How Much is Playing a Game Worth?

NOTE: If you haven’t seen the poll, then click that FIRST, then come back here to read more.

***

I asked this question in a poll:

Player X created 105 runs in 105 games. AFTER which player would you slot him in, wrt MVP?

And I gave a list of Player A (150 runs) to Player F (100 runs). But in all cases, those guys played 162 games.

A straight arrow reader deduced the true intent of the question:

So the question is how you handle 57 games of production from somebody else.
a. Do you ignore it completely and just judge the guy on his 105?
b. Do you assume replacement level production?
c. Average?

If you simply give this player zero credit for the missing 57 games, then you would slot this player who created 105 runs in 105 games in between Player E (110 runs in 162 games) and Player F (100 runs in 162 games).

But perhaps you want to go the other way, and figure that the missing 57 games will be picked up by an average player, and so, you credit Player X with those runs (28.5 runs in this case), and so his 105 runs in 105 games is EQUIVALENT to created 133.5 runs in 162 games. Therefore, you’d slot him between Player B (140 runs in 162 games) and Player C (130 runs in 162 games).

Perhaps you think both those options are unfair:
(i) it’s unfair to presume an average player would pick up the slack
(ii) it’s unfair to presume that those 57 games would be a complete black hole

So, perhaps you decide that those 57 games need to get some runs credited to our Player X. Since the average player would create 28.5 runs, and a black hole player (i.e., pitcher as batter basically) would create 0 runs, then maybe something in-between, say 14 runs is what you should count.

Our Player X, with 105 runs in 105 games would be equivalent to a player with 119 runs in 162 games. And so, you would slot that player between Player D (120 runs in 162 games) and Player E (110 runs in 162 games).

The consensus pick was between Player C (130 runs in 162 games) and Player D (120 runs in 162 games). Therefore, Player X (105 runs in 105 games) would be equivalent to a player with 125 runs in 162 games.

Mathematically, you’d write this as:

105 – 105x = 125 – 162x

Rearranging the terms:
20 = 57 x

Solving for x gives us x = 0.35

Therefore, we give our Player X a rate of 0.35 runs per missing game.

Since the average rate (as noted in the poll) was 81 runs in 162 games, or 0.50 runs per game, then our “replacement level” is 0.35 runs per game, or -0.15 runs relative to average.

And -0.15 runs per game times 162 games is 24 runs per season. That’s where you readers have established the replacement level. And, as luck would have it, that’s pretty much exactly where saberists like to set the replacement level.

How you chose your answer is exactly how you handle replacement level for MVP discussions. For those who slotted him between the 110 and 100 runs created player, then you don’t believe that you should use replacement level for MVP discussions.




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33 Responses to “How Much is Playing a Game Worth?”

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  1. chri521 says:

    Worth more when Jim Hendry is fired!

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  2. Colin says:

    Tango, was there a way to calculate the replacement level based on what you gave in the last poll?

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    • tangotiger says:

      No, if you mean your question literally.

      Replacement level is a concept. And so, you have to make a decision as to how to determine that level, the point at which a team will not pay more for production than they can get off the scrap heap. Basically, it’s free agents who sign minor league contracts in the off-season.

      If you look those players, you will basically find that those players generate about 20-25 runs per 700 plate appearances (i.e., 162 games), below the average player.

      This is why we set the replacement level at around that point, at about 0.15 runs per game below average.

      Some people set the level differently, perhaps at 0.10 runs below average, and others set it at 0.20 runs below average.

      The consensus is roughly 0.15 runs per game below average.

      My question however had one additional parameter: MVP. And that is, how does someone CREDIT a player for those games. Basically, some people are uncomfortable basically GIVING a player 0.35 runs for each missing game. So a guy misses 57 games, but he “earns” 20 runs anyway.

      Remember though, in reality, a team EXPECTS 20 runs to be earned just by playing 57 games, because that’s how many runs the scrap heap player will generate. On average.

      So, I was trying to find out from people if they are comfortable with replacement level talk even for things like MVP, or, do they still expect those players to “earn” their runs, even if they are being “given away” (i.e., scrap heap players basically perform at the minimum acceptable level, and they’ll earn 20 runs in 57 games).

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  3. Telo says:

    Sure, the league average was stated as 81 runs in 162 games, so .5/g, and replacement, as deemed by the results is .35/g. So wRC+ 70 (=.35/.5) is replacement, at the plate

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  4. Chadam says:

    I love this article – but I saw it before I even saw the poll that was posted this morning, and I check Fangraphs daily. Wouldn’t it have been better to let the polll marinate for a day or two before this follow up post? Just curious.

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  5. Corey says:

    I like the idea sure, but I don’t think slotting him between 110 and 100 counts as “not wanting to use replacement level”; you could just as easily think that whatever games that player doesn’t play shouldn’t be counted towards their MVP consideration, whether they are replaced with an amazing hitter or an awful one.

    I would actually argue that slotting them above 110 is misleading: if you have a shortstop who produces 105 runs in 105 games, that’s going to much more valuable than a first baseman who does the same, and so giving the first baseman credit for a higher replacement level in those games that he doesn’t play actually negates the real value of the shortstop when compared to his peers.

    If you told me, for example, that you had a catcher who had produced 105 runs in 105 games and asked for a MVP vote for him over a first baseman who had produced 130 in 162, I wouldn’t add the value of his replacement; I would consider instead how much more the MVP candidate did for his team than his replacement would have done in those 105 games. Maybe I’m old-fashioned.

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    • Mike K. says:

      I think you’re supposed to assume all-else-equal.

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    • Telo says:

      The MVP lens very slightly obfuscated the replacement issue, for the exact reason you bring up. Some people just have different ideas about MVP that don’t directly correlate to “how much value you provide your team”, which is how I interpreted the aim of the exercise.

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      • Telo says:

        But it looks as if Tango really did want to look at in terms of MVP voting for some reason.

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      • Telo says:

        And it’s articulated here, I skipped over it too quickly:

        My question however had one additional parameter: MVP. And that is, how does someone CREDIT a player for those games. Basically, some people are uncomfortable basically GIVING a player 0.35 runs for each missing game. So a guy misses 57 games, but he “earns” 20 runs anyway.

        Remember though, in reality, a team EXPECTS 20 runs to be earned just by playing 57 games, because that’s how many runs the scrap heap player will generate. On average.

        So, I was trying to find out from people if they are comfortable with replacement level talk even for things like MVP, or, do they still expect those players to “earn” their runs, even if they are being “given away” (i.e., scrap heap players basically perform at the minimum acceptable level, and they’ll earn 20 runs in 57 games).

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    • Todd says:

      Corey, I would assume that the number of runs is position adjusted for the purposes of this exercise.

      That said, I agree with your first paragraph, which is why I voted for between 100 and 110. Replacement level isn’t a guarantee. The player who replaces this theoretical candidate could well be average… or he could be below replacement. This candidate has no control over that, and shouldn’t get credit for it. Looking at replacement level for this is useful for roster construction (both MLB and fantasy), but if we’re evaluating the player by himself, he doesn’t get to take credit for a teammate’s contribution.

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      • Scott Clarkson says:

        I couldn’t agree more with your analysis Todd. the Most Valuable Player to me is a bedrock that played 140+ games or made 30+ starts. See my post below with a more drawn out version of a similar argument. Especially with regards to the playoffs, do you really want to roll the dice with 110/110 guy if it was health/platoon issues that kept him from playing 160 games? Maybe I’m risk-averse but I’d take someone 10% less productive per PA rather than risk the roughly 33% chance I can’t/shouldn’t use this 110/110 player in a given situation.

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      • Blue says:

        Exactly. I don’t care if its Barry Bonds, if he only plays 110 games he isn’t going to get my MVP vote. It isn’t a contest for “most valuable roster slot.”

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  6. JP says:

    You can turn the thought process around and break “value” into run creation pace (runs / games played) and durability (games played / 162 games). Then you can assign weights to how important each is.

    Based on the assumptions above (that the “105 runs in 105 games” player is equal to a “125 runs in 162 games” player), the weights break out like this:
    PACE = 0.606
    DURABILITY: 0.394
    For the first player = (162 * .606) + (105 * 0.394) = 139.5
    For the second player = (125 * 0.606) + (162 * 0.394) = 139.6

    So, in terms of value creation, that suggests that production is ~61% of value and durability is ~39% of value. To me, that estimate of the contribution from durability seems somewhat high, but potentially right.

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  7. TK says:

    I think there should be an option in the poll for 1st. The rationale being the MVP should be given to the best player in a year provided a decent sample size, and the 105/105 player is better (when playing) that year than anyone else. I don’t agree with this (I went with the “add replacement level” and crudely added 19 runs (57 games x 1/3)). Just saying it should be an option.

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  8. Scott Clarkson says:

    I am still not quite certain why we should give a player “credit” for what his replacement produces, regardless of what level that production is at.

    Durability/Health also has value and here is my argument for why:

    Sure, you get more production per AB from player X who produces 110 runs in 110 games vs. any player who produces less than a run per game. In Theory, you would rather have this 110/110 guy come to bat in a high-leverage situation/the playoffs.

    I am assuming that he has only played in 110 games for one of the two following reasons:

    He’s had some injuries:

    Rough math says this player’s health level has only allowed him to particpate in ~68% of his team’s games. Would you want to risk the ~1/3 chance that you have to field the replacement player instead of player X come the playoffs?

    Or, He is occasionally platooned/protected from tough RHP/LHP:

    Again, is this guy as valuable to your team as a 10% less productive per PA player who you can confidently use in more situations and who cannot be neutralized by bullpen deployment in a playoff situation?

    Perhaps my concerns about roster optimization and such are not relevant to the point of this study, but this is a circumstance where I feel value over replacement is different than partial value plus replacement.

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    • Andy says:

      Ditto on this. In the context of the MVP discussion it only really matters what the player in question did. The question to me was, in essence, where does player x’s extraordinary 1 run created per game fit in the context of the relatively small amount of games played by players A-E.

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  9. Neal says:

    I was looking at the AL CY Young race, and this exact issue was on my mind. The question was a little different if you add in the extra variable of starts by others in the rotation they currently have (or had). If you only compare Verlander and Weaver, I don’t want to go too far, Verlander has 14.1 extra innings pitched at this point. How would those innings be added to Weaver’s stats?
    1. Not at all
    2. Average Starting Pitcher
    3. Replacement Starting Pitcher
    4. Average current Rotation Replacement (Harren, Santana, Chatwood, Pineiro, possibly others)
    Would this only be considered for the 1 missing start?
    Would the other innings have to based on relief pitchers? If so, would the standard have to include the same issues?

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  10. Jordan says:

    For me, this was partly about replacement level but mostly about the fact that 105 runs created in 105 games is far more valuable than 105 runs created in 162 games. I know ‘runs created’ doesn’t map onto any actual stat, so this is just an example, but one 12 WAR player is more valuable than four 3 WAR players. Another example: one guy compiles 60 career WAR in 8 seasons, the other reaches 60 in 15. I’d say the first guy is at least in the HoF discussion, and the second was just a nice player for a long time.

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  11. Dan says:

    tango,

    One thing to consider is that this relationship may not be linear. For example, is the “penalty” for missing 50 games the same as missing 100 games, on a per game basis? Or, does the penalty increase, per game, the more games the player misses?

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  12. Greg S says:

    See, I thought of this question differently when I responded. I looked at this as a question probing the appropriate balance between rate stats and counting stats in an MVP race.

    I voted for the consensus pick (between 120 and 130 run player) but mainly because I saw that as the proper balance between the rate-based credit due our 105 per 105 player (a 1 run per game player) vs. the counting-stat-based credit due the 120 and 130 per 162 game players.

    On the one hand, we have the overall value of the 120- and 130-run players as indications of a great player performance. However, their run-per-game rates were .74 and .80 respectively.

    On the other hand, our 105 per 105 player had a better run-per-game rate of 1.00, a DIFFERENT indication of a great player performance. However, his overall value of 105 was an indication of a lesser performance.

    Therefore, I balanced these two competing indications of player performance as I saw fit and slotted our 105 per 105 player smack-dab in between our 120- and 130-run players.

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  13. Barkey Walker says:

    Have you ever noticed that when a guy does go on the DL, the player who subs in is *way* below replacement?

    If the 1B player goes on the DL, you usually have to go to your utility infielder who is overqualified to field the position but drastically under qualified to bat as a 1B player–where it doesn’t matter how good you are, you won’t make much run suppression.

    Similarly, when you catcher is on the DL, the backup catcher is usually way, way below replacement.

    In the other extreme, there is no such thing as a replacement level closer (can you imagine if a club said, “The closer accepted a better contract offer from New York, so we’ve decided to grab a guy with the rule 5 draft for the role.” In fact what happens is that the replacements is absorbed down the line… the setup guy becomes the closer, some other player becomes the setup guy, and everyone moves down a chair in the pecking order.

    The only place were the team usually has a replacement level player on hand is starting pitchers and mid-relief where you need a boat load–it’s the only position where a bunch of guys fill the same role .

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  14. Oliver says:

    I object strongly to the use of “Consensus pick” here when not even a majority of voters chose option C.

    On a more serious note, considering that playing in 105 games means that our hypothetical batter wouldn’t even qualify for the batting title, it seems likely that he wouldn’t get into the MVP race at all unless the 57 missed games were at the start of the season when his team was floundering and he came back to lead his team to the playoffs.

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  15. JoeIQ says:

    I gave him credit for average, but that is probably high. He deserves the credit for what a low end repalcement would have done in that stretch.

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  16. YX says:

    It’s interesting… but the poll result would center on C no matter what the options are (provided not too landish)

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    • tangotiger says:

      Why not split between C and D?

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      • Blueyays says:

        Tiger, with regards simply to the MVP,
        I think it depends on whether why he missed those 57 games. If he was injured or platooned, then I’d put him somewhere near the end. If he was benched or in the minor leagues for those games (if it wasn’t his fault he missed them), I’d put him first.
        However, I think there is one more think to remember here. If, say, the player got injured and missed those last 57 games, and the team replaced him with a replacement level player, then presumably they would have had to pay market value for that replacement player. I’m not saying this is the way we should look at it, but one thought could be that since he’s forcing them to spend additional money on those extra runs created by the replacement, he’s not really giving them to his team as extra value.
        Just a thought.

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      • Scott Clarkson says:

        Blueyays brought up an excellent point: If the guy started the year in the minors or on the bench and played his way into a starting role on his way to putting up that 105/105 pace I’d feel very differently about his MVP credentials and effectiveness on a playoff roster. The platoon/injury concerns one might otherwise have about 105/105 would no longer hold true.

        Let’s say 2003 David Ortiz actually competently played a position and had to fight his way into PT the way he did. That would probably garner MVP attention even if a relative unknown would not be a likely #1 pick by the writers etc.

        With this naarative as a third possibility to the Injury/Platoon reasons for only playing 105 games it seems a lot more reasonable to give players a modicum of credit “on average” for games missed.

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