Super Hal and Fatigue - The Mystery Continues

[ergie63]

I think what you're observing depends on how they choose to display limited data. I would not expect that simply rolling off the batter's card is enough of a penalty to make a difference. Sure, there are more hits on batter's cards, but not so much more to simulate pitcher fatigue.

There would indeed be an observed skew if they chose to display the result from the batter's card when that result was selected per my hypothesis above. If this is the case then at F8 there would be a .475/.525 ratio of pitchers cars to batter cards and dropping with each step.

Edit:
It occurred to me over dinner that we can discover whether its one way or the other. If the algorithm simply shifts the number of rolls to the batter's card (say from 50/50 to 60/40) then the percentage hits/walks per batter's roll will remain constant at all fatigue levels, but if it the penalty occurs like I hypothesized then the percentage hits/walks per batter's roll will increase with each drop in fatigue rating.

For example assume (I don't know what the average values are) that pitchers cars get batters out 66% of the time but batter's cards get on base safely 40% of the time then a batter is safe...

F9 = (.5 * .34) + (.5 * .4) = .370
--> batter's cards 50% of results shown with 40% of those safe

F8 = (.475 * .34) + (.025 * 1.0) + (.5 * .4) = .387
--> batter's cards 52.5% of results shown with 42.9% of those safe

F7 = (.45 * .34) + (.05 * 1.0) + (.5 * .4) = .403
--> batter's cards 55% of results shown with 45.5% of those safe

F0 = (.275 * .34) + (.225 * 1.0) + (.5 * .4) = .519
--> batter's cards 72.5% of results shown with 58.6% of those safe

F0-10 (ten steps below F0)
= (.025 * .34) + (.475 * 1.0) + (.5 * .4) = .684
--> batter's cards 97.5% of results shown with 69.2% of those safe

Since the percentage safe/out varies with each pitcher/hitter combo, I would think that a fairly large sample size would be needed to detect the effect.

[MARCPELLETIER]

Apovlika,
Well, I think the way you set your program is the reason why stats look so bad for F2-F7. Typically, if a pitcher is F9, and allows a hit that make him become fatigued, that very single may cause the reduction of the pitcher's state to F3 or F4. The way you set the program, that single will be associated to the F3 or F4 state, but the pitcher was really in a F9 state when he allowed it.

To take one example:

[code:1:4c5a7462af]
*** BOTTOM OF INNING 8 ***
SUBSTITUTE P - Chris Perez (role: Setup)
0 R.Cano 4-9 Walk b-1 F9
0 1 J.Varitek 1-10 Strike Out b-0 F9
1 1 T.Tulowitzki 3-7 Single (RF) 1-3 b-1 F9
1 1 3 A.Jones 6-9 Strike Out b-0 F9
2 1 3 G.Dobbs 2-11 Ground Out (2B)b-0 F8

*** BOTTOM OF INNING 9 ***
0 J.Posada 5-6 Fly Out (CF) b-0 F8
1 J.Crede 3-4 Single (CF) b-1 F2
BSTITUTE P - Todd Jones (role: Closer)
1 1 G.Anderson 6-6 Walk 1-2 b-1 F9


[/code:1:4c5a7462af]

C.Perez was F9 for his whole first inning. After the third out, he became F8. Thus, he was F8 when he faced Posada, and he was F8 too when he faced Crede. After allowing the single, Perez fell down to F2, and the computer decided to remove him instead of facing Anderson.

[The Biomechanical Man]

Apovlika, I agree with Marcus Wilby. I applaud your analytical approach to figure this out, but your data are not correct because using the F-value at the end of the line is not the fatigue level the pitcher was for the roll on that line. In Marcus' example, the pitcher was F8 when he pitched to Crede but you would have recorded him as F2.

Marcus Wilby, I agree with ergie. I think fatigued pitches become automatic hits as simply rolling off the batter's card is enough of a penalty to make the outcome differences we are seeing for really fatigued pitchers.

[MARCPELLETIER]

ergie63 proposal is clever, and could make the sense in the top level of fatigued mode (F9-F4).

But at some point down in the fatigue mode, the system allows hits/walks on the pitcher's card, but never allows an out (except for DEF-X).

this is why, in cases like Papelbon, who's only hits/walks allowed are (going from memory here) 4-5, 4-6, down the stretch (after 4-5 innings of fatigued mode), you get nothing but 4-5/4-6 when reading the pitcher's card.

I interpret to mean that HAL re-plays (re-dices) the results when it gets an out of the pitcher's card, and let's the result go when the result is a hit or a walk.

[ergie63]

Very interesting. Are die rolls still coming up 50/50 pitcher/batter?

One way to concoct a penalty using re-rolls in a framework similar to my earlier post (examples assume .66 out rate on pitcher's card and .6 out rate on batter's card)...

At F8 1/20 times a roll on the pitcher's card that comes up an out is re-rolled once against the pitcher's card only (1=4, 2=5, 3=6) and the result taken at face value. Leading to a total chance of an out being (.475 * .66) + (.025 * .66^2) + (.5 *.6) = .624 which is down slightly from .630 at F9

At F7 2/20 times there are up to 2 re-rolls thereby reducing the chances of getting an out to: (.45 * .66) + (.05 * .66^3) + (.5 *.6) = .611 or only a .311 chance from the pitcher's card

... and so on...

F0 is a .485 chance of getting an out (.185 from pitcher's card) OUCH!
F0-10 is a .317 chance of getting an out (.017 from pitcher's card)

This might be a very good simulation of a pitcher getting tired. Since his card represents his ability to get batters out and when he is tired he is less able to do the good things he does (get outs). Further a top-notch pitcher would still perform better than a mediocre pitcher (.8^n vs .6^n) Whereas my previous hypothesis would penalize all pitchers evenly.

The results shown on the box score still read from the pitcher's card and the 50/50 pitcher's card/batter's card ratio is maintained.

The way to detect this would be to process a large number of box scores for a given pitcher to see whether the distribution of rolls becomes more and more skewed toward the unfavorable with each fatigue level.

[bernieh]

Hi guys, I just wanted to stick my head in and say that when I get a minute to come up for air, I'll try to answer as many of your questions about this topic as I can. It's a bit too much for me to digest right now... :)

One thing I will say is that I am not at liberty to give away full transparency to what's going on in the code, because it is Strat-O-Matic's property and I have to respect their wishes. I've gotten into a LOT of trouble divulging more than I should. That said, I'll do the best I can when I get the chance.

[MARCPELLETIER]

[quote:c63121ca91]Very interesting. Are die rolls still coming up 50/50 pitcher/batter? [/quote:c63121ca91]

No. When a reliever gets really bad (a few innings after being F0), the ratio gets down to roughly 80-20, with DEF-X and hits/walks read on pitcher's card still being observed.

[SGTD]

I thought there was no fatigue as I have seen RP logging more thna +200 IP. I guess this is why I am getting tired of teh game after 7 years. SGT D

[MARCPELLETIER]

Here is a sim game from the disc.

Match-up was Boston vs New York. After one out, I changed the pitcher for Rivera and for Papelbon. Here is the scoresheet:

[code:1:b2d3ea8e2d]
Bronx Bombers... 0 0 0 2 0 0 0 8 9 - 19 26 0
Beantowners..... 0 0 0 0 0 0 412 5 - 21 19 1

Bronx Bombers IP H R ER BB SO HR PC SCORESHEET
J.Chamberlai 0 1/3 0 0 0 0 0 0 2 A1 A1
M.Rivera LOSS 8 19 21 21 4 10 5 184 A2
Totals 8 1/3 19 21 21 4 10 5

Beantowners IP H R ER BB SO HR PC SCORESHEET
J.Beckett 0 1/3 0 0 0 0 1 0 5 A1 A1
J.Papelbon WIN 8 2/3 26 19 18 4 5 1 189 A2
Totals 9 26 19 18 4 6 1


*** TOP OF INNING 1 ***
0 J.Damon 5- 7 5 Strike Out b-0
SUBSTITUTE P - Jonathan Papelbon
1 D.Jeter 3- 8 3 Fly Out b-0
2 B.Abreu 3- 8 3 Strike Out b-0
*** BOTTOM OF INNING 1 ***
0 J.Ellsbury 2- 9 2 Ground Out b-0
SUBSTITUTE P - Mariano Rivera
1 D.Pedroia 1- 9 3 Ground Out b-0
2 D.Ortiz 1- 5 6 Strike Out b-0
*** TOP OF INNING 2 ***
0 A.Rodriguez 6- 6 3 Strike Out b-0
1 J.Giambi 6- 4 3 Fly Out b-0
2 X.Nady 4- 6 7 3 Single b-1
2 1 R.Cano 2- 4 3 Ground Out b-0
*** BOTTOM OF INNING 2 ***
0 K.Youkilis 5-10 5 Fly Out b-0
1 J.Bay 2- 7 5 Strike Out b-0
2 J.Drew 2- 6 4 Strike Out b-0
*** TOP OF INNING 3 ***
0 I.Rodriguez 5- 5 5 Strike Out b-0
1 M.Cabrera 6- 2 3 Fly Out b-0
2 J.Damon 1- 5 2 Double b-2
2 2 D.Jeter 1- 4 6 Ground Out b-0
*** BOTTOM OF INNING 3 ***
0 M.Lowell 3- 7 3 Single b-1
0 1 J.Varitek 4- 6 3 Strike Out b-0
1 1 J.Lugo 4- 5 6 3 Double 1-3 b-2
1 23 J.Ellsbury 5 Fielders Choice 3-o 2-3 b-1
2 1 3 D.Pedroia 6- 5 3 Strike Out b-0
*** TOP OF INNING 4 ***
0 B.Abreu 6-11 1 2 Base Error - RF b-2
0 2 A.Rodriguez 2-12 9 4 Double 2-H b-2
0 2 J.Giambi 3-10 2 5 Single 2-H b-1
0 1 X.Nady 6-10 4 Ground Out Double Play 1-o b-0
2 R.Cano 1- 7 6 2 Double b-2
2 2 I.Rodriguez 2- 7 1 Fly Out b-0
*** BOTTOM OF INNING 4 ***
0 D.Ortiz 4-11 2 Fly Out b-0
1 K.Youkilis 3- 9 5 Strike Out b-0
2 J.Bay 5- 8 5 Ground Out b-0
*** TOP OF INNING 5 ***
0 M.Cabrera 1- 7 5 Single b-1
0 1 J.Damon 2- 5 3 Fly Out b-0
1 1 D.Jeter 2- 8 4 Ground Out Double Play 1-o b-0
*** BOTTOM OF INNING 5 ***
0 J.Drew 1- 2 10 5 Line Out b-0
1 M.Lowell 6- 7 4 Ground Out b-0
2 J.Varitek 5- 7 3 Fly Out b-0
*** TOP OF INNING 6 ***
0 B.Abreu 1- 3 15 5 Single b-1
0 1 A.Rodriguez 1- 7 4 Walk 1-2 b-1
0 12 J.Giambi 4-11 1 7 Single 2-3 1-2 b-1
0 123 X.Nady 4- 9 4 Strike Out b-0
1 123 R.Cano 5- 6 3 Strike Out b-0
2 123 I.Rodriguez 3- 6 5 Pop Out b-0
*** BOTTOM OF INNING 6 ***
0 J.Lugo 6- 6 3 Strike Out b-0
1 J.Ellsbury 3-12 20 3 Line Out b-0
2 D.Pedroia 5- 5 3 Strike Out b-0
*** TOP OF INNING 7 ***
0 M.Cabrera 1- 8 3 Single b-1
0 1 J.Damon 1- 7 5 Single 1-2 b-1
0 12 D.Jeter 1- 5 3 Ground Out Double Play 2-3 1-o b-0
2 3 B.Abreu 1- 2 5 Ground Out b-0
*** BOTTOM OF INNING 7 ***
0 D.Ortiz 4- 8 5 Strike Out b-0
1 K.Youkilis 2- 5 3 Single b-1
1 1 J.Bay 1 Wild Pitch 1-2
1 2 J.Bay 4- 5 2 3 Home Run 2-H b-H
1 J.Drew 3- 8 6 1 Home Run b-H
1 M.Lowell 2- 6 7 5 Home Run b-H
1 J.Varitek 3- 6 6 Strike Out b-0
2 J.Lugo 2- 3 4 Ground Out b-0
*** TOP OF INNING 8 ***
0 A.Rodriguez 3- 9 2 Fly Out b-0
1 J.Giambi 3- 6 2 HBP b-1
1 1 X.Nady 3- 5 1 Single 1-2 b-1
1 12 R.Cano 4- 3 13 5 Single 2-3 1-2 b-1
1 123 I.Rodriguez 1- 8 2 Single 3-H 2-H 1-2 b-1
1 12 M.Cabrera 1-11 6 3 Single 2-3 1-2 b-1
1 123 J.Damon 3- 6 5 Walk 3-H 2-3 1-2 b-1
1 123 D.Jeter 3- 5 1 6 Triple 3-H 2-H 1-H b-3
1 3 B.Abreu 1- 8 5 5 Home Run 3-H b-H
1 A.Rodriguez 1- 5 4 Walk b-1
1 1 J.Giambi 2- 8 16 1 Fly Out b-0
2 1 X.Nady 2- 4 3 Ground Out b-0
*** BOTTOM OF INNING 8 ***
0 J.Ellsbury 5- 7 3 Fly Out b-0
1 D.Pedroia 1- 6 3 Double b-2
1 2 D.Ortiz 3- 7 5 Walk b-1
1 12 K.Youkilis 4- 5 6 5 Double 2-H 1-3 b-2
1 23 J.Bay 3- 7 5 Walk b-1
1 123 J.Drew 3-11 2 4 Single 3-H 2-H 1-2 b-1
1 12 M.Lowell 1-11 3 Single 2-3 1-2 b-1
1 123 J.Varitek 3- 3 7 2 Single 3-H 2-3 1-2 b-1
1 123 J.Lugo 3-10 5 Single 3-H 2-3 1-2 b-1
1 123 J.Ellsbury 1-12 4 Single 3-H 2-H 1-3 b-1
1 1 3 D.Pedroia 1- 7 3 Single 3-H 1-3 b-1
1 1 3 D.Ortiz 1- 4 5 Walk 1-2 b-1
1 123 K.Youkilis 3- 4 3 Home Run 3-H 2-H 1-H b-H
1 J.Bay 1- 6 15 3 Fly Out b-0
2 J.Drew 3-11 20 1 Fly Out b-0
*** TOP OF INNING 9 ***
0 R.Cano 1-11 18 2 Single b-1
0 1 I.Rodriguez 3- 6 6 Single 1-2 b-1
0 12 M.Cabrera 4- 5 3 Double 2-H 1-3 b-2
0 23 J.Damon 2- 7 1 Ground Out 3-H 2-3 b-0
1 3 D.Jeter 2-10 5 Single 3-H b-1
1 1 B.Abreu 4- 6 15 2 Single 1-2 b-1
1 12 A.Rodriguez 2- 8 1 Single 2-H 1-2 b-1
1 12 J.Giambi 1- 8 5 Walk 2-3 1-2 b-1
1 123 X.Nady 3- 6 6 Single 3-H 2-H 1-2 b-1
1 12 R.Cano 1- 6 16 1 Double 2-H 1-H b-2
1 2 I.Rodriguez 4- 3 10 5 Single 2-3 b-1
1 1 3 M.Cabrera 4- 3 4 3 Single 3-H 1-2 b-1
1 12 J.Damon 2- 7 3 Ground Out Double Play 1-o b-0
*** BOTTOM OF INNING 9 ***
0 M.Lowell 2- 2 15 2 Line Out b-0
1 J.Varitek 3- 7 6 Walk b-1
1 1 J.Lugo 1- 8 6 Single 1-2 b-1
1 12 J.Ellsbury 1- 9 5 Single 2-3 1-2 b-1
1 123 D.Pedroia 1- 5 5 Double 3-H 2-H 1-3 b-2
1 23 D.Ortiz 2- 5 5 5 Home Run 3-H 2-H b-H
[/code:1:b2d3ea8e2d]