Jul
18
2013

Every play in every game has some effect on the odds of winning  baseball game. Whether you are down by ten runs in the second inning or tied up in the bottom of the ninth, every action can be measured.

Baseball has been played for over a century and a half, and Major League Baseball has been around for over a century, and most situations have been played out over and over again hundreds of times, so we have a good idea of how every action affects a team’s chances. This is called Win Expectancy. We can use those thousands upon thousands of games from history, and look at a team in a particular situation and know their odds. We know that if a team is down by one run in the bottom of the seventh inning with runners on second and third with no outs, they will win approximately 66% of the time, because roughly 66% of teams in the past have won in those cases.

To utilize these win expectancies in analyzing how each action affects the odds, we simply take the difference between the old and new win expectancy and award it to the player who accomplished the action, and penalize the pitcher who allowed it. It’s simple and easy.

There are some issues with WPA, however. While it finally solves the problem of context-neutral stats like Batting Average, On-Base Percentage, and Weighted On Base Average, it’s only good at telling a story, not predicting the future. Many of the new sabermetric statistics are predictive, but this one is certainly not. It also brings up an issue that comes up frequently when talking about RBI and Runs Scored. A player can only change the course of a game so much with his bat if he isn’t put in the right spot at the right time by his teammates. Someone might not get the opportunity to hit a walk-off home run just by chance, therefore losing out on the opportunity to pad their WPA numbers.

One thing WPA definitely solves is this: No more arguing about the turning point of the game. Instead of looking at a play as a “clutch RBI hit,” you can now define how much that run-scoring double in the eighth inning meant to the overall outcome. Take game 4 of the 2004 ALCS for example. That was the year the Red Sox were down 3-0 in the series, and won a hard-fought 12-inning game to stay alive. Here is how the win expectancy shifted throughout the night:

This is a very handy chart from Fangraphs that shows the leverage (how important a moment in the game was going to be) and how the action that took place affected the odds of one team wining. As you can see, the game starts with each team at 50 percent and ends with one team at 100 percent, with fluctuations in between. The most important moment of the game was David Ortiz‘s walk-off home run, bringing the odds of Boston winning from a shade above 73 percent to 100 percent, ending the game.

Overall, Win Probability Added is a great way to see how influential moments in a game were, but it does not tell the story of how good a player really is. In order to conduct a complete evaluation, we must use context neutral statistics like wOBA and wRAA, as well as stats like WPA.

### In Context

In every game, a player, in theory could have a WPA of -1 to 1, or even more extreme than those numbers. In practice, it is usually close to zero, but a player’s actions could almost completely determine the outcome of a game in rare scenarios. For David Ortiz’s walk-off home run in the 2004 ALCS, he added about 25% (73% WE to 100% WE) on that play alone. For that, he was awarded roughly 0.25 WPA. In every game, the WPA of each player on the winning team will amount to 1 and the WPA of each player on the losing team will always amount to -1. Over the course of a season, a player can have a negative WPA or positive, with each integer representing a win. Last season, Mike Trout finished the year with a 5.32 WPA, meaning in terms of win probability, he was worth over five wins.

(Both charts courtesy of Fangraphs.)

#### About the Author: Connor O'Brien

I'm a 16 year-old blogger, high school student, and lifelong Mets fan. I've been blogging about the Mets in some form or another for about four years. I embrace the new age, sabermetric way of thinking, but also recognize the importance of scouting and player devlopment. Follow me on Twitter @UpAlongFirst

• OK so everything was pretty clear until you got to the “In Context” section and everything took a right turn and I think you need to add some context to this. So I get using past experiences to determine what is the probability is that a team will win at any point in the game but how does that connect into a player being assigned a WPA rating?

• The player is assigned WPA based on the specific event. Here’s an example. The game is tied in the 7th and the home team is at bat. The first batter comes up and singles. His WPA for the event will be the probability of the team winning with no outs in the bottom of the 7th and a runner on first minus the probability of winning with no outs in the bottom of the 7th and no runners. If the next guy comes up and sac bunts then his WPA earned for the event will be the probability of winning with 1 out in the bottom of the 7th and a runner on second minus no outs bottom 7th runner on first.

Here’s
a WPA calculator. The run environment metric is how many runs per 27 outs the home team scores. Using my example the team coming to bat in the bottom of the 7th in a 4.5 run environment has a wpa of .5877 (58.77% chance to win the game). The single moves the WPA to .6440 so the batter would have accrued .0563. The sac bunt moves the WPA to .6236 and the players earns a -.0104. If the next guy after that singles home the run the WPA is now .7923 and that player earns a WPA of .1687.

• Thanks for the explanation, that helps.
I don;t know what I think about this stat. Why not just follow WAR instead? I get WAR does not care about situational aspects, but I would feel much better about WPA on a personal level if it went against the player as well. So that way in a situational event where the player doesn’t come through, the should get penalized. To Mr. North Jersey’s comment below, this seems to take “that game winning RBI” and expand it to more things. I’ll have to drink on this one.

• WAR is a better stat no doubt. Myself, I’ve never like WPA. It’s neat to use to look at singular events but it’s value in the long run is limited.

• Here you go. I’m eventually going to edit this. I wrote it late at night. I see how that can be confusing.

A WPA value can be anywhere from -1 to 1 in theory, with the whole number being the game. Say a player hits a walk-off homer as Ortiz did, and raises the Win Expectancy from 75% to 100%, he is credited with a 0.25 WPA for that play. A critical strikeout, allowing runs, etc. can give you negative WPA, which you wil usually see on the losing side. WPA is cumulative, so over the course of the season, having a net gain of 4-6 “wins” is a very good sign. I hope that clears things up.

• I feel like this has some of the pitfalls that the Game-winning RBI stat used to have.

• I think it’s different from a game perspective. It’s just trying to take all past results where we know what happened and applying it to in game occurrences to say this is what the teams chances are. But probability always takes a back seat to reality since it cannot predict the future. Where is comes into a metric for a player I have no friggen idea how you correlate it or why.

It would be a cool element to see on TV during a close game or playoffs to know what the WPA is in real time. Add more juice to situational plays.

The game winning RBI was just dumb, LOL.

• But correct me if I am wrong. Isn’t this basing a players WPA higher or lower on if they actually win the game? So I’m think a player that hits a 2 run hr for the lead in say the 6th will have his WPA lowered if the pen is unable to hold the lead as opposed to if they do. Is that about right?

• I have no clue. And how would the weigh one situation over another. I get a tie game in the ninth and someone hits a HR to win ranks higher then someone walking in the same situation but there are SO MANY situations that to weigh all of them doesn’t provide value to me.

• No WPA is a cumulative stat. If a players earns positive WPA in the 6th, they don’t lose even if other events erase that event.

• If a player hits a 2-R HR in the sixth, the bullpen’s performance has no effect on that player’s WPA.

• “One thing WPA definitely solves is this: No more arguing about the turning point of the game.”

Connor: Is there more weight to earlier or later inning or even weight? A three run homer by the opposition in the first puts your team in a hole If this is done in the eighth inning it could be the “turning point in the game” as the clock is running out unless its a 20 inning game. I realize a three run homer in the first dramatically increases your chances to win. But the de factor clock factor: Is. theretime to chip away or have a big inning of your own or not. It would seem this “clock factor” would therefore make the 8th inning 3 run homer more “clutch” or the turning point.

This post is not intended to be snarky but a legitimate inquiry.

• Leverage is taken into account, so yes, it is different if it happens in the seventh vs the second.

• Hotstreak, there is weight for later in the game because as you said, as the game progresses and the losing team runs out of outs, the percentage that the winning team will in fact win is greater. Being down 3-0 in the third isn’t swayed as heavily in favor of the winning team as it is win the 8th, because there’s 15 or so more outs for the losing team to make a move.

• Your exactly correct in that clock is taken into account. WPA does this in the form of Leverage Index (LI). To show you this play by play using your examples

On the first pitch the probability for both teams winning is 50/50, the LI is .87
Runners on first and second no outs, wpa is 41/59 adv away team with a LI of 1.87
3 Run homer, wpa 23/77 and the LI drops to .54

That same situation in the 8th

Before first pitch 50/50
Two men 1st and second 33/67, LI of 3.22
3 run homer, odds are now of 7%/93%, LI drops to .26

The batter who hits the homer earns .17 WPA in the first scenario and .27 in the second scenario. So you are absolutely correct in that the later homer has more value than the earlier one, and that the player is rewarded more.

Now to go a step further what happens in the bottom of the 8th if a 3 run homer is hit?

2 runners on down by 3 bot 8th the percentage of the home team winning is 22%, up from the 7% when there wan no one on, and the leverage index is 3.25.

3 run homer to tie, still bot 8th. The odds are now 60/40 in favor of the home team and the player who hit the homer earns .38 WPA (+ 38% chance of team winning).

• Funny.. you’re saying this stat can’t be used to predict outcomes, but it sounds to me like something straight from the Vegas odds-makers.

I think it’s very cool that people are analyzing all the situations over the course of baseball history to determine probability of winning a game at various points during the game.. It reminds me of watching poker on TV when certain hands come up, they show each player’s win probability (much easier to do with card games).. I could see the guys at Elias doing this in the near future based on research like this; soon you’ll see a little percentage chance of winning under each team in the TV score graphic..

And gamblers will throw away lots of money based on it!

• Im sure thats what the casinos use for “Live betting”

• You’re exactly right about the poker thing. The only real difference is the poker calculation is far simpler, but the concept is the same.

• Connor, meant to share this with you on Tuesday and I forgot so I’m putting it here. It’s an email I got that afternoon.

Hope you’re doing better Joe.

I just wanted to thank you for the two posts by Connor on the explanation of the new stats we keep seeing used so often now. I think it’s a good idea to take some time to explain how these stats work to those of us who never used them before.

Your writer does a fine job explaining them so that even a person like me can understand and as you know that’s not easy for some of us oldtimers.

Please keep up the great work. At some point soon the team will reward you and the rest of us with the championship we all crave.

• Thanks to whoever sent in that email!

• I bet (pun intended) this actually would have meaning in basketball. Particularly last quarter as most games are still “winnable” In another words a 15 point deficitt entering the 4th QTR is still “winnable”. “Defense’, Defense”. The anatomy of a comeback. Each second of the game is pivot point. Turnover, rebound, or a crucial 5th foul or 4th foul which forces a star player to the bench or even a player injury.

Back to baseball. If a pitcher has a QS which I think is a good predictor better than the BS written here (QS is NOT BS) as shown in this link:

Keep it simple stupid.

http://www.baseball-reference.com/blog/archives/14497

• You do realize that the article you linked to determined that the quality start stat isn’t useful right? QS is better than W/L but it’s quite mediocre since it ultimately values a 9 inning shutout as much as 6 innings and 3 er.

A better stat is the one QS is based on which is game score. The scales off, it’s harder to get from 80 to 90 than 60 to 80, but it at least seperates actual quality starts from ones that are average.

• Vig. I love QS and the writer doesn’t. It was sloppy on my part because I presented my case that QS are better than WPA and much simpler. I hope I clarified my position. I agree with you giving up 3 runs or less in a 4-3 win with a QS is more of an accomplishment than the score with a QS being 10-3. Is there such as stat as QS based on game score? Is really is needed. Just look at a pitcher like Dickey last year and look at his QS and the score. Also add on runs after the pitcher left may make the score look lopsided when it wasn’t. Again I love BABIP, WHIP and QS.

• Per Team 2013 Average RS per team Computed
GP Runs Average RS
American League 94 415 4.415
National League 94 383 4.074
Major League Baseball 94 399 4.245

You may asked if a pitcher gives up 3 EARNED runs OR LESS IN six innings or a 4.5 ERA and the average RS is less than that why is it a QS. Its because he in effect kept his team in the game or gave it a chance to win. The QS team could be trailing 3-0 with a chance to win. Right now QS win 66% of games (It could be both teams have QS). In the case of the team winning 3-0, naturally the WPA is higher BUT we all knew that.

• Alright, I get what you’re saying now. In that case QS isn’t bad for a long haul look so as a counting stat, it’s not bad. With the proper sample 1+ seasons it’s most definitely going to separate good or great from average.

Just to prove your point here’s Johan’s career rate vs John Maine’s

Johan: 184 qs in 284 starts, 65%
Maine: 48 qs in 105 starts, 48%

• The problem I have with QS is the qualifier. Someone can have 32 QS a year and finish with a 4.50 ERA. Is a 4.50 ERA pitcher a “quality” pitcher?

• No but as a counting and compilation metric it evens out over time. The guys who get a lot of average quality starts but less better quality starts end up not having the same rate of quality starts. Steve Trachsel for instance had a quality start percentage of 52%, slightly better than Maine, significantly worse than Santana. Bill James added GEMS as an alternative to QS but it never really caught on.

The underlying metric Game Score may be a better way to judge pitchers. In that case Santana had an average GS of 59, Trachsel had 49, Maine had 51.

Along with raw totals a clearer picture of the 3 players career quality comes into focus.

Just for fun, Matt Harvey has 21 QS in 29 starts (67%) with an average game score of 64.

• I do prefer game score over QS. Maybe its my age, but I can’t get behind something that lauds a 4.50 ERA. To me, a 4.50 ERA pitcher is a mop-up/long reliever or spot starter, not a starter “good enough” to start every fifth day.

If the QS metric was adjusted to include every start in which that game’s ERA was 3.99 or lower, I’d me more accepting. I’d also like to see them add something like GS (great start, or something to that effect), where your game ERA is lower than 3.00.

• “An early criticism of the statistic, made by Moss Klein, writing in The Sporting News, is that a pitcher could conceivably meet the minimum requirements for a quality start and record a 4.50 ERA, seen as undesirable at the time. Bill James addressed this in his 1987 Baseball Abstract, saying the hypothetical example (a pitcher going exactly 6 innings and allowing exactly 3 runs) was extremely rare amongst starts recorded as quality starts, and that he doubted any pitchers had an ERA over 3.20 in their quality starts. This was later confirmed through computer analysis of all quality starts recorded from 1984 to 1991, which found that the average ERA in quality starts during that time period was 1.91.[3]“

http://en.wikipedia.org/wiki/Quality_start

I like the quality start stat — more precisely the percentage of quality starts. Over the course of a season, it says a lot about a starter’s stamina and ability to manage innings and pitch counts. Winning is as much about this ability and stamina as it is about stuff.

In the link above, it says Doc Gooden had the highest percentage of quality starts ever for a single season. 33 of his 35 starts in 1985 were quality. Amazing!

• Metro, the 1980′s were on of those most offensively-void eras in baseball history. It’s a bit skewed to just take the eight years in which pitcher’s dominated baseball. I’d like to see the same study done from 1995-2002, if we’re randomly choosing eight year stretches.

I do understand the point that it would be near impossible for a pitcher to throw 32 starts of exactly 6IP/3ER, but if the resulting average ERA is so low anyway, then why make such a nondescript start count towards that.

• xtreem, rather than the 80′s being an offensively-void era, I think it was the norm rather than the exception. The average run scoring for those 8 years was 4.32 runs/game. That’s where it’s been the last few years since PEDs testing was implemented. This year it is 4.23 runs/game. Last year it was 4.32 runs/game. (Numbers are for both leagues.)

Also, the 8-year period isn’t random. The fellow who did the study did it in 1992. So he used the most recent data at the time. And since run scoring today is basically the same as it was back then, then I’d say today a quality start is once again more relevant (vs. in the steroids era).

Why make such a “nondescript” stat count? Because the idea is to count “quality” starts, not “exceptional” starts. No, really, the idea is to have a floor or a minimum level of performance for giving your team a good chance to win. Average run scoring per game is usually above 4, so then 3 runs in 6 innings would give a team a good chance to win.

And, again, QS isn’t really about isolated games. It’s about the percentage of those games a pitcher will produce over a period of time. If a starter can achieve a QS in around 2/3′s of his games, say over 1 season, then that is very good.

• I see your point, but it doesn’t do much to change my opinion. If average RPS floats around 4.2-4.3, how is an ERA of 4.5 considered “quality”?

• xtreem, a quality start isn’t necessarily an ERA of 4.50. It could very well be 0.00. Or 1.00. At any rate, again, it’s not about a single game. It’s about the ability of a pitcher to achieve a high percentage of quality starts over the course of time. The higher the percentage, the better the pitcher. That’s where the real value of a quality start comes in.

• I know that it COULD be 0, but it also COULD be 4.50, and I can’t call any start in which a pitcher actually gives up more runs than the offense scores on average to be “quality.” Like I said, I’d be more accepting of the metric was amended to maybe a game ERA of 3.99 or lower.

• I wouldn’t get so caught up in the extremes when it comes to QS. Yes the bar should be higher, but sample size will fix smooth over aberrations like a QS with 3 runs in 6 innings. As you can see here, even in a smallish sample it does show that.

• That’s a great study, actually. I think it actually proves my point. If a stat can only be understood by breaking it down, then it’s not really a great stat. That’s my problem with OPS. Now if a QS had a higher bar, then you wouldn’t need to see how many of them were actually good. If, hypothetically, a QS was a game ERA under 4, or even under 3.50, you wouldn’t have to look at how many were good, how many were average, and how many were not good. You’d know because the threshold automatically locks you into a good start.

• xtreem, if you set the bar higher, there are always going to be some people breaking down the stat anyways. Someone will go looking for how many starts were good, better or best.

If you set the bar higher, the stat also becomes less useful. Because you really want to see how well a starter can do given a reasonable standard — reasonable being 3 runs or less in 6 innings or more. I’ll take that from a starter every time.

I would bet that many GMs use QS as part of their criteria for assessing starters. I know players and their agents do.

You know what the problem with average game score is? It doesn’t tell you anything about the stamina of a pitcher and his ability to go 6 innings or more over the long course of a season. Number of quality starts and QS% does that. That’s why I like it.

• Connor, you’re doing an excellent job here explaining the basics of some key advanced stats. Kudos to you for your well-thought-out logic and understandable prose.

I especially like WPA as it is applied to some of the newer clutch stats today. Plain old-fashioned situational stats are fine to a certain extent, but they have serious flaws. WPA goes one stop further to better define how crucial a spot in a game really is, instead of just lumping all at bats with RISP into the same category.

Now, if only a stat could be created that would also take into account a team’s place in the standings and chances to make the playoffs. That would add even more valuable context to a “clutch” stat.

• Connor you are one of my favorite writers on this site! You are intelligent and optimistic and that’s how I like my guys. lol

• Thanks guys for the clarification. Interesting WPA leaders of all time.

Carlos Beltran No. 74
David Wright No. 104

• You know it’s pretty crazy that Votto is already 88th after only seven years.

• But as you can see, there are names in the top 75 that you would not expect. Again why WPA is not predictive.

• I updated the “In Context” section to make clearer how WPA adds up over a season. Also, tried to make clearer the difference between win expectancy and WPA.

• So I thought of an interesting scenario… What if a game really flip flopped in terms of win probability. For instance team A 75% chance of winning, then team B has 85% chance of winning, then team A goes back up to 70% chance of winning, finally team B takes it in extra innings (100%)… Wouldn’t it be possible for a single player to get more than +1 (or -1) during that game?

If that’s the case, it makes me a little bit skeptical of the career totals / yearly leaders of this stat. I guess what I’m getting at, is that there’s still some “objectivity” built into this stat. If they really wanted to make it non-objective, I think it would need to be scaled so that the bonuses and penalties of the winning team’s players (maybe cumulative offense, defense, and pitching) would add up to 1, while the losing team’s players would add up to -1.

That would tell a very accurate story. Although it might be unfair to players on bad teams.

In either case, I really like WPA.. It’s more of a “study” on baseball probabilities, than it is the type of stat you’d look for in a box score or league-leader list, IMO. It will be interesting to see how (or if) this is applied to live broadcasts in the future.

• In your scenario, you’re looking at a lot of ten run innings, just based on your hypothetical of the massive fluctuation in win expectancy where team A has a 75% chance of winning, and then all of a sudden a 15% chance of winning (Team B has 85%). And in that case, a player can’t have more than a 1 because there’s no such thing as a ten-run home run.

Look at it this way. Mets are down 10-0 and the Braves (hypothetically) have a 90% chance of winning. The most a player can do is hit a grand slam. So now the 10-4 deficit cuts the WE to say 75% and that player has a .150 WPA. Six batters later, another slam and the 10-8 deficit gives the Braves a 60% chance and that hitter has a .150 WPA. Next inning, a little later in the game and the WE has shifted slightly. Braves are back up to a 65% WE and that first player hits yet another grand slam to put the Mets up 12-10 and gives THEM a 65% WE, which brings him to .450 WPA for the game.

Get it? Because big leads can only be chipped away at, each event only adds a little WPA at a time.

• There’s been quite a few players with a WPA over 1 in a single game. Art Shamsky has the highest at 1.5, and it’s an insane performance, came in as a PH got 3 total at bats his 3 homeruns. The most recent WPA over 1 was Cody Ross in 2008 with a WPA of 1.139.

• It is possible for that scenario to happen, but very unlikely. There have been cases where one action gives the player 0.95 WPA, so theoretically if that happens, and then the other team comes back, the player would have an opportunity to get a WPA higher than 1.

• Actually, in thinking about this scenario a little more, it doesn’t matter. Just based on mathematics, the cumulative total of all hitters + pitchers WPAs (assuming defense isn’t factored in, which, I’m not sure how it could be) for the winning team, will always equal +1, while the same for the losing team will always equal -1. No matter how many massive lead changes occur (which admittedly is highly unlikely anyways). There might be an exception for a rain-shortened non-tied game after the 5th inning (unless they credit the final WPA boost to the umpire or the weather man!).

So while a player could have a 1.2 WPA for a game, the cumulative total of all other players on the team would have to be -0.2 (this player more than won the game single-handedly for his team, making up for lack-luster play from his team-mates).

One thing that confused me a little is saying both teams start at 50% chance of winning. It’s easy to confuse percent chance of winning with WPA. If a “win” counts as 1 in WPA, that is actually equivalent to moving your percent chance of winning from 50% (at the beginning of the game) to 100% (at the end of the game). From a WPA perspective then, you’d have to consider that both teams start at 0 and over the course of the game, they approach +1 or -1 (a total range of 2). So in other words, if one team has a cumulative-player WPA of +0.5, then that means they have a 75% chance of winning.

• Just to demonstrate that I’m learning things here (thanks Connor!) I want to put WPA into a real-world application. This also shows that some of these new stats are very intuitive..

“In other news by Puma, he reports that the Mets are considering starting righthander Chris Schwinden against the Washington Nationals on Friday July 26 when the Mets have a day-night doubleheader.”

The Mets WPA for the 7/26 game just went to -99%

• Ha. Well done.

• Actually the bookmakers in their betting line at Vegas would take care of the matter. But remember that’s why they play the game. To clarify they play for the bookmakers. Put it in the books.

• 100% agreed.

I think this is a cool stat, but it takes nothing away from playing the game. Or in my case watching the game (which in the end, is a lot more fun than looking at stats!).

However, if you were a betting man, I would suggest this is the closest equivalent, to say, “basic strategy” in blackjack. Over the long-term, the odds will very likely even out based on a statistic like this, which is grounded in the history of actual events in baseball (i.e. empirical data). Nonetheless, on any given day, anything can (and will) happen.

• Hi Connor,

One can be on he opposite side of the fence and still appreciate the time and effort put into such a detailed explanation of something you obviously love. Great job and you should be proud of this series.

Those like me simply relax on the couch watching the games unfolding on TV (since we can’t afford the tickets anymore LOL) using our own lazy empirical WPA way to second guess the manager. That’s why it’s called our national “pastime” – taking in the game at a slow pace and passing the time away. Tracking the game and referring to those advanced stats is certainly not a lazy man’s way of watching a ball game, that’s for sure.

Hey, is any credit given to a pitcher who beans an opposing hitter to get him out of the lineup? That could very well be the turning point of any game.

Again, a very professionally written and polished series explaining the game from your perspective. Look forward to our friendly disagreements in the future and don’t let anyone discourage you from presenting your own point of view.

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