Adjusting to scoring environment

For those of you using Dean's linear weights formula or other formulas, I argued a few months ago that actually, linear weights change across environments. Of course, linear weights are good estimates in any environment, but they can go off line, particularly in extreme environment, because of this simple fact that different types of hits have different values in different environments, and that's particularly relevant in extreme situations, such as having Kershaw on the mound or a bunch of 1M starters in Coors Field.

Of course, SOM's pricetags (which, we know from first hand, are based on weights that are NOT adjusted to any environment) can also go off line similarly.

Anyway, in the aftermath of Tulowitzki being traded to Toronto, I came across this article below that gives a pretty good summary of the impact of adjusting linear weights to its environment.

Interactions

The fact is, a team’s on-base ability, slugging, and speed all interact with each other when it comes to the process of scoring runs, such that one factor can add or subtract value from another.

I’ll now break down some of the ways the abilities impact each other:

The more runners that are on base, the more value any subsequent hit has, all else equal, as there are more RBI opportunities. (Up to a point… more on that later)

If the team has a very high OBP, it will be able to sustain longer rallies, and will therefore be less dependent on the home run to score runs (i.e., singles, walks, etc. will be more valuable relative to the home run, compared to low OBP teams).

In a low-OBP team, however, while a home run is likely to score fewer runs than it will in an otherwise similar high-OBP team, the value of a home run relative to other hit types will be greater, as the team will be less likely to rally.

Digging even deeper, if a team hits a lot of home runs, the average value of a home run actually drops, due to more runners having been cleared from the bases by previous home runs.

Base running ability becomes more relevant the closer to 1B the runner is, as only during a couple particular types of batted ball (some grounders and some flyouts) will the speed of a runner on 3B make the difference between a run and a non-run. So, good baserunning is relatively more important to a low-OBP team, as there will be fewer rallies that allow the runners to advance.

The abilities of the base runners are made less relevant, the greater the value of the hit that advances them; home runs and triples automatically clear the bases regardless of the speed of a base runner (only in rare occasions does a slow or stumbling runner on 1B prevent the batter from reaching 3B). So, good base running is also more important to low-slugging teams.

This one is pretty important: the fewer outs the batter makes, the more opportunities (plate appearances) he allows his teammates and himself to have, which by itself allows the potential for more run-scoring.

Most probably seem obvious to you now, yet linear weights formulas ignore, or don’t properly deal with these interactions. They assume that a walk, or a single, or a home run is each worth a fixed value based on league averages.
[...]
So, where do we go from here? If a context-neutral stat [for example, Dean's ERP final numbers before a season start] is good enough for your needs, then this is the end of the line [...]. But if you want to see how much a player impacts a particular team, or you want to analyze a hypothetical team (e.g. estimating how many runs your team will score next year based on projected stats), you’ll need to go deeper.

p.s. In case you wonder why this article was forwarded in the aftermath of Tulowitzki, it's because it was argued that adding a very good offensive player boosts even more a very good offensive lineup (vs a poor offensive level).

This is the same argument why it works so well to boost a powerful lineup in Coors.

Interestingly, this very week, I also came acrosss a 2014 interview with the king of ATG, Bruce Foster (who happens to be again among the best players in the ATG's Barnstour). He argues that the winnigest strategy for ATG is to pick up 4 ACES in Petco and while I don't have any experience in ATG, I thought it's probably the mirror argument of the Coors Field strategy

(Bruce F. also argues to multiply the platoons across the field---but that's another issue).

Anyway, just wanted to share, but I'll try to write in the next days how I tried to get deeper in my linear weights system and adjust for different environments.

Here's part of the interview with Bruce F.

(all rights to the http://www.ultimatestratbaseball.com. Of course, I invite you to subscribe to this newsletter).

Wolfman: Now lets talk about how did you become the latest champion? What would you say are the keys to your success? Obviously building the right team via the draft and picking the right stadium have a lot to do with it?

Bruce: The key to success is to build upon value players. I use spreadsheets and give each player a value number. I build my teams on these value numbers. I draft the highest value players in the order of my spread sheet computations.

(...)

Wolfman: So if we could summarize the strategy you use to build a team in a simple and clear way, what would be the keys you follow?

Bruce:
1. Use 9 pitchers and 15 hitters instead of 27 players. This gives you an extra 1.5M to use on the field

2. Choose the best 4 Aces that you can get. Use a cheap bullpen with strong R/L splits.

3. Use the best pitcher's park available so that your Aces can get more innings.

4. Use 6 platoons in DH leagues and 8 platoons in non-dh leagues.

5. Do not platoon at SS.

6. (Find the good values)

Bruce: If Dale Murray and Hoyt Wilhelm were SP's, then they would be the best values. However, when you combine them with any SP rotation in the sim, their value diminishes. Therefore, Four Aces or Five Kings will bring you more wins than a super-reliever.

Bruce F's way of playing Strat...seems pretty boring. The fact that you cannot just value everything is what allows for endless strategies. Obviously, you just should in general know what kind of player you should get for different parks. The question that is impossible to really know is what are the exact tipping points for your team. You put Tulo in Coors with stacked line-up you are going to get more value than expected from what playing in Coors would project. And where is the line drawing for cheap pitchers as to whether by suitable match- ups park and defense they can provide better than expected value? Every team is different and some teams you nail those lines and others you don't but if the game were just about calculating vales...how dull. Get the best pitchers, put them in the best pitching park, put your most one-sided platoons and one-sided relievers.... That's all about value. Boring. You have to find the nooks and crannies...

Just double checking, this is Bruce F. and not Bruce B.?

Bruce F. Is the king of Barnstournament--the Tour for ATG. He won it once or twice and finished in top 5 several times.

What he proposes is what he believes is best strategy to win in ATG. I know that Bruce tried other strategies and he 's been succesful, but I kinda agree that, in an environment with such outstanding hitters as in ATG, the strategy he proposes is probably the best indeed---because I haven't played yet, I speculate more than analyse carefully.


But ATG is such an unreal environment, especialy in 100M and 200M in which the run average is over 6.00, that the value of outs become much more important than in 20XX 80M, and it's my conviction that the ATG salary structure doesn't reflect that extra values of outs found on outstanding pitchers.

This conviction comes from posts by childmsc (bbrool) who contributes heavily in establishing prices for SOM, and he argued that he doesn't buy in the argument that linear weights change values in different environments, as is expressed in the first post of this thread---other than adjusting for stadium ratings. So the ATG pricing system creates a large bias among the pitching aces.

Of course, on a smaller scale, some of this is true for 80M 20XX leagues, but to what extend I'm still unsure.

And, as we know, there has been much success in 20xx (I don't know about ATG) with a low-salary starting pitching (with no aces) - even the 5 mil SP. What is so great about this game is that there are so many ways to build a winning team.

And, as we know, there has been much success in 20xx (I don't know about ATG) with a low-salary starting pitching (with no aces) - even the 5 mil SP

As I wrote in the other thread, what helps a lot with the low-salary rotation in Coors in 20xx is to have opposing teams with holes in their lineups---lineups with players with low on-base (who will generate many outs) (and when these hitters are weak, you get the bonus that your pitchers allow singles instead of homeruns too).

Here's a little simulation I did. I took three pitchers and generated the number of singles, doubles, homeruns, outs etc. they would generate (in 216 PA) against a typical 20xx lineup. I won't write down all the assumptions, but here are the most important: home field: Great American Ballpark; lefty/righty hitters: 54%/46% for rhp; 23%/77% for lhp. I calculated the "ra" for each pitcher. "ra" stands for the same as "era", except that errors are computed as hits so the "ra" are inflated compared to "era".

So, when I assume an average 20xx lineup (roughly 45M starting roster, 5M per position), here is the "ra" for these three selected pitchers:

the best pitcher in the set: Kershaw: ra=3.20
the best pitcher under 1.5M in this environment: Treinen ra=6.40
the worst non 0.5M starting pitcher in this environment: Cain ra=7.69

Then I did the same, but instead of taking a typical line-up, I assume a no-cap league composed of the best ATG players in the ATG set. I took ATG because the offense is so loaded that it creates an extreme environment. Nothing has changed from the pitcher's card. Kershaw's card is the same vs the typical 80M 20xx team or vs the ideal ATG lineup. What changes is the offence generated by the offensive players

(yet, they all affect the overall total linearly (roughly speaking I added a few walks, 6 singles, 3 doubles/triples, no homerun (as many top ATG has few homeruns) and substracted 12 outs (for every 216 PA) on each pitcher). Yet, the overall effect on run scored is NOT linear:

Against typical 80M.....against an ideal ATG lineup
Kershaw.....ra=3.20.......ra=4.37
Treinen.....ra=6.40.......ra=8.50
Cain........ra=7.69.......ra=9.69

The effect on Kershaw is that it increases his "ra" of only 1.17 against. The effect is worst on Treinen than on Cain (2.10 vs 2.00) because Treinen has more on-base on Cain.

I didn't adjust the number of double plays, which would increase with the added runners on base, so these "ra" are a bit inflated. Still, this shows clearly that the top pitchers are not as much affected by the high-scoring environments than the cheapies.

Terry made me realize something.

While the difference of runs per game between Kershaw and Treinen appears bigger in ATG (4.13) than in 20XX (3.20) environment, this might not reflect in a win-loss difference because in high-scoring environment, it takes more runs to secure a win.

To verify this, one must know that the pythagorian exponent has to change based on the average run per game. Here's one formula (they are a few in the market)

Exponent = 1.50 * log (RPG. both teams) + 0.45
(coming from http://www.baseballprospectus.com/artic ... icleid=342)

In 80M environment
A team with Kershaw: 33*3.2 + 129*4.2=647
Offensive team: 162*4.2= 680
Using 1.84 for the pythagorian: 84.7 wins

A team with Treinen:32*6.4+130*4.2=751
Offensive team: 162*4.2= 680
Using 1.84 for the pythagorian: 73.7 wins

Difference of 11.0 wins (this assumes a 9 inning of Treinen, which would not happen, but anyways)

in ATG environment
A team with Kershaw: 33*4.37 + 129*6=918
Offensive team: 162*6= 972
Using 2.07 for the pythagorian: 85.8 wins

A team with Treinen:32*8.5+130*6= 1052
Offensive team: 162*6= 972
Using 2.07 for the pythagorian formula: 74.4 wins

Difference of 11.4 wins.

So you get a slight edge for using Kershaw in the ATG environment, but it's on a smaller scale that what the runs indicated. That 0.4 wins between the two environment is inflated by the assumption that Treinen pitches 9 innings. Assuming 6 innings, we're down to 0.3 wins. Assuming 8 innings by Kershaw per start, we're down to 0.26 wins. On the other hand, if you repeat the process for all five starters, you get 1.3 wins.

For your information, I found out a post in 2012 by childsmwc-bbrool that stated that, in ATG, it was indeed easier to win in low HR environments. Here is the break-up:

In ATG
low-HR environment: home teams outscore their opponents by 23 runs (roughly 2.5 wins)
LH-favorable park: home teams outscore their opponents by 17 runs
RH-favorable park: home teams break even with their opponents
high-HR environment: home teams are OUTSCORED by 9 runs
neutral environment: home teams are OUTSCORED by 57 runs.

Childsmwc-bbrool states that he wanted to correct this bias by changing the salary structure (he was in charge of overviewing the salary structure of ATG), so then ATG8 came out with some salary corrections, so perhaps these stats don't hold as much as it used in the past.