I think that would be a great resource to have alongside the win probability inquirer. When I'm watching a game I always feel like the runner should try to score from 3rd with 2 outs because the breakeven rate is almost always going to be below 50%, and it would be great to have a place to look that up. In this case, I think saying that the average Gardner SB attempt has added 1% to his team's chances of winning makes sense.

Thanks Tango/Studes. Breakeven rate is entirely independent of the leverage. It is driven by the same things that compose WPA--inning, score, outs, bases, etc. It's dictated by the value of a base vs. the value of an out at any moment. With 1 out and a man on 2nd, the value of a base is higher than average, resulting in a low breakeven rate, whereas in a 2-run game with a man on first, the value of an out is higher than average, resulting in a high breakeven rate. Another way to put the Gardner thing: Coming into the year he attempted 100 steals and added 1.0 total WPA. His average WPA per stolen base attempt was 1%. The BP WE tables are based on actual historical data. I liked the idea of using historical ones so as to include home field advantage and time period adjustments. The tables aren't perfect, as some 10-run games or something might have numbers that don't jibe with a theoretical table.

I prefer this definition. I appreciate you keeping consistent with the offered capitalization.

Greg, we can leave that topic to the physicists--I certainly wouldn't call it impossible--but R to the A and triple T picked up what I was putting down. All about perception.

Greg Maddux did get some of his pitches recorded by PITCHf/x. By that time, he was throwing low 80s, which nobody did yesterday, but I think it's possible to make out from the data that he had great location. As for Radbourn, all I can go off of is the James/Neyer Guide. Radbourn threw a rising fastball, a dry spitball, an inshoot, a slow change, a fadeaway, and a sinker. "Radbourn pitched like Marichal, Pedro Martinez, David Cone, or El Duque, throwing a bewildering mix of pitches from a variety of arm angles, thrown with outstanding control." Kyle Gibson displayed the widest mix of pitches I think, so maybe him?

Everything you say makes sense, but to me you're describing why the method works as opposed to the method's flaws. The control groups were almost always better than the experimental groups. However, I'm not comparing them directly. I'm comparing the control group in year 1 to the control group in year 2, and the difference between them, with the difference between the experimental group in year 1 and the experimental group in year 2. There is no assumption being made that the experimental groups in both years will be equal in skill.* In fact, I am trying to find the difference in skill between the two groups. If good young players are replacing bad old players, then the league is truly getting better. *There is an assumption being made that the control groups are equal in skill both years.

I doubt anyone was able to parse the explanation of my methodology, which certainly wasn't written too thoroughly. My methodology was to find how the same hitters perform against the same pitchers over two consecutive years as well as against everyone else. For example, same hitters strike out 10% of the time in year one and 9% in year two. The "environmental" effect is -1%. Those same hitters strike out against everybody else 5% of the time in year one and 4% of the time in year two. The change in pitcher quality effect is 0%. That's about it.

Exactly, it will be represented by many old players in year 1 and many young players in year 2. They are represented proportionate to their plate appearances.

That's very interesting. What might that mean with regards to the results shown?

The paragraph tries to explain how I plan on interpreting the chart. It tries to translate into the numbers in all of the following charts.

Studes, I didn't regress, and I hadn't really given the matter of regression any thought. Could you elaborate?

Every player is included in the experimental group. It consists of players who did not fit in the control. So, some pitchers faced Derek Jeter two years in a row and he is part of the control group, while other pitchers are facing him for the first time, and for them, he is part of the experimental group.

Pull% is actually 1 minus the number listed. The bigger the lead, the more likely the starter remains in the game.

Just a writing device, forming an imaginary argument against the reader. No offense intended.

I have no idea how good Mo would have been as a starter. He failed as a starter, which is why, he, and mostly all other relievers, are moved to the pen. He probably could not have survived with the same one-pitch repertoire as a starter. The best starters are more valuable than the best closers, but it's tough to know if Mo would have been one of the best starters.

Very fair.

Don't think the data supports you here.

Cool.

Sure, you can consider it, but using a reliever today won't have much of an affect on tomorrow. Good point that I should control for the pitching team's lead. The quality of pitcher brought back out for the ninth certainly depends on that lead. Running the numbers: Runs Pull% Instances Pull-RA Stay-RA 0 35% 133 3.14 4.21 1 45% 174 3.41 3.30 2 60% 209 1.82 5.33 3 59% 240 3.58 3.55 4 66% 242 2.17 4.81 5 70% 202 3.10 4.98 6 68% 165 3.81 3.66 7 70% 121 5.00 2.22 8 68% 95 3.00 3.60 9 79% 66 5.79 3.29 10 86% 42 1.50 6.25 >10 75% 65 5.06 2.94 Another way to put the half-run thing, which isn't a hard rule, and I'm not even sure if this line of thinking is correct, is that the starter's talent level to start the game had to be around 0.5 runs-per-nine better than the closer's, because after eight scoreless, the average starter is half-a-run worse than the average alternative. That might not make sense.

Sorry if I didn't make this clear. This analysis only included a team's runs allowed. Ten-run games were treated the same as tie games. I also tried to make it clear that the objective was to win that one game. I am surprised that so many people seem to think that using a single reliever in one game will have any sort of significant impact on a team's win expectancy in following games.

Guy, I've only looked at release points/platoon splits by run value before. I think looking at components like groundball rate and whiff rate would be much more meaningful, and I can't recall if it's been done before, but if it hasn't I'm sure it will be soon.

Yeah, that little section at the end didn't really belong there. Probably should have expanded it into a separate piece. I think announcers should use the best descriptors possible and call it vulcan or split or circle or palm or whatever type of changeup it is. PITCHf/x guys shouldn't try to force the clusters into any pitch type bucket ideally.

Didn't mean any offense by it!

I agree with everything Kevin says here, though I don't think it should matter which world is more interesting.

Yes, though that didn't show up in the scope of my research, meaning that similar game states must have occurred at least once in some other game, I should have made note that 12 runs is the largest deficit overcome.

When I ran this analysis, I actually included expansion teams as those with entirely new rosters. Not sure if that was the right call. It turns out that no non-expansion team has started Opening Day with 0 of its previous years starters. Therefore, the 0 data point is showing you the winning percentage of expansion teams. The Marlins have twice started years with only one opening day starter retained from the previous year, and the 1991 Atlanta Braves actually went 94-68 under this criterion. The 1980 O's kept all 10, and there have been several non-DH teams keep 9. The 1970 Os went 108-54 by using the exact same opening lineup as the previous year. The 1971 Twins went 74-86. Others, the 1971 Twins, the 2004 Phillies, 1978 Dodgers, and 1968 Cardinals.

Thanks. The coefficients are statistically significant for the guys I showed in the sense that their p-values are less than .05 or whatever. I'm not sure if that's really what you're getting at, though. The mix of pitches thing is an issue, but check out the Sanchez graph. He's never thrown harder than 93 past 80 pitches, and he routinely throws 94-95 to start the game. And part of the point I was trying to make is that all pitchers tire at different rates and stuff, so of course I agree choosing one number like 25% as a cutoff isn't great. Wakefield's distribution was definitely messed up. Maybe I should've chosen top 50% of all pitcher's fastballs. Hope my tone isn't somehow coming off defensive or anything. I really appreciate all comments.

Yeah, running a regression on this stuff is tough. Lot of noise. It's mainly about how I can control for stuff to isolate temperature. And of course physics guys could tell you how temperature actually affects a ball's velocity and stuff.

No, that's absolutely something I should have done. I plan to revisit this topic sometime soon, so I'll look into it.

OK, thanks for clarifying. I had misinterpreted your point.

MGL, yes, I've controlled for pitcher with that chart and controlled for that pitcher's velocity within each game. I'm not sure I did either the correct way, however. My original purpose for this article was actually to find the role of temperature on pitcher fatigue, so it's funny you ask that. I spent a day looking for something and couldn't find anything for a multitude of reasons. I did not separate out day and night games when I looked at it, which I probably should have. I do not know what the best way for testing temperature would be. Please let me know if you have any ideas on how I might go about it, because I find the topic interesting, but I'm rather stumped.

Compensating for one pitch with another on a given day is an intriguing thought. Data is mostly from 2009-2010. I normalized velocity by game, though, so starting vs. relieving shouldn't matter. I'm confident in saying that Sanchez fades at an exceptional rate throughout the game.

Can you be more specific? I have the data and would be willing to test what theories you may have.

Yeah, you're probably right. I sometimes try to be clever with my lead-ins, and that can come as a fault. Thanks for the comment.

But Jeff, that's not realistic. Because if you take the 5 man rotation that has Halladay, you also have to take a 5th starter like Josh Towers or something. I don't think we should dismiss such radical strategies out of hand.

Gregg, as Mike says, that would be tough to tease out from other effects, but that is the ultimate goal of this line of work.

OK, I checked it out, and I think I've made it clear I don't feel Marcel is competent in projecting playing time. Using simply year n-1 to predict year N obviously comes in with a higher average error than Marcello, as Marcello is simply a best fit and year n-1 is unregressed. But year n-1 and Marcello have practically the same average absolute errors. Marcel has a much larger average absolute error.

Yes, I think games per game started would be a good variable in a more sophisticated model. I might revisit projected playing time more toward opening day.

I should have tested using simply year n-1 as a predictor of year N. I also should have used the absolute error or RMSE or something to have tested. I will try to get to those later.

Mike, right, the mode method would go through both of those clusters. I believe that would entail simply using the exact same number of opportunities from one year to the next.

Clearly you both have a lot to learn about pitching mechanics.

Great stuff, Mike.

I strongly disagree, both with the magnitude of importance between a 19% and 21% K rate and with the study being anywhere near as significant as a player's first at bat to his career. Think of it this way: a 2% bump in strikeouts is equivalent to a 20-point loss in OBP. That's not trivial. If you're talking about statistical significance, that's different, but at face value, a 2% difference in strikeouts is fairly big. And every single time I watch a player make his debut, one of the announcers who used to be a ballplayer will reminisce about his first time up. It certainly means a lot to the player.

Yeah, I'm no projections expert, but I'd probably take Sizemore over Rhymes, too (in baseball, not names). There's probably something similar in Houston, too, with Chris Johnson and Brett Wallace.

Joe, thanks for the catch. The mapping somehow got screwed up when I created the chart. That should've been Napoli. Should be fixed.