Thoughts on Expected Run Charts/Added Win Probability

[topper09er]

Here is a link to Tom Tango's Expected Run chart which simply calculates the percentage of time that a certain number of runs were scored based on all possible runner/out situations from 1999-2002.

http://www.tangotiger.net/RE9902score.html

These are used to calculate the added win probability of at bats by players by seeing the change in expected runs from before the at bat vs after the at bat based on the score.

 

There is no future prediction type equation which can confidently predict the actual winning percentage of any situation, all that is done is what has happened is compared to average results over many previous games which were played by different players in different stadiums in different weather conditions etc etc.

Some people contend that a teams best strategy is to make offensive decisions at all times which lead to the highest run expectancy. Run expectancy is like the weighted average of all of the columns in the link, so for example in a bases loaded 0 out situation the run expectancy is greater than 1 because it is the average runs scored in that scenario from past games, not the percentage of times a certain number of runs are scored. They contend that if you always follow this it will cause you to score the most possible runs over the course of the entire season, or maximize your offense. So for example, if you are losing by 1 run in the middle of the game and you think you could score that run by bunting or something you should never try to score that 1 run if a different strategy has a higher run expectancy, because over the long season it will be better for you.

 

I contend that this entire reasoning, although interesting, is not the best appraoch because the assumption that all baseball events (at bats) are basically the same so over the long run the average values in the charts will be very accurate is incorrect. Actually, the variation in runs scored is very large so it is unreasonable to think that just because something has happened 40% the time over some past amount of games it will surely happen close to 40% over the 50 times it happens to a team in a season (just examples of #s there). This is because it is unlikely that that 40% number came from values of 38%, 39%, 43%, 44% etc, but rahter values like 20%, 30%, 40%, 50%, 60% etc. So even though 40 is the average it does not have a small spread of values. I would say that it is better to handle all situation son a game by game basis, so if you are in a close game and down by 1 you should try to tie the game up if you can manufacture a run without the need of a hit rather than just sit back and wait for HRs, especially if they player you want to bunt is a good bunter, has a reasonable chance of even bunting for a hit and is not one of the best hitters on your team. So, basically I would say that there are situations where, as manager, I would consider bunting even with Albert Pujols for very extreme situations, whereas some people would immediately call for my head if I did that.

 

Any thoughts?

[RobDeer 45]

If baseball was as simple as just going w the numbers we'd have computers as managers. I think you use numbers to help you but you have to go on the feel of the game and your players.

[zzzmanwitz]

If baseball was as simple as just going w the numbers we'd have computers as managers. I think you use numbers to help you but you have to go on the feel of the game and your players.

I will argue that a computer could manage teams better than most managers do.

[rluzinski]

I am proposing that the best approach is to either use aggregate stats that best represent your particular scenario and then try to adjust that as best as you or try to simulate it. I'm not sure what the alternative is. I agree that you shouldn't always do just about anything all or none of the time. For example, I think there is a time and a place for bunting, I just think it is used too often and that's based on the studies I've read.

 

 

They contend that if you always follow this it will cause you to score the most possible runs over the course of the entire season, or maximize your offense. So for example, if you are losing by 1 run in the middle of the game and you think you could score that run by bunting or something you should never try to score that 1 run if a different strategy has a higher run expectancy, because over the long season it will be better for you.

 

That is simply wrong and I tried to explain as much in the in game thread from today. I gave you the obvious example of a tie game in the bottom of the 9th. Why would you try to maximize runs scored when one run ends the game? You are trying to maximize the odds of winning the game, not the odds of scoring the most runs.

 

This is because it is unlikely that that 40% number came from values of 38%, 39%, 43%, 44% etc, but rahter values like 20%, 30%, 40%, 50%, 60% etc. So even though 40 is the average it does not have a small spread of values.

 

If I flip a coin 10 times, I can calculate the odds of flipping 0 to 10 heads. That's the binomial uncertainty. We can estimate the same kind of thing with runs scored, probability of winning, etc... although with many additional layers of uncertainty (true skill level of the players involved is a big one). You select the strategy that results in the most wins for all possible results, weighted by their chance of occurring. The uncertainty is huge but what is the alternative? What exactly are you proposing that is diametrically opposed to what I am? You need to adjust for the situation at hand.... agreed.

I think you use numbers to help you but you have

to go on the feel of the game and your players.

 

If you have additional information that the numbers don't consider, great. You have to consider all information. If a manager is saying, "I know the numbers tell me to do one thing but I have a good feeling about this", I have a problem with that.

[TooLiveBrew]

If baseball was as simple as just going w the numbers we'd have computers as managers. I think you use numbers to help you but you have to go on the feel of the game and your players.

I will argue that a computer could manage teams better than most managers do.

The computer lacks the gut instinct though. How can you manage if you don't know how to talk yourself into a zim-zam?!

[topper09er]

If I flip a coin 10 times, I can calculate the odds of flipping 0 to 10 heads. That's the binomial uncertainty. We can estimate the same kind of thing with runs scored, probability of winning, etc... although with many additional layers of uncertainty (true skill level of the players involved is a big one).

I think this analogy is not correct because you know that all coin flips are independent and will assume a tight normal distribution with large numbers. You know that the expected value of 10 flips is 5 heads and getting 0, 1, 2, 8, 9 OR 10 heads has a probability of 2(1+10+45)/2^10 = 112/1024 = 10.9%, so 90% of all results will end up near the average, which means the average is a good indicator for future prediction. Baseball run scoring is not as tightly distributed, so for example say you have thousands of at bats with R3 1 out, whatever, and the chance of scoring 1 run is 48% over all at bats. If that is a reliable number, you should be able to take your 10,000 samples and randomly break them up into groups of say 10 and then see that also the percentage of 1 run should be near 48% for any randomly selected group of 10 at bats. I am saying there is waaaaay too much variablity in at bats and what you would actually find is that the numbers from the groups of 10 would be all over the map...the average would still be near 48% but any random group would have a much better chance of being on the fringes, unlike the coin example where 60% of the possible outcomes have 10% chance of happening.

 

Thus I believe the estimations that you make are not that good/reliable so you should not try to use them for future prediction.

 

I was wrong to say you would advocate scoring the most runs all time because it is about doing the thing with the highest win %, but end of game situations are pretty obvious, if it is tied in the bottom of the ninth I think we have understand that no one would advocate playing for 2, Im sorry if you actaully thought I meant that. I was refering to the situations in less obvious times where reasonable people can disagree, such as the 5th inning today. Another example is the IBB on Giambi, I will assume (correct me if I am wrong) that you would basically never support a IBB in any situation (except obvious late game times) because there is no time when adding a player to 1B would decrease the run expectancy. It clearly worked because the brewers actually got the DP they wanted, even though it was obvious to everyone in the park they did that to try to get the hitter to groundout and he knew it and did it anyways.

 

 

[endaround]

Your same argument could easily be applied to say batting average and there fore batting average is useless. Of course it would be just as wrong in that case as well. The differences in a given situation are far less than the similarities.

[topper09er]

A player's season or career batting average is useless in terms of 1 game scenarios. Carlos Gomez went 4-5 on Monday, he is not near a .800 hitter. Also, players can be on streaks and things like that managers need to pick up on and evaluate on a game to game and even at bat to at bat timespan to make a decision on what to do. Batting averages cannot be used for reliable future prediction on the time scale of 1 game. Whatever a players batting average is the thing basically came from different combinations (and permutations and zim-zam) of .000, .200, .250, .333, .400, .500, .666, .750 etc and it will fall somehwere between .250 and .333.

[topper09er]

Some of the plays we were talking about from the 4/7 game:

Gomez bunting Weeks over in 5th inning: -2% chance of brewers winning the game

IBB to Giambi in 5th inning: -1% for brewers

and heres the interesting one:

Kottaras' SF in the 6th inning that caused the game to go from 3-4 to tied: -1% for the brewers....so the SF to TIE the game in the 6th inning decreased the brewers chances of winning the game.

 

Some thing to take from this,

-all of these plays have only a 2% or 1% difference in the game, easily within the margin of error of win%...so all the number crunching on these 3 plays tells us nothing reliable.

-this system thinks that when a backup catcher ties the game in the bottom of the 6th inning, in a situation where a double play was a possibility and the following hitters are a rookie and Corey Hart, that is a bad thing.

[topper09er]

Maybe a better analogy would be poker. There is a concept called pot odds, which basically say you want the odds on your money to be better than your odds of winning a hand and in the long run you will come out on top. So if you have to pay $10 to win $100 and you think your odds against winning are 3:1, then you should pay that $10 because over the long run you will win $100 for every $40 you spend, so you come out on top. If you do this in every cash game or tournament you play for your entire life you will come out way ahead. Now pretend that your goal is not to come out on top over the entire span of the 1000s of hands you will play in your life, but to just win 1 tournament. In a tournament the only way you can lose is if you lose with all of your money at risk. When you get 2 Aces you have a ~80% of beating any hand, which means 1 out of 5 times you will lose. So in general, every single time you get 2 Aces you want to risk all your money with a chance to double up because you will come out ahead in the long run. However, if you get dealt Aces 5 times in a tournament you do not just want to risk all of your money every time because it will cause you to lose all of your money once which means you cannot win the tournament, which is your goal. So instead you need to analyze each play on their own and not put as much weight into the average values you know based on past results, maybe you know a certain hand is playable but the opponent is very strong and most of the other players at the table are weak, so theory would say to play your hand but the better decision is to let it go and wait until you can play against a weaker player. Maybe if you have 2 Aces against who think is the best player at the table you would want to risk all your money because you want to play against him with the best hands, but not so against a weaker player because you know you can outplay them later in the hand so you dont want to risk all your money right away.

 

In this example a baseball game is like a tournament that you want to win.

[rluzinski]

Thus I believe the estimations that you make are not that good/reliable so you should not try to use them for future prediction.

 

The estimates certainly aren’t as precise as calculating the odds of a coin flip. That goes without saying, since we can only estimate the true skill of players, whereas we basically know the exact odds of flipping a coin. There are many other variables we can’t even quantify, which means that they are impossible to account for by any means. They are intangible.

 

The estimates can certainly be reasonably accurate, though. The important thing is to make sure your model isn’t biased one way or another. Or else you lose your accuracy. But I'll ask again, if you don't want to use an accurate but imprecise estimate for the correct strategy to use, what is the alternative?

 

Another example is the IBB on Giambi, I will assume (correct me if I am wrong) that you would basically never support a IBB in any situation (except obvious late game times) because there is no time when adding a player to 1B would decrease the run expectancy.

 

I have my doubts that it was the correct move but I honestly don’t know. It is a very complicated question, which would require a decent amount of work to analyze. But even a rough estimate would be better than using no estimate at all.

 

It clearly worked because the brewers actually got the DP they wanted, even though it was obvious to everyone in the park they did that to try to get the hitter to groundout and he knew it and did it anyways.

 

Some percentage of time even the worst strategies are going to work, so knowing the outcome of this particular situation gets us no closer to figuring out what the best strategy was. Even a terrible strategy can turn out well a third of the time.

 

all of these plays have only a 2% or 1% difference in the game, easily within the margin of error of win%...so all the number crunching on these 3 plays tells us nothing reliable.

 

It just tells us that those plays had little effect on who might win the game (based on a very simple model for calculating win probability). That's it.

 

this system thinks that when a backup catcher ties the game in the bottom of the 6th inning, in a situation where a double play was a possibility and the following hitters are a rookie and Corey Hart, that is a bad thing.

 

No it doesn't. As I’m sure you know, those win probabilities don’t consider strength of teams, batting lineups or anything of the kind. But no one is suggesting managers should use Fangraph’s win probability estimates to make decisions so I have no idea why you keep bringing it up.

 

So instead you need to analyze each play on their own and not put as much weight into the average values you know based on past results, maybe you know a certain hand is playable but the opponent is very strong and most of the other players at the table are weak, so theory would say to play your hand but the better decision is to let it go and wait until you can play against a weaker player. Maybe if you have 2 Aces against who think is the best player at the table you would want to risk all your money because you want to play against him with the best hands, but not so against a weaker player because you know you can outplay them later in the hand so you dont want to risk all your money right away.

 

At the heart of that paragraph, you seem to be saying is that you need to consider all the variable of the particular situation at hand, to come up with optimal strategy. No reasonable person would disagree with that. But even your framework suggests making decisions based on incrementally increasing your win probability. But really, how couldn't it?

 

I honestly am not sure what you are arguing for or against that this point, nor am I sure what are are actually disagreeing with me about. I'm not advocating a manger use tango's/fangrapghs Win Probabilities, nor war run expectency/frequency numbers. I'll repost the first sentence of my first post in this thread:

 

I am proposing that the best approach is to either use aggregate stats that best represent your particular scenario and then try to adjust that as best as you or try to simulate it.

[topper09er]

I am basically responding to this post that you made:

 

rluzinski wrote:

--------------------------------------------------------------------------------

When discussing optimal game strategy, it's pretty irrelevant how it turned out in one instance. We have thousands of games of data that suggests it is generally a bad move to sacrifice bunt in that kind of situation. If Gomez was on his own and thought he could get a hit, so be it. I can't imagine he caught the corners napping, though.

 

Where it appears you are actually saying you should use past game data to tell you what to do. Now you are saying this:

 

But no one is suggesting managers should use Fangraph’s win probability estimates to make decisions so I have no idea why you keep bringing it up.

 

My other point deals with this issue:

 

It just tells us that those plays had little effect on who might win the game (based on a very simple model for calculating win probability). That's it.

 

So you are supporting a system that says a play which causes a team to go from behind to tied had no effect on the game?

 

Also, the entire system is just not really necesary because

 

As I’m sure you know, those win probabilities don’t consider strength of teams, batting lineups or anything of the kind. But no one is suggesting managers should use Fangraph’s win probability estimates to make decisions so I have no idea why you keep bringing it up.

 

Which seems to contradict your original statement that you knew that the bunt was wrong. Its like saying in basically every scenario you should instead analyze the entire situation instead of use the win% based on previous games as a guide, thus making the entire effort of calculating win% pointless. For most at bats in baseball not much thinking is required for optimal strategy, it is too hit the ball as hard as you can which increases your chances of getting on base. I dont need a computer to tell me that it is better for Ryan Braun to get on base than strikeout or I shouldnt bunt if down by 4 in the 8th inning, everyone already knows that. The times when a computer may be useful is a play like the Gomez bunt play, but when the computer is applied the result is: inconclusive, make this decision based on your intuition of situation...which is what you use to make all decisions anyways.

So if you should make the decision based on the all factors for the situation how can you say you know that bunting is wrong based on thousands of past games. I felt like it was a close game, at home, we have a good bullpen, the rockies closer looked bad on Monday, Braun and Fielder will still bat again later in the game, I think if we have an oppurtunity to tie the game without needing a hit it is a good strategy and we should do it. I would rather take that then deal with leaving a runner on base that we could have scored without getting a hit which we may reglret later in the game.

[topper09er]

It just tells us that those plays had little effect on who might win the game (based on a very simple model for calculating win probability). That's it.

 

The 5 most significant plays from the game were:

Inn	Score	Out	RoB	Pit(cnt)Sequence	R/O	@Bat	Batter	Pitcher	wWPA	wWE	Play Description
b6	4-4	1	-2-	4,(2-1) ..BBFX	R	MIL	J. Gerut	R. Flores	16%	76%	Double to RF (Ground Ball); McGehee Scores
b6	3-4	0	1--	4,(2-1) BSB>X		MIL	C. McGehee	A. Cook	16%	61%	Single to RF (Ground Ball thru 2B-1B); Edmonds to 3B
t1	0-0	0	12-	7,(3-2) CCB*BBFX	R	COL	T. Tulowitzki	D. Davis	-13%	28%	Double to LF (Line Drive to LF Line); Gonzalez Scores; Fowler to 3B
t7	4-5	2	-23	7,(3-2) .*BBBC>S.FS	O	COL	M. Olivo	C. Villanueva	12%	79%	Strikeout Swinging
b5	2-4	0	-2-	1,(0-0) 2X	R	MIL	R. Weeks	A. Cook	10%	46%	Single to CF (Ground Ball thru SS-2B); Counsell Scores

Ok, obviously, the go ahead run turned out to be the most important, getting the tying run to 3rd with 0 outs was really important. Everyone already knows this, if you go back through the IGT for each of these plays you will mind multiple people saying things like great job, clutch play, that was huge right there.

 

I just dont see that value, all this is good for is telling you things you already know.

 

 

[MJLiverock]

Sort of jumping in the middle here but I took Topper09er's original beef to be one that I think about with the run expectancies and such as well. Yes, over the long run aggregate of all the data out there a runner scoring from second with no outs is x%.

 

But that percentage has to vary significantly if the next three batters are Ryan Braun, Prince Fielder, Casey Mcghee vs. Royce Clayton, Chad Moeller, Ben Sheets (just to think of the rally killing black hole the bottom of the order used to be).

 

A manager would be pretty foolish to bunt the runner to third with Braun coming up given the much higher than average likliehood of he or Fielder getting the runner home and chance for more runs.

 

 

But using a guy like Clayton to bunt and hope a guy like Moeller can just hit a flyball or hit to the right side and score the run may make more sense because the odds of getting more than one run with those guys coming up is pretty small.

 

 

I think this the sort of game situation/player situation stuff that makes those long run aggregates less important or less of a rule to live by where you have to trust the manager to recognize the situation.

[Darnell Junior]

This is because it is unlikely that that 40% number came from values of 38%, 39%, 43%, 44% etc, but rahter values like 20%, 30%, 40%, 50%, 60% etc. So even though 40 is the average it does not have a small spread of values.

Just because a value has a higher uncertainty, that doesn't mean that the overall average still isn't useful in predicting future occurances. As in all statistics, the more samples that are taken, the better the data taken will be. Obviously for blocks of 10 at-bats (like you mentioned), the results aren't likely to match the predicted outcome. In the long run, however, basing decisions on the averages will come out to your advantage. It would be foolish to disregard a statistic because of a high standard deviation, as the mean itself still has value.

What I'm trying to say is, these 3 year compilations of data are obviously useful. Take a look at the Gomez situation. The chances of scoring 1 run with a man on 2nd and none out is 34.8%, with a total run expectancy of 1.15. The chances of scoring 1 run with a man on 3rd and one out is 47.8%, with a total run expectancy of .967. This obviously doesn't look at the possibilities of a failed bunt attempt, or a bunt for a hit, but lets just *assume* those would roughly cancel out. This data is obviously useful. If you're playing for one run, bunt him over. If you're playing for the big inning, swing away. It's that simple. The manager should use that data, and make a decision based on those two options. You have to take into account, most importantly, the score, the inning, the 3 batters due, and the pitcher, in that order (in my opinion).

A computer and a "gut" manager are the two extremes of using the data. A computer disregards the personel, and the manager pays no attention to the data. All I really want is someone who will look at both to make a decision, and not just bunt because Gomez is fast.

[topper09er]

It would be foolish to disregard a statistic because of a high standard deviation, as the mean itself still has value.

 

This is very incorrect, as a mean with a high standard deviation is very useless, such as the values of 1,1,9,9. The mean is 5, which is a very poor prediction of the actual sample set and the standard deviation is high.

 

The chances of scoring 1 run with a man on 2nd and none out is 34.8%, with a total run expectancy of 1.15. The chances of scoring 1 run with a man on 3rd and one out is 47.8%, with a total run expectancy of .967.....You have to take into account, most importantly, the score, the inning, the 3 batters due, and the pitcher, in that order (in my opinion).

 

So are you saying the numbers you quoted are correct or not? I dont get it, first you list these numbers and use it justify something, then qualify it by saying you cant take the numbers at face value because they dont consider everything involved. And to say that you know one thing will happen with 34.8% chance and another with 47.8% chance is very rediculous in my opinion because there is no way to prove this and there are so many things that these numbers dont take into account they are very useless on their face value. Are you saying that they are so good that when you take everything into account they might swing to 38% and 52%....or 12% and 87% or....you have no idea really how much the current batter/pitcher matchup swings those numbers around and there is no way you could quantify the other things you need to take into account.

 

If you're playing for one run, bunt him over. If you're playing for the big inning, swing away. It's that simple.

 

Was this not obvious before? Did you need a computer to tell you this, was it really so ambiguous as to what to do if you want to play for 1 run vs a big inning?

I already knew this based on reasoning through the situation and I dont see why the average results from games over a 3 year span in the height of the steroids and wait around for HRs era should be considered?

Also the point of this is that it makes the decision of what to do for you, you should not decide whether or not to play for 1 or a big inning because this is telling you the right answer is big inning.

 

My arguement all along has been that sure you have these numbers but you dont need them because you intuitively have a feeling for they are relative to each other and knowing that when I analyzed the current game situation I came to the conclusion that by bunting the added win % would be increased the most and I listed several reasons why. Everyone is saying you have to take other things into account besides just these numbers at face value, but I still have not heard any argument saying: The numbers say you should not bunt here by a little, and when I analyze the situation I think with all things considered (and listed several reasons) that these numbers are even more confirmed and the best decision is to not bunt. Instead, the only argument is:

We have thousands of games of data that suggests it is generally a bad move to sacrifice bunt in that kind of situation.

[rluzinski]

Where it appears you are actually saying you should use past game data to tell you what to do.

 

I said the aggregate data from thousands of games SUGGESTS it was a wrong decision. I used that word to indicate it isn’t PROVING anything. If I wanted to be more certain, I would have to make all kinds of adjustments to the aggregate data, to apply it to that specific situation. But my larger point in that comment was, whatever you do, don’t use the result of one play to determine if the move was statistically the correct one.

 

So you are supporting a system that says a play which causes a team to go from behind to tied had no effect on the game?

 

Where exactly have I explicitly given my support of Tango/Fangraph’s win probability system for use in making in-game decisions? I’ve explicitly stated the opposite, in fact. It’s an interesting and enlightening metric but it’s calculation of win probability is VERY basic. You don’t need to continually point out this fact because no one is disagreeing with you.

 

I find my self repeating the same thing over and over but when I use the term “win probability” I am NOT referring to that stat. I am simply referring to the general concept of estimating the influence different possible decisions can have on the odds that a team will win or lose. One way or another, managers are making those kinds of estimates every time they make an in game decision. The question we are debating is HOW they should do it. I sure hope they aren’t simply using their Blackberry to surf to Fangraphs.com and then hitting up Tango’s run frequency and expectancy tables at tangotiger.net. A franchise can (and many do) make much better estimates.

 

Which seems to contradict your original statement that you knew that the bunt was wrong.

 

Neither I nor any other mortal will ever know with absolute certainty whether any in-game move was right or wrong. If I gave you the impression that I thought I did, I apologize. We can only estimate (with some uncertainty) whether it was right or wrong. I didn’t make any estimate when I shared my opinion. Please remember, it was someone else who had originally brought up the relative run expectancies; I simply replied to it.

 

The times when a computer may be useful is a play like the Gomez bunt play, but when the computer is applied the result is: inconclusive, make this decision based on your intuition of situation...

 

I would take option C:

 

1. Use a computer to make the best statistical estimate you can

2. Allow your manager to adjust that estimate based off his knowledge of whatever variables the statistical estimate didn’t and/or couldn’t account for.

 

Basically, use all the information you have at your disposal. That appears to be what Darnell Junior is suggesting as well. If you are suggesting that even the best statistical estimates have no value in making in-game decisions; at least we can finally agree to strongly disagree about something specific.

 

This is very incorrect, as a mean with a high standard deviation is very useless, such as the values of 1,1,9,9. The mean is 5, which is a very poor prediction of the actual sample set and the standard deviation is high.

 

And using only your intuition will result in an estimate with more precision? I think a combination of stats and personal experience will yield the most accurate estimate but precise? Much of the uncertainty of any estimate is a result of the luck of a coin flip. Even intuition is just based off observing many individual “matchups” and noting the results. It sounds like you’ve taken some kind of stats 101 course and if you have, you are fully aware of the limitations of estimates based off samples. That’s baseball.

 

Look, you seem to be suggesting that you can intuitively come up with better estimates for optimal in-game strategy in 30 seconds than the most sophisticated statistical estimates could ever come up with. I do don’t see the utility in continuing to argue against that position. You are entitled to your opinion.