid colored lines in each of the two charts.
On the right is the percentage of PA that ended with a ball in play (BIP) or ended with a non-contact (SO, BB, HBP). Those lines are black dotted.
The DIFFERENCE between the two charts is simply where you prefer to see the HR. The top chart has the HR with the non-contact events, which together are called "Three True Outcomes" (tto), or HR, BB, SO (with HBP part of BB). The bottom chart has the HR with the BIP events (1b, 2b, 3b, and batted ball outs), which together are "contact" events.
***
Let's take each chart one at a time. The first one is a split between TTO and BIP events. We see that the wOBA on BIP is pretty flat. Notice that since 1994, it has basically hovered close to .300. So, through all the changes in the era, as HR proliferated and subsided, as strikeouts keep rising, as shifts keep increasing, as fielding alignments keep evolving, the wOBA on BIP is... flat.
The wOBA on TTO is another matter. Since those are driven primarily by HR and strikeouts, we see alot of fluctuations. K rates were very low prior to the 1960s, and therefore, the wOBA on TTO was very high. From the 1970s through to 2000s, we see wOBA on TTO was still high, but stable. There was a certain "balance" between HR and SO that was accepted.
In the 2010s however, we've reached a low in wOBA on TTO, once we haven't seen since the deadball era of the 1900s and 1910s. Except instead of a deadball, we have the livearm era. The low wOBA on TTO is driven by the unprecedently high K rates.
And with the high K rates comes the low BIP rates.
***
The second chart might be more interesting. We see that up until the age of Mays/Mantle, the wOBA on non-contacts was higher than the wOBA on contacts. This is driven primarily by the low K rates. But then we're getting a divergence, slowly, and since the 1980s, surely and continuously. The wOBA on contact is going up, while the wOBA on non-contact is going down. This is driven by the fight between HR and strikeouts.
Since we've seen the wOBA on BIP be fairly constant, it's the increase in HR that drives the wOBA on Contact to keep going higher. And similarly, the increase in K rates is driving the wOBA on non-contacts to go down.
As Meg Rowley noted with clarity and succinctness:
you're embracing a particular aesthetic of baseball
This is what it's all about. This is what has to be answered.
Monday, November 26, 2018
?Data from 2018 season, includes first 8 innings, of games that lasted at least 8 innings. Excludes bunts.
"P100" is "per 100 pitches". Red is more runs. Blue is less runs. Hopefully everything in there is decipherable.
Sliders continues to be the revelation as we've learned recently. Batters not swinging at first pitches when they are down the middle has got to be a huge inefficiency in batter approach (you would think).
http://tangotiger.net/files/run_values_2018_Totals_Transposed.html
Thursday, June 14, 2018
?Rob does a good job of finding examples that highlight the differences.
The first key one is the IBB. OPS, and by extension, OPS+, treats them identically to regular walks. wRC+ uses wOBA, and wOBA treats the IBB as neutral. TAv, I think, treats it somewhere between the two.
The next is that TAv uses, essentially, wOBA24, meaning the run expectancy by the 24 base out states, using the wOBA framework (then converted to batting average scale). I think that's what it does. So, if you wanted to see the biggest outliers between TAv and wRC+, then head over to Fangraphs and compare RE24 to wRAA.
Finally, as Rob points out, the park factors. Everyone uses their own, so, it's subject to the peculiarities of their park factor system
Sunday, June 10, 2018
?One of the elements of WAR is the baseline comparison point for RP and SP, essentially at about 107% of league average RA/9 for RP and 128% for SP. In other words, if the league average is 4.50 RA/9, the comparison point is around 4.80 for RP and 5.75 for SP. And the reason we do this is because it's easier to pitch well if "you know" you are going 1-2 innings as opposed to "it's expected" you will go at least 5. It's a pace v gas issue. But for someone designated as TheOpener, he's not going to pace himself. So, we've been using the designation of SP to mean "pace yourself".
Those numbers represent roughly a .470 win% comparison point and .380 win% comparison point. This means at a 9-inning level, we have a .090 win% difference or 0.01 wins per inning.
What is the impact if we do it the wrong way? Well, for an Opener, each inning, he's being overcompensated by about 0.01 wins. So, if someone Opens 50 games, he's going to get 0.5 wins too many. If it got to that level, 50 Openers, I'd think we have to make the adjustments. If it's going to be 20 Openers, that's 0.2 wins, and not worth making the adjustment. Or, at least you can make a case that it's not worth it.
For the Main Event pitcher, he's being hurt the other way, being told that the baseline level is a .470 win% pitcher when it's in fact a .380 win% pitcher. It works the same way, each inning, it costs him 0.01 wins. So, if he pitches 50 innings as a Main Event pitcher, it'll cost him 0.50 wins.
So, I think we'll have to look at this and wait it out a bit. Once we get to 20-25 innings of Opener or Main Event pitcher status, we'll have to reconsider the need for the adjustment.
Wednesday, November 29, 2017
?Aaron Judge. And the Yankees.
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Monday, November 27, 2017
With two outs, a strikeout is just like any other batting out, in terms of its impact to scoring. The inning is over. With the bases empty, a strikeout is also just like any other batting out: we have an extra out and we still have the bases empty.
So, in these situations, the two outs or bases empty scenarios, a strikeout is just as costly as a batting out. These situations happen 76% of the time. So, three-quarters of the time, a strikeout is functionally equivalent to other batting outs, in terms of its impact to scoring.
We are therefore left with the other 24% of the time to consider.
Let's first consider with a runner on 1B, or 1B&2B and less than 2 outs. This situation happens about 15-16% of the time. And in this situation a strikeout is LESS costly than a batting out. That's because the groundout can give you two outs. The net effect is around 0.05 runs.
How about when we have a runner on 2B and less than 2 outs, the classic "move the runner over" scenario? In this situation, it is indeed more costly to strikeout in comparison to other batting outs, by just over 0.04 runs. This situation however happens only 4% of the time.
Bases loaded and less than 2 outs has all kinds of things happening, with both the strikeout potentially being more costly and less costly than other batting outs. Overall, the net effect is that strikeouts are indeed costlier at an impact of almost 0.08 runs. But bases loaded, less than 2 outs, happens only 1% of the time.
That leaves us with the runners on 3B and less than 2 outs, a situation where it is clearly and obviously far more costly to strikeout than get other batting outs, most notably because of the potential SF. How costly? It is an enormous 0.26 runs. Each strikeout costs about 0.26 more runs than a regular batting out. However, this happens 3-4% of the time.
This is our tally:
Strikeouts as costly:
Strikeouts less costly:
- 15-16% of time: by 0.05 runs
Total net impact of 0.05 x 15.5% = +0.01 runs
Strikeouts more costly:
- 4% of the time: 0.04 runs
- 1% of the time: 0.08 runs
- 3-4% of time: 0.26 runs
Total net impact of the above = -0.01 runs
(All numbers rounded for ease of illustration.)
***
In other words, while strikeouts are FAR costlier with runners on third and less than 2 outs, the sheer frequency of when they are less costly (runners on 1B and less than 2 outs), is enough to basically cancel that out.
If you are going to make an out, don't make it a K with runners on 3B and less than 2 outs. And don't make it a groundout with runners on 1B and less than 2 outs.
To the extent that you DO want to track a hitter's strikeouts, and how they are costly in relation to other batting outs, just track the number of strikeouts with a runner on third and less than 2 outs. And when you do that, you will find the league-leader to basically have about 10 such outs. So, all of this consternation for the ten times that a batter strikes outs with a runner on third and less than 2 outs.
Friday, September 15, 2017
?Let's say you bet on a game of 8-ball. You and your buddy each put 50 cents down. You win the game, you pick up 50 cents. Your buddy obviously is left with nothing. In other words, you are up $0.50 and your buddy is down $0.50. Similarly, you have a 1-0 record, while your buddy is 0-1. The average W-L record would obviously have been 0.500 record. So, you are +0.5 wins above average.
You play 9 more matches, of which you win seven of them. Each time you win, you earn 50 cents. Each time you lose, you lose 50 cents. So, in these seven wins, you added another 3.50$ to your 50 cents from the first game. So your 8 wins generated 4$ of profit. But your two losses cost you 50 cents each time, or 1$. Overall, after the 10 matches, you made 3$. You now have an 8-2 record.
What record would you have needed in order to have neither made a profit or a loss? A 5-5 record. In other words being +3 wins above average is +3$ above not having played at all (or having split the 10 games evenly). Each win ABOVE EXPECTED is worth 1 dollar. That ABOVE EXPECTED is important to remember.
***
The next day, you ask your buddy if he wants to go for round 2. Your buddy, having known you a long time, and knowing that you are a pretty good pool player, and him being passable, said: "You know, if this is going to be fair, you gotta give me some odds." So, you guys agree that you will put up 75 cents and he puts up 25 cents. So, each time you win, you gain your friend's quarter (+0.25$), while each time he wins, it'll cost you -0.75$.
You think this is fair. Your 8-2 record from the day before might be indicative of the strength of your play. If you went 8-2 today, you'd get your buddies 25 cents 8 times (+2.00$), and you'll give up 75 cents twice (-1.50$). You would still be up +0.50$.
***
If you have an opportunity to make an out on a play that you'd expect an average outfielder to make 25% of the time, you'd earn +0.75 outs for each catch.
If you have an opportunity to make an out on a play that you'd expect an average outfielder to make 75% of the time, you'd earn +0.25 outs for each catch.
Suppose you have 4 opportunities to make a tough play, of which you catch two. And you have 6 opportunies to make an easier play, of which you catch all but 1.
For the 4 tough plays, you earn +0.75 each for the two catches (+1.50 total), and -0.25 for the two tough ones you didn't make (-0.50 total). For these 4 tough plays, you will have earned +1.00 outs.
For the 6 easier plays, you earn +0.25 for each of the five catches you made (+1.25 total), and it cost your 0.75 outs for the one you didn, for a total of +0.50.
Overall, you will have earned +1.00 +0.50 = +1.50 for these 10 plays (7 outs, 3 hits). This is your value, your "profit". You made +1.50 more outs than an average fielder would have, GIVEN THE SAME NUMBER AND DIFFICULTY of opportunities. Remember this number. +1.50.
***
Now, you don't have to add up every single one like this. All of this gets reduced to simply:
profit = (actual minus EV*opps)
where EV = expected value per play
In this case, you had 4 tough plays, with an EV of 25%, and 6 easier plays with an EV of 75%.
4 x 25% plus 6 x 75% all divided by 10
= 55%
In other words, in YOUR OPPORTUNITY SPACE, the expected value is to have caught 55% of the balls. Given 10 plays, you are therefore expected to have caught 5.5 outs.
And what did you actually do? You were 7-3, so you caught 7. Going back to this:
profit = (actual minus EV*opps)
We plug in our numbers
profit = (7 minus 5.5)
profit = +1.5 outs
Remember the number I mentioned? That's how partial plus/minus works.
Friday, July 21, 2017
?Just a little reference. Another thing we should automate at some point in the off-season
http://tangotiger.com/images/uploads/linear_weights_2014_to_present.html
There are two ways to calculate these values. One way was described in Table 5 in The Book. You take the "run value" of the starting state of the event. And then you add up all the runs that actually scored following that event, to the end of the inning. The second was described in Table 7 in The Book. You take the "run value" of the starting state and of the ending state, subtract the two and add up the runs in-between. The results will be very close to each other, either way you do it.
The above chart was done the first way (the Table 5 method) mostly because given the dataset I have to work with, it was easier to do it that way.
Thursday, May 12, 2016
?A noble effort. However..... the use of regression is not only unneeded, but in fact worse than the simple logical solution.
If all you want to know is the run expectancy for the rest of the inning with a particular batter at the plate, all you have to do is figure out his run impact for that particular plate appearance over and above what the average expectancy.
For example, with bases empty, 0 outs, let's say run expectancy is .480 runs to end of inning. That's with an average batter. But, what if it's Mike Trout? Well, you calculate his linear weights for bases empty, 0 outs (using a table like this). Maybe for Trout, he's +.060 runs in that situation. So, you add that to .480 and you get .540. That's the run expectancy with Trout at the plate, bases empty, 0 outs.
Very straightforward, logical, and no regression.
?A very good primer by Neil on what FIP is. That people USE it for more than its intended construction, that's not a FIP-issue. As I noted in the comments:
I agree with the analogy of FIP to wOBA. They both:
- use a subset of performances(*)
- weight the values based on their run impact, regardless of when they happened
- scaled to a common scale
(*) FIP ignores batted balls in field of play, and baserunner movement (SB, CS, WP, etc). wOBA ignores baserunner movement.
Tuesday, March 22, 2016
?I have a simple method to determine True Talent wOBA at the component level. I posted it in a post-by five years ago (see post 11), and it's never been referenced since, whether by me or anyone else. And it may be one of the most insightful things you come across.
For example, we all know that the run value of a HR is 1.40. But, what if instead we did this for a hitter’s HR coefficient:
PA/(PA+132) * 1.40
That becomes the new “skill” value for the HR.
Whether you regress the number of HR or you regress the coefficient for the HR, it comes out to the same thing, because we want to do this anyway:
PA/(PA+132) * 1.40 * HR
So, whether you do:
X * HR
where X = PA/(PA+132) * 1.40
Or you do:
X * 1.40
where X = PA/(PA+132) * HR
We still have the exact same thing.
And then go to post #12 for examples of the method in action.
See the typical thing is to regress wOBA, but that would make each individual component regress the same amount.
Almost everyone else will regress the amounts of each component (component-level regression), and then feed it back into wOBA or Linear Weights. And that's perfectly fine.
But if you want an incredibly sweet shortcut, follow the method I posted above: instead of regressing the amounts, you can instead regress the coefficient values!
Sunday, March 13, 2016
?Yes!
If you look at his batting-neutral numbers, the ones that treats the value of a HR and a walk and a single the same regardless of the base-out situation, Votto is +348 runs better than average according to Fangraphs (look for wRAA), and +354 runs according to Baseball Reference (look for BtRuns).
But if you walk with first base open or you hit HR with the bases empty, the actual run impact would end up going down. However, if you take advantage of the situation, and walk when there's a runner on first, and not strikeout when there's a runner on third, etc, the actual run impact would end up going up.
So, what happens when Joey Votto is batting? Well, on both sites, you can look for RE24, which looks at how Votto does in each of the 24 base out states and gives him credit for his performance relative to the base-out states. And on Fangraphs he's +395 runs and on BR.com he's at the identical +395 runs.
Instead of being at +350 runs in neutral situations, he's close to +400 runs in actual situations. So, Votto is a situationally smart hitter.
(Technical interlude: what we actually want is to compare RE24 to batting runs times boLI, the Leverage Index of the base-out state. But that's really getting into the weeds there. We can do that in the comments if you want to.)
Looking at all 200 hitters with at least 2700 PA from 2007-2015, Votto is 26th in best situational hitter in MLB, putting him at the 87th percentile. Remember, this is comparing Votto situationally to Votto in neutral conditions. Number 1 is Jason Heyward. He's followed by Cargo, Giancarlo Stanton, Chase Utley (naturally), Drew Stubbs (yup, below average hitter who actually is above average based on the situation), Dexter Fowler, Ryan Braun, Victorino, Jimmy Rollins, Todd Helton. On the flip-side, the hitter that is the least situationally-aware is Kyle Seager, followed by AJ, Delmon Young, Navarro, and Mike Aviles.
So, if you want to know how a hitter SHOULD hit, talk to the guys who are actually performing above expectation. They'll tell you how to approach a situation. That means listen to Heyward and Utley and Rollins... and Joey Votto.
Sunday, February 28, 2016
?This is very heavy on the math. But the payoff will be there.
Saturday, February 20, 2016
?There's nothing really new here for the Straight Arrow readers. This is more for those stumbling across wOBA for the first time.
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