Win Probability Changes

You may have noticed the Win Probability numbers have changed slightly. Don’t panic! There have been a few changes, for the better.

First off, we’re now using Tangotiger’s updated win expectancy tables which are no longer a flat 5.0 Runs per Game environment. Instead, we’re using the home team’s league, average run environment. This now puts batters and pitchers on “equal footing” and you should now be able to accurately compare batters and pitchers using WPA.

Second of all, we’re also using Tangotiger’s run expectancy tables to calculate Batting Runs Above Average (BRAA) for both batters and pitchers. Once again the run environment is set at the home team’s league, average run environment.

Next to BRAA there is a column titled “REW”, which stands for Run Expectancy Wins. This is a replacement for OPS Wins because we no longer need to estimate wins in a context neutral environment since we’re now using run expectancy.

Finally, Clutchiness has been shortened to Clutch (Clutchiness was excessively long) and is calculated as WPA/LI – REW.

Update (3/4/2007): Clutch has been switched back to being calculated with OPS Wins. More on this later.

Typically players remain in the same order, but their values have changed slightly. Batters should be slightly more valuable and pitchers slightly less valuable based on WPA scores.

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David Appelman is the creator of FanGraphs.

13 Responses to “Win Probability Changes”

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  1. tangotiger says:

    REW: note that this does include “clutch” with respect to men on base. To exagerrate for illustration, say you have someone who hits .000 with bases empty and .500 with men on base. His REW will be much higher than someone who hit .500 with bases empty and .000 with men on base.

    Therefore, the “clutch” portion only distinguishes between the timing in terms of inning and score, and does not also include the men on base clutch portion.

    You could start with Linear Weights Wins (LWW I guess), and then have REW, and the difference would be his clutchiness based only on the base/out. Then the gap between REW and WPA is his clutchness base on the inning/score. WPA minus LWW is his overall clutch.

    Jeter’s Clutch score dropped alot (used to be +2.5 wins and now he’s below 1.0 wins). My guess is that he performed great with men on base, and performed a bit better with the game on the line.

    If you look at his performance with men on base and bases empty:

    You will see it bears that out.

    (There is an extra technicality with using the LI as well, but not important right now.)


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  2. tangotiger says:

    Thanks for cleaning that up. I apologize for instigating the confusion. If we look at Jeter, we’ll see what this means:

    OPSwins: 3.42
    BRAA: 54
    REW: 5.20
    WPA: 6.03

    If Jeter hit his OPS the same with men on base or not, in close games or not, he’d add 3.42 wins to an average team.

    His BRAA is +54 runs, which is +5.20 wins. BRAA accounts for the differing performance with men on base. Since we know that players do in fact change their approach based on men on base, or outs be 0,1,2, then this is an interesting category. Therefore, regardless of the close score or late innings, Jeter is +5.20 compared to the neutral +3.42, meaning he’s an incredible +1.78 wins based on men on base an outs. This has got to be one of the best performances ever. I’m impressed when someone can add +1.0 wins with their performance with men on base or outs.

    Top add to that, Jeter is +6.03 in his WPA, which accounts for men on base and outs, plus late and close. So, on top of his +5.20, he adds another +.83 with his performance late/close.

    Compare that to A-Fraud. His OPSwins is +3.18, which was just a bit worse than Jeter. And with men on base, he comes out to +3.34 wins, which means he didn’t do particular better or worse in this category. And when you include the close/late, he was only +1.18 wins.

    Because he benefited with an LI of 1.05, that 1.18 WPA becomes 1.12, so that his Clutch score is -2.06 (don’t know why it shows -2.16).

    (The astute person will notice that we need a boLI, or base-and-out Leverage Index, so that someone who benefits with alot of juicy base/out situations doesn’t get an unfair advantage. That is, when bases are empty the LI is 0.7, and with men on base, it’s 1.4. If a batter only faced men on base situations, his performance would really benefit, if he was a plus hitter. There are of course 24 LI for the 24 base/out situation. Just showing a quick example here.)

    This becomes more important when looking at relievers.


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  3. Tom: Thanks for clearing everything up!

    The reason his clutch score shows -2.16 (and not -2.06) is because instead of dividing WPA by LI, I’m multiplying OPS Wins by LI. I’ve been using the original formula on the Clutchiness blog.

    On a side note, sometime this week I’m hoping to have a scoreboard where you can quickly see all the WPA graphs (and WPA leaders, etc…) for the day. Play-by-play for each game should be soon to follow.

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  4. tangotiger says:

    Wow, if you are going the PBP route, this would be wonderful. I was recommending to to add win prob and LI on a PBP basis, but if you are going to do it, I won’t hassle Sean.


    It would be helpful if you can provide MLB-level totals of all the REW, OPSwins, WPA, BRAA on a year-by-year basis, to further troubleshoot if necessary.

    Fantastic job, regardless!

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  5.  Season    WPA     BRAA    REW  OPS Wins   Clutch
       2002 -11.76   322.02  31.94    -94.69    84.28
       2003 -27.84   314.99  31.27    -58.84    30.60
       2004  -7.01   234.30  22.84    -11.97     5.06
       2005  -7.37   360.43  37.12    -90.96    84.94
       2006   7.73   338.29  33.26     19.00   -11.29

    These are the season totals for batters. I’m guessing in a perfect world, they would all equal 0?

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  6. tangotiger says:

    In a perfect world, yes. However, you are probably not handling SB, CS, and the non-PA events, right? If you just created a single bucket for all non-PA events, would that be easy enough for you to do (i.e., RRAA… running runs above average)?

    I’m bothered that the BRAA is so high. It would be interesting if all the non-PA events had a huge negative in RRAA to balance the big positives in BRAA, but that they’d have a positive rWPA to counteract the negative bWPA for the batting (where rWPA is for nonPA events and bWPA is for PA events).

    For OPSwins, that’s the easiest to fix. Make sure to solve for “a” in this equation:
    a * lgOBP + lgSLG = 1

    Same applies for FIP, where you solve for the constant so that it balances out to the league average. I would, by the way, include HBP and exclude IBB. So,
    (13*lgHR + 3*(lgBB-lgIBB+lgHBP) – 2*lgSO)/lgIP – lgERA = a

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  7. I think BRAA is that high because of how I’m doing “walk off” situations.

    When there’s a walk off hit and the game is over, I’m not dropping RE back to 0. Whether this is correct or not, my thinking was that just because the game is over, shouldn’t mean the batter is penalized. Here’s what things look like in that situation.

    Season  sum(RE)  NEW_BRAA
    2002    354.91   -32
    2003    313.09     1
    2004    325.36   -91
    2005    320.72   -30
    2006    305.29    33

    So, I think if I were to always drop RE back to 0 at the end of the game, things would be very close to 0.

    SB, CS, and just runners advancing in general are all in the pbp data I’m using, so they should all be accounted for. There are some situations like double steals that might be considered 1 play (instead of 2). I think this is generally accredited to the lead runner.

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  8. tangotiger says:

    You are correct that in walk-off situations, the RE does not go back down to zero. From 1974-1990, I averaged about 100 extra runs left on base per year, with still outs to go because of that. It is very interesting that in the chart you present, there’s 300 to 400 runs left on base in those situations.

    Therefore, I think we’re doing pretty good with the BRAA, and my concerns are likely not justified.


    As for SB, CS, BK, PK, PB, WP, DI: are you crediting that in all your measures (BRAA, WPA)? If so, are you giving credit to the runners who are affected, and if you have multiple runners who change bases, you split the difference?

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  9. SB, CS, etc… are credited in all the measures. I’m fairly certain everything is credited to the lead runner when multiple runners change positions.

    I don’t really have a quick fix right now for splitting credit between runners. I think fixing the constants for OPS Wins and FIP will be pushed to the top of my to-do list this week.

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  10. tangotiger says:

    The splitting or the lead runner is no big deal. You’re talking about at most a 1 run difference over a season in those cases. I was more curious than anything.


    You can also create Linear Weights by doing:
    select event, average(BRAA) from table group by event

    That’ll give you the average run value per event (-.31 for a K, +.33 for a walk, .17 for an IBB, 1.40 for HR, more or less, etc). You can then apply those numbers to each player’s event to figure out his Linear Weights. Then you can divide by a runs-per-win converter. This is the measure would replace OPSwins. However, you will find that you’ll get a correlation of .99 (if not higher). This really impacts Bonds and guys with lots of IBB.

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  11. That’s actually really cool. Here’s the complete list of events for 2006. I’m not sure why Fielder’s Choice shows up twice, but I’m there’s some distinction between the two that I’m not getting in the play-by-play data.

                Result Description           Runs
                Inside the Park HR           1.45
                          Home Run           1.39
                            Triple           1.09
              Sacrifice With Error           0.89
               Sacrifice Fly Error           0.81
                            Double           0.77
        Sacrifice Fielder's Choice           0.74
                Ground Rule Double           0.72
        Dropped Third Strike Error           0.49
                            Single           0.47
                             Error           0.47
                 Assist With Error           0.42
                          Advanced           0.39
                      Interference           0.38
         Dropped Third Strike (PB)           0.35
                      Hit By Pitch           0.35
                      Double Steal           0.34
                            Walked           0.32
                              Bunt           0.30
                              Balk           0.28
                       Passed Ball           0.28
                        Wild Pitch           0.26
         Dropped Third Strike (WP)           0.24
                             Error           0.24
        Caught Stealing With Error           0.23
              Intentionally Walked           0.18
                       Stolen Base           0.16
            Defensive Indifference           0.12
           Advance On Interference           0.04
                     Sacrifice Fly          -0.08
                    Fielder Choice          -0.16
                   Additional Base          -0.18
                         Sacrifice          -0.20
                          Bunt Out          -0.23
                        Ground Out          -0.24
              Dropped Third Strike          -0.27
                           Fly Out          -0.28
                 Strikeout Looking          -0.28
               Batter Interference          -0.29
      Dropped Third Strike (Taken)          -0.29
                      Foul Fly Out          -0.30
                         Strikeout          -0.30
                  Advance On Throw          -0.31
                  Fielder's Choice          -0.31
                        Line Drive          -0.33
        Touched By Own Batted Ball          -0.35
       Caught Stealing Double Play          -0.40
                        Tagged Out          -0.45
                   Caught Stealing          -0.45
                        Picked Off          -0.49
                       Infield Fly          -0.55
                        Forced Out          -0.58
                     Non-Force GDP          -0.72
         Grounded Into Double Play          -0.85
                       Double Play          -1.06
             Fielder's Choice GIDP          -1.32
                       Triple Play          -1.40

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  12. tangotiger says:

    The list echoes what I’ve shown in The Book (but your list has about 2x more events).

    The 1974-1990 data is here (under column LWTS):

    And this is also useful:


    David, two things:
    1 – I suggest adding column “PA?”, to show whether it’s a PA event or not. I would guess that might explain the FC.

    2 – I suggest adding column “n”, to show the number of occurrences.

    These two will go a long way in giving a bit more context to the event.


    And, multiplying the LWTS value by the n should give you the “+300” figure you are reporting.

    If you want to get real technical about it, you should exclude all partial innings, as well as excluding all home-half of 9th and later innings (these provisions will take care of the selective sampling issue, plus the left-on-base issue). If you follow these rules, then LWTS times n will be extremely close to 0.

    If you generate your own RE chart for 2006, instead of using my estimate, you would get *exactly* zero (using the same exclusions).

    Here’s two other charts that you may find fun to generate for 2006:


    I’m not suggesting you do all this work. But, you will find that you will appreciate RE, WE, and LWTS more by doing so.

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  13. tangotiger says:

    For those who want that last part clearer, you can create your own RE chart by simply doing:

    select base, out, sum(1) as n, sum(r + reoi)/sum(1) as RE
    from table
    group by base, out

    reoi = runs to end of inning
    r = runs during that PA

    select base, out, (r + reoi) as runs, sum(1) as n
    from table
    group by base, out, (r + reoi)

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